RepData_PeerAssessment1/PA1_template.html at master · keli559/RepData_PeerAssessment1 · GitHub

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<p>Activity monitoring devices measuring human movements regularly is aiming to find patterns in human behavior, and improve human health.
Data is downloaded from <a href="https://d396qusza40orc.cloudfront.net/repdata%2Fdata%2Factivity.zip">Activity monitoring data</a> to explore insight of monintered steps every 5 minuntes daily from October 1st to November 30th 2012.</p>

<h2>Loading and preprocessing the data</h2>

<p>The data can be downloaded from <a href="https://d396qusza40orc.cloudfront.net/repdata%2Fdata%2Factivity.zip">Activity monitoring data</a>, and saved as &#39;activity.zip&#39;</p>

<pre><code class="r">url = &#39;https://d396qusza40orc.cloudfront.net/repdata%2Fdata%2Factivity.zip&#39;
download.file(url, &#39;activity.zip&#39;, method=&#39;wget&#39;)
</code></pre>

<p>Decompress the zip data, using the &#39;unzip()&#39; command in R:</p>

<pre><code class="r">unzip(&#39;./activity.zip&#39;)
</code></pre>

<p>After unzipping, find the file &#39;activity.csv&#39;:</p>

<pre><code class="r">list.files()
</code></pre>

<pre><code>##  [1] &quot;Abcd1234&quot;          &quot;Abcd1234.pub&quot;      &quot;activity.csv&quot;
##  [4] &quot;activity.zip&quot;      &quot;doc&quot;               &quot;figure&quot;
##  [7] &quot;figures&quot;           &quot;instructions_fig&quot;  &quot;missfont.log&quot;
## [10] &quot;PA1_template.html&quot; &quot;PA1_template.md&quot;   &quot;PA1_template.Rmd&quot;
## [13] &quot;q.log&quot;             &quot;README.md&quot;
</code></pre>

<p>Read in &#39;activity.csv&#39;, using &#39;read.csv()&#39; in R. Name the read-in data &#39;activity&#39;:</p>

<pre><code class="r">activity = read.csv(&#39;./activity.csv&#39;,
                    colClasses = c(&#39;numeric&#39;, &#39;factor&#39;, &#39;numeric&#39;))
</code></pre>

<p>Explore the structure of the data, using &#39;str()&#39;, &#39;head()&#39;, &#39;summary()&#39; functions in R:</p>

<pre><code class="r">str(activity)
</code></pre>

<pre><code>## &#39;data.frame&#39;:    17568 obs. of  3 variables:
##  $ steps   : num  NA NA NA NA NA NA NA NA NA NA ...
##  $ date    : Factor w/ 61 levels &quot;2012-10-01&quot;,&quot;2012-10-02&quot;,..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ interval: num  0 5 10 15 20 25 30 35 40 45 ...
</code></pre>

<pre><code class="r">head(activity)
</code></pre>

<pre><code>##   steps       date interval
## 1    NA 2012-10-01        0
## 2    NA 2012-10-01        5
## 3    NA 2012-10-01       10
## 4    NA 2012-10-01       15
## 5    NA 2012-10-01       20
## 6    NA 2012-10-01       25
</code></pre>

<pre><code class="r">summary(activity)
</code></pre>

<pre><code>##      steps                date          interval
##  Min.   :  0.00   2012-10-01:  288   Min.   :   0.0
##  1st Qu.:  0.00   2012-10-02:  288   1st Qu.: 588.8
##  Median :  0.00   2012-10-03:  288   Median :1177.5
##  Mean   : 37.38   2012-10-04:  288   Mean   :1177.5
##  3rd Qu.: 12.00   2012-10-05:  288   3rd Qu.:1766.2
##  Max.   :806.00   2012-10-06:  288   Max.   :2355.0
##  NA&#39;s   :2304     (Other)   :15840
</code></pre>

<p>Therefore, data &#39;activity&#39; contains three variables:</p>

<ul>
<li><p>steps</p></li>
<li><p>date</p></li>
<li><p>interval</p></li>
</ul>

<p>with 17568 records, where 2304 records have &#39;NA&#39; as steps value; date is not recognized as Date variable in R. Therefore, convert the date column from Factor format into Date format using &#39;as.Date()&#39; function. Once conversion is done, delete the orignal date column to avoid confusion.</p>

<pre><code class="r">activity$dateformat = as.Date(activity$date, format = &#39;%Y-%m-%d&#39;)
activity$date = NULL
</code></pre>

<h2>What is mean total number of steps taken per day?</h2>

<ol>
<li>To plot the histogram, first of all, the sum of all steps are calculated. </li>
</ol>

<pre><code class="r">daily = tapply(activity$steps, activity$dateformat, sum, na.rm=T)
</code></pre>

<p>The histogram of the total number of steps taken each day is plotted as following:</p>

<pre><code class="r">par(mfrow = c(1, 1), mar = c(4, 4, 1 , 1), oma = c(1, 1, 0, 0))
hist(daily, xlab=&#39;number of steps&#39;, main=&#39;histogram of daily steps taken&#39;)
abline(v=mean(daily, na.rm=T), col = &#39;red&#39;)
abline(v=median(daily, na.rm=T), col = &#39;blue&#39;)
legend(20000, 20, c(&#39;mean&#39;, &#39;median&#39;), lty=c(1, 1),col = c(&#39;red&#39;, &#39;blue&#39;))
</code></pre>

<p><img 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" alt="plot of chunk unnamed-chunk-10"/> </p>

<pre><code class="r"># to save it:
#dev.copy(png, file =&#39;./figures/histogram.png&#39;)
#dev.off()
</code></pre>

<ol>
<li>The mean and median total number of steps taken per day are calculated as:</li>
</ol>

<pre><code class="r">mean(daily, na.rm=T)
</code></pre>

<pre><code>## [1] 9354.23
</code></pre>

<pre><code class="r">median(daily, na.rm=T)
</code></pre>

<pre><code>## [1] 10395
</code></pre>

<h2>What is the average daily activity pattern</h2>

<ol>
<li>Make a time series plot (i.e. type = &ldquo;l&rdquo;) of the 5-minute interval (x-axis) and the average number of steps taken, averaged across all days (y-axis):</li>
</ol>

<pre><code class="r">#intervalMean is the mean of the steps at each 5 minute interval over all the days
intervalMean = with(activity, tapply(steps, interval,  mean, na.rm=T))
#intervalDaily is the minutes number of the intervals.
# Everyday appears the same pattern in munites (ex, 0, 5, 10, .....2355)
intervalDaily = unique(activity$interval)
# plot time series
plot(intervalDaily, intervalMean, type=&#39;l&#39;, main = &#39;Average steps and daily interval&#39;,
     xlab=&#39;5-minute interval&#39;, ylab=&#39;average steps&#39;)
</code></pre>

<p><img 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" alt="plot of chunk unnamed-chunk-12"/> </p>

<pre><code class="r"># to save the plot into file:
#dev.copy(png, file =&#39;./figures/5minAve.png&#39;)
#dev.off()
</code></pre>

<ol>
<li>Which 5-minute interval, on average across all the days in the dataset, contains the maximum number of steps?</li>
</ol>

<pre><code class="r">intervalDaily[which.max(intervalMean)]
</code></pre>

<pre><code>## [1] 835
</code></pre>

<h2>Imputing missing values</h2>

<ol>
<li>Calculate and report the total number of missing values in the dataset (i.e. the total number of rows with NAs)</li>
</ol>

<pre><code class="r">table(is.na(activity$steps))
</code></pre>

<pre><code>##
## FALSE  TRUE
## 15264  2304
</code></pre>

<ol>
<li>To fill the NAs in the data &#39;activity&#39;, strategy is developed to replace NAs with the average steps at the minute interval when the step is recorded over the days. To develop this strategy, the data &#39;activity&#39; is duplicated to a data table called &#39;DT&#39;.</li>
</ol>

<pre><code class="r">library(data.table)
DT = data.table(activity)
#In DT, a new variable &#39;intervalMean&#39; is set to take the mean of the subsets of records, categorized by interval values
DT[, intervalMean := mean(steps, na.rm=T), by=interval]
</code></pre>

<pre><code>##        steps interval dateformat intervalMean
##     1:    NA        0 2012-10-01    1.7169811
##     2:    NA        5 2012-10-01    0.3396226
##     3:    NA       10 2012-10-01    0.1320755
##     4:    NA       15 2012-10-01    0.1509434
##     5:    NA       20 2012-10-01    0.0754717
##    ---
## 17564:    NA     2335 2012-11-30    4.6981132
## 17565:    NA     2340 2012-11-30    3.3018868
## 17566:    NA     2345 2012-11-30    0.6415094
## 17567:    NA     2350 2012-11-30    0.2264151
## 17568:    NA     2355 2012-11-30    1.0754717
</code></pre>

<ol>
<li>Fill in the NAs in the new data set (DT):</li>
</ol>

<pre><code class="r">DT[is.na(steps),]$steps = DT[is.na(steps),]$intervalMean
</code></pre>

<ol>
<li>With all the NAs filled in step variable (DT), the daily steps taken are calculated and passed to the variable &#39;daily_fill&#39;:</li>
</ol>

<pre><code class="r">daily_fill =tapply(DT$steps, DT$dateformat, sum, na.rm=T)
</code></pre>

<p>the mean and median are calculated to compare with the steps in raw data activity with NAs (activity). After filling the NAs the median and mean become the same(10766.19) while before filling up NAs, median (10395) is bigger than mean (9354.23). The way to calculate means and medians for both daily steps with NAs or filledups are listed for comparison.</p>

<pre><code class="r">mean(daily, na.rm=T)
</code></pre>

<pre><code>## [1] 9354.23
</code></pre>

<pre><code class="r">mean(daily_fill, na.rm=T)
</code></pre>

<pre><code>## [1] 10766.19
</code></pre>

<pre><code class="r">median(daily, na.rm=T)
</code></pre>

<pre><code>## [1] 10395
</code></pre>

<pre><code class="r">median(daily_fill, na.rm=T)
</code></pre>

<pre><code>## [1] 10766.19
</code></pre>

<p>Two histograms of steps in DT and activity are plotted to compare. Number of bins are chosen to be 10 to reveal the more detailed change due to filling NAs. First of all, the peak value of filled-in data (20-25 in frequency) is higher than one of raw data (around 17 in frequency). The frequency around &ldquo;zero&rdquo; bin of filled-in data (&lt;5) is lower than raw data (around 10). This indicates that filling the NAs with interval mean would truly recognize the days of absolutely no steps from days of limited records that result in &#39;zero&#39; steps. </p>

<p>Secondly, as said in the previous point, the median and mean overlap at filled-in data, but not the same at raw data.</p>

<pre><code class="r">par(mfrow = c(2, 1), mar = c(2, 2, 1 , 1), oma = c(1, 1, 0, 0))
hist(daily_fill, breaks = 10, ylim=c(1,25), main =&#39;Histogram of Filled-in Data&#39;)
abline(v = mean(daily_fill), col = &#39;red&#39;)
abline(v = median(daily_fill), col = &#39;blue&#39;)
legend(15000, 20, c(&#39;mean&#39;, &#39;median&#39;), lty=c(1, 1),col = c(&#39;red&#39;, &#39;blue&#39;))
hist(daily, breaks=10, ylim=c(1,25),main = &#39;Histogram of raw Data&#39;)
abline(v = mean(daily), col = &#39;red&#39;)
abline(v = median(daily), col = &#39;blue&#39;)
legend(15000, 20, c(&#39;mean&#39;, &#39;median&#39;), lty=c(1, 1),col = c(&#39;red&#39;, &#39;blue&#39;))
mtext(&#39;Steps&#39;, out=T, side=1)
mtext(&#39;Frequency&#39;, out=T, side=2)
</code></pre>

<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAfgAAAH4CAIAAAApSmgoAAAACXBIWXMAAAsSAAALEgHS3X78AAAgAElEQVR4nO3deVxTV94/8BMCgQgREFBWQ1gURQQRVCpFBRXGhYJYRVvnqVP3+rRO5ecM1rp1qnV5rLbaZaJFqq2O2ikWBQWmbCooYNxQFCjIppIoi2EP3N8fd8owQRCSSwLXz/vVV1/hcO893xyuHy4nNycciqIIAACwl462CwAAgL6FoId/UygUHA6Hw+EUFBS0N86ZM4fD4Xz22WeNjY0cDkdXV1eLFfa169evjxgxgsvlfvHFF0rfMjEx4XSyf//+jsPS1eMeunPnDofDcXFx6fwt1Qbf1ta2vVQjIyNPT88dO3a0trb26iDADmz+dwsM4nA4rq6uXC63+828vLxycnIyMjImTZqkmcIYtH///vz8fF9fXw8PjxduYG9vb2ho2P6lmZlZD4dFTer0IhQKjYyMnj17JpFIJBJJfn5+VFRUN9sP6J8gdAVBDz2ir69/584dbVfRt549e0YI+fOf/+zn5/fCDY4dO+br66vUqIFhUWfwDx8+PH36dELIhQsXgoODo6OjIyIiXF1dGS0Q+jtM3UCPKM0epKWlvf766wKBwMLCYu7cuXQM0ReDhBAfH5+TJ08SQurq6iIiIkaMGEFPHURHR7e/+F9VVbVo0aIhQ4ZMnDgxPj6ew+F4eXkRQh4/fszhcMzNzTMyMry8vM6cOUMISUpK8vHxEQgEpqamAQEB169fJ4QUFBRwOBxHR8fPP//c1tZWKBQeOHAgMzPT09PTyMho6tSpv/32W+cn0lVJXl5e58+fJ4SEhYVt2rRJtWHpSnFxcUhIiLm5ubm5eXh4eFlZGd1eWVkZFhZmamrq7u6emZnZk17ax+fnn38eM2aMQCCYO3fukydPXlpqUFDQvHnzKIo6duwY6WJIO/8EX7gZDDwUAEVRFNXS0kKfEi4uLu6/EwgEhJCdO3c2NDQQQrhcLkVRjx8/NjQ05HA4b7zxBn3xa21tXVdXd/78eXt7e0LIli1bioqK2traAgICCCG2trazZs0yMDAghOzfv5+iqLa2NvrS2MrKysPDg+5l/PjxFEU9evSIEGJoaGhnZ0cIOX36dElJCZ/P53K5U6dOnThxIiFEKBS2tbXl5+fTBfN4vJEjR7Y/dnR0pCdYQkNDlZ5jNyWdP3/e3d2dEPLBBx9IJBKlHY2NjQkh6enpSu0dh6Wrx8+fP7eystLV1Z07d25gYCAhRCQSyeVyhUIxduxYuhgPDw8dHR1CyMiRIzv/aDoejR4fLpcrEAg8PT3pvZYtW9Z5LxsbG0JIYmJie8u+ffsIIWFhYV0NqdJPsKvNenNaQb+AoId/aw/6zpSCPiEhgRDi6Oj48OFDiqLWrVsXFhaWn59PUdT48eMJIRkZGRRFpaamEkJsbGyqqqooivrXv/5FCDExMWltbaW/NXz48Orq6ra2trVr1yoFPd2pTCZrbGxMSUkJDAzcvn07RVFVVVX0ha1UKm0P+nv37lEURf/KWbRoUVtb26+//kpXqPQcuymJoqjZs2cTQn7++efOg0MHfUeurq5Uz4L+wIEDhJA//elPUqlUKpVOmzaNEPKPf/wjJiaGEDJq1Ci5XN7W1vbuu+/2POgJITdu3KAoKjo6mhDi5ubWea/OQX/06FFCyKRJk7oaUqWfYDebwcCCqRtQRkc2jc4+JZ6enkKhsLCwUCgUurm56ejo7Nq1y8nJSWmzW7duEUKCg4NNTEwIIf7+/jY2NtXV1WVlZRKJhBDyxhtvGBsbczicFStWKO1rYGCwYcMGMzMzfX39KVOm7N69Wy6X+/v729nZKRQKQgj9f0KIjY0NfacK/ReAv78/h8OhH7dv05OSejIy9vb2rr/r/Hy7cvv2bULId999Z2FhYWFhkZycTAjJy8ujB2H+/Pn0n0dLlixp32X58uUGv4uLi+t8THq2hxDi7e1NCKmvr+9JJfSLELa2tt0Pabsebgb9H4Iees3MzOz+/fvff/99WFjYw4cP9+3b5+rqmpubq7QZ1em9ePQ8Q2tra3NzMyGk/TaSznPchoaG9MaEkMuXL3t6eorFYg8Pj6NHj5qbm3fcUmnf7qfLuympm73aHTt27M7v6OvxnqCf7AcffJDYQXh4ON0ph8PpWAmtpaWl6XdtbW2dj9m+cfvuPXH16lVCiJOTU/dD2q6Hm0H/h6CHXouJiXnvvff09fXPnDkjlUoDAwObmppSUlLaN6Av+ugJ6NjY2JqaGkJISkpKaWmpsbGxUCikr8FjY2Plcjkh5Lvvvuumu59//rm1tXXFihX79u2bMGHC06dPVa68m5JUPuZLjRo1ihAil8unT58+ffr0wsLCCxcuyOVy+pL8zJkz9fX1FEUdP368fZejR4+2/1E1Z84cRspISEj45z//Sf/p8NIhpX+CDI48aBdur4ReEwgER44c+eGHH6Kjo/X09JKTk3V0dF577TVCiJGRESFk69atu3fv9vPzmzZtWnJyspub29ixY+l5823btuno6AQFBTk7O+fn548ePdrCwoKexOiKlZUVIeTQoUO5ubnZ2dn0VfkLr3NfqpuSVDhaDy1btmz37t1HjhypqalpaGg4f/68g4PDli1b3NzcHBwc7t69O2rUKDMzs+4HQZ3ejYyMqqqqKioqCCHvvvvu6NGjuxnSjj9BBkcetAtX9NBrAQEBJ06ccHNzu3TpUmJioqur6+nTp8eNG0cIiYiIsLKyyszMLC8v53A4Z8+eXbduHY/HS05OdnFxOXr06Pvvv08I0dPTS0hICAwMrK6ubmlp+fHHH7vpbtWqVW+99RaHw7l3715kZCT9G4V+Qbi3uimp75ibm1++fDkwMDApKenatWtLlixJS0sTCAR6enqpqalz586tqampr6//7LPP+qL3hw8f5ubmVldXe3h47Ny589tvvyXdDmnHnyCDIw/axek8awnQ1yoqKq5duyYQCOibHVNSUqZNmxYYGHjhwgVtlwbAQpi6AS1oaGhYuHBhc3NzZGSkk5MTfTG7YMECbddFzkRkKprbwr94TduFADCJgaCXSqV6enr0/WoAPeHo6JiQkLBly5ZvvvmmubnZ2dlZLBYvXbpU23WR+uetihb8jQtso8ocfVBQEP2W6/Ly8smTJ1taWg4dOnT69Ontb+UAeKkpU6akpKQ8e/ZMLpdLJJJly5b16k5BAOg5VYL+4sWL9Fv11q9f7+DgUFtbS98rRr+/EQAA+hW1pm6ysrLi4uLodUXoyVaGqgIAAMaoeHtlRUWFQqFwdXUtLi6mW3Jzc4cNG8ZYXQAAwBBVruj9/PzCw8MrKyv5fH5JSUlgYGBaWlpISMiuXbsYrw8AANSkStDTSwA2NzeXlJRIpVJCCJ/Pj42N7fyZDB3du3ePXmmvo6amJhsbm4iICBXKAACAnlB9jr6urs7R0ZGel/f29m5tbZXJZN0se2RjY/Pmm28qNRYUFOCNdgAAfUqVoM/NzV2wYMG9e/dEItGBAwfoRZdKS0tFIlE377MdPHgwvdR1Rzwe7/LlyyrUAAAAPaTKi7ErV64MCwtrbGyMiopatWpVdnY242UBAABTVAl6iUQSERHB4/H8/PwOHTq0atWqHi7nDQAAmqdK0Ds7O7dPrAcHB9vZ2W3evJnRqgAAgDGqBP2ePXuWLl3q4+NTWVnJ4XDEYnF8fHxoaCjjxQEAgPpUeTF2xowZDx48SEtL4/P5hBBzc/OMjIyYmJjr168zXR4AAKhLy+vR3759WywWf/HFF1qsAVjvo48+unbtWk+2HHLPm1DcZ6Mz1ezxrbfeeuedd9Q8CABTsB49sN+VK1eSk5N7suX3Ky8rWqg/ffeJOt3duHGj83sDAbQIHyUIAMByCHoAAJZD0AMAsByCHgCA5RD0AAAsh6AHAGA5BD0AAMsh6AEAWA5BDwDAcgh6AACWQ9ADALAcgh4AgOUQ9AAALIegBwBgOQQ9AADLIegBAFgOQQ8AwHIIegAAlkPQAwCwHIIeAIDlEPQAACyHoAcAYDkEPQAAy6kV9BRF1dbWtrW1MVUNAAAwTpWgr6+v37Fjx4gRIwwMDIyNjXk8nrOz87Zt25qamhivDwAA1KRK0K9ZsyY5OVksFldUVDQ3Nz958iQqKionJ2fNmjWM1wcAAGrSVWGfmJiYu3fvWltb01+amZn5+vq6u7uLRKIjR44wWh4AAKhLlSt6kUgUHx+v1HjhwoXhw4czURIAADBJlSt6sVg8f/78vXv3urm5CQQCuVyem5tbVVX1yy+/MF4fAACoSZWg9/LyKigoSE1NLS4ulslkpqamK1asmDJliq5ud0eTSCQ7d+5Uaqypqel+LwDoO1u3br179662q+gvlixZMnfuXG1X0SdUDFldXV1PT09/f38Oh0O3tLa2ymQyc3PzrnZxc3P79ttvlRrv3r37448/qlYDAKgpOTk5JiZG21X0C1lZWSkpKQj6/8jNzV2wYMG9e/dEItGBAwfmzJlDCCktLRWJRBRFddmTrq6pqalS4+DBg7lcrgo1AID6dHR0Ov+rfDUJBAJtl9CHVHkxduXKlWFhYY2NjVFRUatWrcrOzma8LAAAYIoqQS+RSCIiIng8np+f36FDh1atWtXa2sp4ZQAAwAhVgt7Z2TkhIYF+HBwcbGdnt3nzZkarAgAAxqgS9Hv27Fm6dKmPj09lZSWHwxGLxfHx8aGhoYwXBwAA6lPlxdgZM2Y8ePAgLS2Nz+cTQszNzTMyMmJiYq5fv850eQAAoC4Vb6+0srJauHBh+5f6+voLFy7s2AIAAP0E1qMHAGA5BD0AAMsh6AEAWA5BDwDAcgh6ANCmvLy8yZMnR0REmJub+/r6ZmRkeHt7CwSCdevW0Rukp6ePGzfO0NAwKCiovLycbhSLxSKRiM/nT5o06f79+/RxfH199+7da2NjIxKJfv31V609pf4HK0cCQNeuXiXPn6u+O4dDJk8mBgbdb5WZmfnee+9t3Lhx5syZISEh165de/TokY+Pz0cffaSjoxMaGhoVFeXr6/vxxx+//fbbycnJpaWla9euTUxMHD169P/7f/9v37599IKJN27cmDNnTn5+/rZt2zZt2nTlyhXVK2cXBD0AdO3SJaJQqHUEBwciEnW/iZWV1eLFiwkh06dPr66uFv6upqbm8uXLU6dOpReV3Lt3r5mZWWtrq4WFRX5+/vDhw+vq6szNzUtLS+njcLnciIgIXV3dJUuWnD17Vq2y2QVBDwBdW79eA50YGRnRD3R1dS0tLdsfE0JKS0sTEhLs7e3pRh6PV1lZaWFhcfjw4fj4eGNjY319/faFJy0tLem98CkXSjAcANB/WVlZzZgx46effiKEtLa2SiQSS0vLkydPnj9/PjExcciQIcePHz937hy9cfvHY4ASvBgLAP3X7Nmz09PT4+LiZDLZX//613Xr1nE4nKdPnxoZGfH5/MrKyi+//LKhoUHbZfZ3CHoA6L8sLS2PHz++YcMGoVCYk5Pz/fffE0KWLFmir69va2sbGhr68ccfX7169dixY9qutF/D1A0AaJOLi0teXh79+G9/+1t7e0FBAf1g5syZd+7c6biLsbFx+0rphJDHjx/TD9qP0/GYQHBFDwDAegh6AACWQ9ADALAcgh4AgOUQ9AAwgFVXV5uYmBBCsrOzvby8tF1OP4WgBwA2EIlE27dv13YV/RSCHgC0SbXVK7/88ks7Ozs7O7vvvvuObikqKtq8eTP9GGtbKkHQA4CWZWZmenp6PnjwoLGxMSQk5MyZM4mJiQcOHJBKpU+fPg0NDd2+fXtZWZmTk9Pbb79NCElPT9+yZcsPP/yQmZl5/vx5paPRa1tGR0eXlpaOGjVq3759dPuNGzcUCkV+fv6CBQs2bdqk6SepVXjDFAB0KSyM1NaqdYTPPydjxrxkm96uXvnTTz+tXLnSz8+PEPLJJ5/MmjWr49GwtmVnCHoA6NJPP2mil96uXvn48ePp06fTLQ4ODkpH09XVxdqWSl65JwwAA8gLV6+0trYuLCykNygqKlLa5fTp01jbUgnm6AGg/3rh6pXz58//9ttv09PTKyoqNm/erJTgWNuyMwaCXiqVVldXq38cAAAlL1y98rXXXtu+ffvixYsnTJiwePFiQ0PDjrtgbcvOVJm6CQoKio6OHjZsWHl5+YIFCzIzM7lcrp+f37Fjx6ysrBgvEQBYTIXVKwkha9euXbt2Lf146dKlhBAvL6/s7GyCtS1fRJUr+osXL9J/Da1fv97BwaG2tlYul7u7u7ePOwAA9B9qvRiblZUVFxdH/90UGRnp5OTEUFUAAMAYFefoKyoqFAqFq6trcXEx3ZKbmzts2DDG6gIAAIaockXv5+cXHh5eWVnJ5/NLSkoCAwPT0tJCQkJ27drFeH0AAKAmVYI+NTWVENLc3FxSUiKVSgkhfD4/NjbW19e3m72ysrI2btyo1CiXy42NjVWoAQAAekj1OXoej+fk5ETPy3t7e790e29v78TERKXG27dvi8VilWsAAICXwhumAABYTpUr+m5uQXVxcVGjGAAAYJ4qQf/hhx/Gx8cPGjTI1NRU6VtlZWVMVAUAmtDQ0IB7KGglJSUsfr1QlaCPi4tbvny5vr7+wYMHGS8IADTm0KFDVVVV2q6iXxg/fryzs7O2q+grKr4YGx4eLpFImC0FADRs/Pjx2i4BNEHFoA8ICAgICGC2FAAA6Au46wYAgOUQ9AAALIegBwBgOQQ9AADLIegBAFgOQQ8AwHIIegAAlkPQAwCwHIIeAIDlEPQAACyHoAcAYDkEPQAAyyHoAQBYDkEPAMByCHoAAJZD0AMAsByCHgCA5RD0AAAsh6AHAGA5BD0AAMsh6AEAWA5BDwDAcgh6AACWQ9ADALAcgh4AgOXUCnqKompra9va2piqBgAAGKdK0NfX1+/YsWPEiBEGBgbGxsY8Hs/Z2Xnbtm1NTU2M1wcAAGpSJejXrFmTnJwsFosrKiqam5ufPHkSFRWVk5OzZs0axusDAAA16aqwT0xMzN27d62trekvzczMfH193d3dRSLRkSNHGC0PAADUpcoVvUgkio+PV2q8cOHC8OHDmSgJAACYpMoVvVgsnj9//t69e93c3AQCgVwuz83Nraqq+uWXXxivDwAA1KRK0Ht5eRUUFKSmphYXF8tkMlNT0xUrVkyZMkVXt7ujXb16ddOmTUqNcrl88ODBKtQA0G+Vl5f/+OOPd+7c0ViPz549i4uLGzZsmMZ6hIFFlaAnhOjq6gYEBPRql4kTJyYmJio13r59WywWq1YDQP8kl8ttbGw6n+19Z9myZXK5HEEPXcEbpgAAWE6VK/q8vLyuvuXi4qJGMQAAwDxVgv7DDz+Mj48fNGiQqamp0rfKysqYqAoAABijStDHxcUtX75cX1//4MGDjBcEAADMUnGOPjw83N7entFKAACgT6h4101AQEBv77oBAACtwF03AAAsh6AHAGA5BD0AAMsh6AEAWA5BDwDAcgh6AACWQ9ADALAcgh4AgOUQ9AAALIegBwBgOQQ9AADLIegBAFgOQQ8AwHIIegAAlkPQAwCwnIrr0QOorKCg4PDhw5rs8eHDh5rsTvPKysr27NljYmKisR49PT0XLFigse5ATQh60LScnBwOhzN//nyN9fjVV19prC+tKCoqCg0N9fLy0kx3jY2NO3bsQNAPIAh60ILhw4ePHz9eY91xuVyN9aUtI0aM0NiQ1tfXa6YjYArm6AEAWA5BDwDAcgh6AACWQ9ADALAcgh4AgOUQ9AAALIegBwBgOQQ9AADLIegBAFgOQQ8AwHIMBL1UKq2urlb/OAAA0BdUCfqgoKAnT54QQsrLyydPnmxpaTl06NDp06c/evSI6fIAAEBdqgT9xYsXGxoaCCHr1693cHCora2Vy+Xu7u5r165lujwAAFCXWqtXZmVlxcXFGRoaEkIiIyOdnJy633jjxo1KjU1NTSNGjFCnBgAA6J6KQV9RUWFra+vq6lpcXDxy5EhCSG5u7rBhw7rZxdvbOzExUbXuAABAZaoEvZ+fX3h4eGVlJZ/PLykpCQwMTEtLCwkJ2bVrF+P1AQCAmlQJ+tTUVEJIc3NzSUmJVColhPD5/NjYWF9fX4arAwAAtak+R8/j8ZycnOh5eW9vb+ZKAgAAJuENUwAALIegBwBgOQQ9AADLIegBAFgOQQ8AwHIIegAAlkPQAwCwHIIeAIDlEPQAACyHoAcAYDm1limGvpCXl5eWlqbJHouKikQikca6y87OHj58uMa6AwAEfb9z+vRphUIxZswYjfX44YcfRkVFaay78vLy58+fa6w7AEDQ90d+fn4BAQEa627FihVvvvmmxrq7fPky/VGUAKAZmKMHAGA5BD0AAMsh6AEAWA5BDwDAcgh6AACWG3h33Rw7diw2NlZj3bW1tT169MjGxkZjPd67d4/+gEYA0JaNGzcWFBRosscPPvhg8uTJfXTwgRf0CQkJW7Zssba21kx3Dx8+/MMf/nDu3DnNdEcICQkJKS8v11h3ANDZpUuXzp49q7Hu4uPjr127hqD/L8bGxqampprpq7q6WkdHR2PdEUJ0dQfkDwWATbhcrib/1RsaGvbp8TFHDwDAcgh6AACWQ9ADALAcgh4AgOUQ9AAALIcbPACgd1paWi5fvjxjxgyN9VhdXX3o0KEJEyZorEeWQdADQO8oFAoej5eYmKixHnfv3i2TyTTWHftg6gYAgOUQ9AAALIegBwBgOQQ9AADLIegBAFhu4N11U1hYKBaLNbbe0NOnT+Vy+f79+zXTHSGktLQ0PT1dhaXNiouLhUIhh8Pp7Y5NTU2afIISieT58+ea7LGhoaGH3ZXfNqBaOfv3Z6vTnUQiqays1OQTrKqqOnPmzM2bN3u7Y3Fxsb29fW/3qqur6/mQMiI9Pb2wsPDBgwca67G4uLiqqkpj3dXV1fXp8TkURXX8+v33358/f/7kyZO5XG6fdqyysWPH6unp6evra6a7trY2qVQ6bNgwzXRHCKmqquLz+QYGBr3dMS8vz9nZWYUf3JMnTzT5BOvq6lpbWwcPHqyxHiUSybhx43qypVGdMYdwnhtWq9NdS0tLTU2Nubm5OgfpFalUampqqsLFQW5urqura2/3oiiqsrJSk+dMTU0Nj8fj8/ka6/HmzZuzZ8/WWHeEkJUrVwYEBPTRwZXPDFNT0//93/998uTJvHnz5s+f7+fn199WzXV3d9+5c6etra22C+l35s6de+LECSMjI20X0u9MmzYtOTlZ21X0RxiZrkybNu3UqVParoIxynP027Ztu3nz5pUrV5ycnLZu3Wpra7tixYqEhISWlhat1AcAAGp68YuxQ4YMsbOzc3R0bG5uvnLlytatW0UikSY/bwUAAJiiHPR79uyZOnWqra3t4cOHPT09c3Jy7ty5c+XKlePHj69atUorJQIAgDqU59/v3bv3/vvvz5gxQyAQdGz39vb+6quvNFgYAAAwQ/mK/uuvv66qqpJIJISQ48eP79+/v7m5mRBiaGgYGhqqhQIBAEA93K1bt3b8eu3atb/88suCBQssLS3r6ur27NmTlZX1xhtvaKm8F9DR0RkzZoyenp62C+l3uFyuu7u7jg7eBKeMx+O5ublpu4r+CCPTFZaNjPJ99GZmZllZWQ4ODvSXv/32m6enZ3W1WrcVAwCAFilf/Zmamkql0vYvnzx5osn3fQAAAOOUX4z99NNPZ8+evXjxYqFQWFZWduzYsc8//1wrlQEAACOUp24IIffv3z99+nRZWZmlpeW8efPGjh2rlcoAAIARLwh6AABgE+Wpm3/9618ff/zxs2fPOjbm5eVpsCQAAGCS8hW9UChctGjR22+/3XEtMxcXF40XBgAAzFAOemtr68LCQk0uBwoAAH1K+fbKDz/88IsvvmhtbdVKNQAAwDjloI+Jifnkk0+GDBkycuRIl99ppbLOsrOzPT09TU1Nly5d2tDQoO1yNGrKlCmc3wUFBdGNLxyQnjcOdLNmzer46pGao8GmIVIaGZw8hJCkpCQPDw9DQ0NfX9/c3Fy68RU6Z6j/du9FqH6gpaVFKBSKxeKysrKAgIBPP/1U2xVplJ2d3eXLl4uKioqKih4/fkx1MSA9bxzQkpKSli1bRghpPznVHA3WDFHnkaFw8lBURUWFkZHRqVOnqqurN23aNHr0aOoVO2eUg56mUCgqKira2to0XE03kpKSXFxc6MfJycnOzs7arUeTmpqa9PX1FQpFx8YXDkjPGwe0PXv2vPfee4MGDWqPMzVHgzVD1HlkcPJQFHXy5MlJkybRj5uamjgczrNnz16pc0Z56qa8vHzatGmDBw8ePXp0Tk7O66+/XlRUpIU/NDopLi5uX2PIzc3t4cOH1CvzDoCSkhI+nx8aGurk5LR48eLy8nLSxYD0vFErT4QpERERBw8e7PgB8WqOBmuGqPPI4OQhhMyaNav9c5MyMzPt7e1NTExeqXNGOeiXLl06ZsyYp0+fGhsbe3h4TJo0afny5VqpTIlMJmtfIn/w4MHNzc3Pnz/XbkkaI5VKhULh6tWrz507x+VyFy5cSLoYkJ43auWJ9B01R4PFQ4SThxAiEAiGDh1KUdTZs2cXL1584MABDofzSp0zym+YunTp0qlTpwwMDAghurq6f/nLX4RCoTYKU2ZqaiqXy+nHtbW1urq6r86nYPv4+Ny4cYN+/PXXXxsbG8tkshcOSM8bNf8s+pSao8HiIcLJQ3v69Ony5ctLSkpiYmK8vLzIK3bOKF/ROzs7X7p0qf3Lq1evti9ZrF0ODg7tr5Xfu3fP3t7+1Vl4PSsrKy0tjX7M4/G4XK6uru4LB6TnjZp/Fn1KzdFg8RDh5CGENDU1zZw5c9SoUVevXqVTnrxq54zSnH1KSoqZmVlYWJhAIJg3b56FhcXFixc18mrBS7S0tFhbW58+ffr58+fBwcFbt27VdkWak56ebmJikpqaKpPJ1q9fHxAQQHUxID1vZAEbG5uOd92oM15XXd4AACAASURBVBosG6KOI4OTh6KokydPuru7F3WgUCheqXPmBXfdyGSyqKioTz755PDhw48ePdJ8TV3Jyspyd3cfMmTIO++809jYqO1yNKetre2bb75xdnYePHhwaGhoRUUF3f7CAel540DXMc4otUeDTUPUcWRw8lAUtWHDBqULXKlUSr1K5wxWrwQAYDnlF2MnTZrUeaPMzEyNFAMAAMxTDvr9+/fTDyiKKisrO3To0Nq1azVeFQAAMOYlUzcymczf3//WrVsaKwgAAJj1kvuBSktLi4uLNVIJAAD0CeWgn9SBl5fXhAkT/vSnP2mlMujPFAoFvRpiQUFBe+OcOXM4HM5nn33W2NjI4XA6fnYN+1y/fn3EiBFcLveLL77QTI+2trbti1AaGRl5enru2LEDK4pDT3Q5R08zMTEZOXKkBusBNuBwOK6urlwut/vNvLy8cnJyMjIyXngLQD+3f//+/Px8X19fDw8PTfYrFAqNjIyePXsmkUgkEkl+fn5UVFQ32w/oQQam9OiuG4Be0dfXv3Pnjrar6Fv05yr/+c9/9vPz02S/hw8fnj59OiHkwoULwcHB0dHRERERrq6umqwBBhzlqRtbW1uTrmmlRBhwlKZu0tLSXn/9dYFAYGFhMXfuXPp3AH2lSQjx8fE5efIkIaSuri4iImLEiBH0vER0dHT7nQJVVVWLFi0aMmTIxIkT4+PjORwO/Ub2x48fczgcc3PzjIwMLy+vM2fOEEKSkpJ8fHwEAoGpqWlAQMD169cJIQUFBRwOx9HR8fPPP7e1tRUKhQcOHMjMzPT09DQyMpo6depvv/3W+Yl0VZKXl9f58+cJIWFhYZs2beq4S89LmjhxIofDSUxMJIRERkZyOJy5c+cSQvLy8jgcjo2NTfc3SgQFBc2bN4+iqGPHjnXVRedBfuFmwH5Kb6D66quv/P39L1++XFFRceXKFX9//wMHDlT9TrNv5oL+q6WlhT5/XFxc3H9HL+a3c+dO+tN2uFwuRVGPHz82NDTkcDhvvPEGffFrbW1dV1d3/vx5e3t7QsiWLVuKiora2toCAgIIIba2trNmzaKX1du/fz9FUW1tbb6+voQQKysrDw8Pupfx48dTFPXo0SNCiKGhoZ2dHSHk9OnT9Kq8XC536tSpEydOJIQIhcK2trb8/Hy6YB6P1z4byePxHB0dDQ0NCSGhoaFKz7Gbks6fP+/u7k4I+eCDDyQSSce9el4S/Rti27ZtFEX5+/sTQoYNG9bW1hYdHU0IWbp0qVI9NjY2hJDExMT2ln379hFCwsLCuupCaZC72oz58wP6GeWgt7GxKS8vb/+yrKzM1tZWsyXBANAe9J0pBX1CQgIhxNHRkV6we926dWFhYfn5+RRFjR8/nhCSkZFBUVRqaiohxMbGhr6e+Ne//kUIMTExaW1tpb81fPjw6urqtrY2+o0dHYOe7lQmkzU2NqakpAQGBm7fvp2iqKqqKvqvCqlU2h709NoA9K+cRYsWtbW1/frrr3SFSs+xm5Ioipo9ezYh5Oeff1baq+cl0WuNBQUFtba2Dh482MLCghDy8OHDNWvWEEJOnDihdOTOQX/06FFCyKRJk7rqQmmQu9kM2E156kZHR6fjfRSFhYVtbW1d/ZMGoCObRmefEk9PT6FQWFhYKBQK3dzcdHR0du3a5eTkpLQZ/V6N4OBgeobQ39/fxsamurq6rKxMIpEQQt544w1jY2MOh7NixQqlfQ0MDDZs2GBmZqavrz9lypTdu3fL5XJ/f387OzuFQkEIof9PCLGxsaE/A5m+3Pb39+dwOPTj9m16UtJLh6UnJU2aNMnIyCgzMzMvL6+2tpb+4IesrKxr165xOBx6Ir579OsEtra23T/rdj3cDNhHOeg3bdoUEhISGRl5+PDhyMjIkJCQP//5z1qpDNjBzMzs/v3733//fVhY2MOHD/ft2+fq6tq+vms7qtN8NL3oa2tra3NzMyGk/R6ezndtGhoatq8Qe/nyZU9PT7FY7OHhcfToUXNz845bKu3b/Q2g3ZTUzV49L0lPT8/f37+6upqeZF+2bJm+vn5aWtrNmzfHjx+vVPkLXb16lRDi5OTU/bNu18PNgH2Ug37FihUXL15saWlJSkqSy+VnzpxZv369VioDdoiJiXnvvff09fXPnDkjlUoDAwObmppSUlLaN6CvKMeOHUsIiY2NrampIYSkpKSUlpYaGxsLhUL6Gjw2Npb+nIfvvvuum+5+/vnn1tbWFStW7Nu3b8KECU+fPlW58m5K6tVxuilp5syZhJC///3vNjY2IpHIw8Pj+PHjLS0tgYGBLz1sQkLCP//5Tw6Hs2TJkpc+a3qQGRwcGFhecEXj7e3t6elZWVlpaWnJ4XA0XxOwiUAgOHLkyA8//BAdHa2np5ecnKyjo/Paa68RQuhP5Nm6devu3bv9/PymTZuWnJzs5uY2duxYet5827ZtOjo6QUFBzs7O+fn5o0ePtrCwoGdyumJlZUUIOXToUG5ubnZ2Nn1Vrtr0Yzcl9eo43ZREB/2zZ8/CwsIIId7e3vRFOt3+QsuWLTMyMqqqqqqoqCCEvPvuu6NHj+6mi46DzODgwMAyYD4cHAaogICAEydOuLm5Xbp0KTEx0dXV9fTp0+PGjSOEREREWFlZZWZmlpeXczics2fPrlu3jsfjJScnu7i4HD169P333yeE6OnpJSQkBAYGVldXt7S0/Pjjj910t2rVqrfeeovD4dy7dy8yMpL+jUK/INxb3ZTUK92U5OTkRP99QL9/hb5n1MjIyMfHp6ujPXz4MDc3t7q62sPDY+fOnd9++233XXQcZAYHBwYW5UXNZs6cOXLkyD179ri4uBQUFERGRkokkqSkJG3VB1BRUXHt2jWBQEDf7JiSkjJt2rTAwMALFy5ouzSAgUE56AcNGlRRUWFiYmJvb19cXCyTyYRCYV1dnbbqAygsLBw9enRzc3NkZKSTk9Nnn32Wn59/5MiRf6/CtHgx6fYavyvnz5PqavLWWwxXC9APMfDh4FKptLq6mvnSAAghhDg6OiYkJEyZMuWbb755//33DQ0NxWLx0qVL//3t3+9b7y25nNTWMlYkQH+m/GLsF198ERYWNnXqVPoFovT09OPHjyttExQUFB0dPWzYsPLy8gULFmRmZnK5XD8/v2PHjtGv9gAwa8qUKR1v1AGAXlG+op8yZcr9+/fnzJmzYcOGWbNm3bp1q/MNABcvXqTf+rh+/XoHB4fa2lq5XO7u7o7PogIA6IeUr+jHjh174sSJd955pyc7Z2VlxcXF0UuF0POnjNcHAABqUr6iX7Bgwd69e5uamrrfraKiQqFQuLq6tn/+VG5u7rBhw/qiRAAAUIfyFX1SUtKNGzd+/PFHOzu79jeI5+XlddzGz88vPDy8srKSz+eXlJQEBgampaWFhITs2rVLQ1UDAECPKQf9wYMHX7oPvapfc3NzSUmJVColhPD5/NjYWHot2a5cvXpVaeVu+iAuLi70mz4AAKAv/CfojYyMysrKxowZQwj58ccfg4OD6TdPd6Wurs7R0ZGel/f29m5tbZXJZN0skzRx4kT6MxY6un37tlgsVusZAABAt/4zR9/xXVFr1qyRyWRd7ZObm+vq6mpmZubk5HTu3Dm6sbS0lF5QGwAA+pXeLc9EW7lyZVhYWGNjY1RU1KpVq7KzsxkvCwAAmKJK0EskkoiICB6P5+fnd+jQoVWrVvVkhW4AANCK/wp6iUSSnZ2dnZ2tUChu3bqV/TulfZydndtXvAsODrazs9u8ebOG6gUAgF76z4uxZmZmb775Jv3YwMDg3ytGEUIIUZqv37Nnz7x58/7v//7v7NmzQ4cOFYvFM2fOjIuL00zFAADQK/8J+m5efVUyY8aMBw8epKWl8fl8Qoi5uXlGRkZMTMz169f7pEYAAFBDd5+Z2Q0rK6uFCxe2f6mvr79w4cKOLQAA0E+o8mIsAAAMIAh6AACWQ9ADALAcgh4AgOUQ9AAALIegBwBgOQQ9AADLIegBAFgOQQ8AwHIIegAAlkPQAwCwHIIeAIDlEPQAACyHoAcAYDkEPQAAyyHoAQBYDkEPAMByCHoAAJZD0AMAsByCHgCA5RD0AAAsh6AHAGA5BD0AAMsh6AEAWE6toKcoqra2tq2tjalqAACAcaoEfX19/Y4dO0aMGGFgYGBsbMzj8Zydnbdt29bU1MR4fQAAoCZVgn7NmjXJyclisbiioqK5ufnJkydRUVE5OTlr1qxhvD4AAFCTrgr7xMTE3L1719ramv7SzMzM19fX3d1dJBIdOXKE0fIAAEBdqlzRi0Si+Ph4pcYLFy4MHz6ciZIAAIBJqlzRi8Xi+fPn7927183NTSAQyOXy3NzcqqqqX375hfH6AABATaoEvZeXV0FBQWpqanFxsUwmMzU1XbFixZQpU3R1uztaVlbWxo0blRrlcrmxsbEKNQCA+hYtWiSTybRdRb/Q2Nj41ltvrVq1StuF9AlVgp4Qoqur6+np6e/vz+Fw6JbW1laZTGZubt7VLt7e3omJiUqNt2/fFovFqtUAAGp6/PhxcnKytqvoFzIyMmJjY7VdRV9RZY4+NzfX1dXVzMzMycnp3LlzdGNpaamFhQWjtQEAAANUCfqVK1eGhYU1NjZGRUWtWrUqOzub8bIAAIApqgS9RCKJiIjg8Xh+fn6HDh1atWpVa2sr45UBAAAjVAl6Z2fnhIQE+nFwcLCdnd3mzZsZrQoAABijStDv2bNn6dKlPj4+lZWVHA5HLBbHx8eHhoYyXhwAAKhPlbtuZsyY8eDBg7S0ND6fTwgxNzfPyMiIiYm5fv060+UBAIC6VLy90srKauHChe1f6uvrL1y4sGMLAAD0E1iPHgCA5RD0AAAsh6AHAGA5BD0AaFNeXt7kyZMjIiLMzc19fX0zMjK8vb0FAsG6devoDdLT08eNG2doaBgUFFReXk43isVikUjE5/MnTZp0//59+ji+vr579+61sbERiUS//vqr1p5S/4OgBwAty8zM9PT0fPDgQWNjY0hIyJkzZxITEw8cOCCVSp8+fRoaGrp9+/aysjInJ6e3336bEFJaWrp27dro6OjS0tJRo0bt27ePPs6NGzcUCkV+fv6CBQs2bdqk1efUv6h41w0AvBK+/prU1qq+O4dD/vhHYmnZ/VZWVlaLFy8mhEyfPr26ulr4u5qamsuXL0+dOnXu3LmEkL1795qZmbW2tlpYWOTn5w8fPryurs7c3Ly0tJQ+DpfLjYiI0NXVXbJkydmzZ1Uvm3UQ9ADQtVGjiEKh1hH09V+6iZGREf1AV1fX8vffCvSy56WlpQkJCfb29nQjj8errKy0sLA4fPhwfHy8sbGxvr6+QCCgv2tpaUnv1f2S6a8gDAcAdG3qVO32b2VlNWPGjJ9++okQ0traKpFILC0tT548ef78+cTExCFDhhw/frx9Dd32VdNBCeboAaD/mj17dnp6elxcnEwm++tf/7pu3ToOh/P06VMjIyM+n19ZWfnll182NDRou8z+DkEPAP2XpaXl8ePHN2zYIBQKc3Jyvv/+e0LIkiVL9PX1bW1tQ0NDP/7446tXrx47dkzblfZrmLoBAG1ycXHJy8ujH//tb39rby8oKKAfzJw5886dOx13MTY2bl9AlxDy+PFj+kH7cToeEwiu6AEAWA9BDwDAcgh6AACWQ9ADALAcgh4AgOUQ9AAwgFVXV5uYmBBCsrOzvby8tF1OP4WgBwA2EIlE27dv13YV/RSCHgC0SbVlir/88ks7Ozs7O7vvvvuObikqKtq8eTP9GIsYK0HQA0CX6upIVZXq/1VX96iX3i5TnJ6evmXLlh9++CEzM/P8+fNKR8Mixp3hnbEA0KW1a0ldnVpH2LaNjBr1km16u0zxTz/9tHLlSj8/P0LIJ598MmvWrI5HwyLGnSHoAaBLUVGa6KW3yxQ/fvx4+vTpdIuDg4PS0XR1dbGIsZJX7gnDK+ijjz66du2aUuOTJ1NbWgT//GdsX/T41ltvvfPOO31x5FfNC5cptra2LiwspDcoKipS2uX06dNYxFgJA0EvlUr19PToO5wA+qErV64kJycrNf7jH+TZM7J69fuMd3fjxo3o6GjGD/tqmj17dmRkZFxc3IQJE3bt2pWRkXHp0qX58+fPmTNn1qxZjo6OmzdvVkpwpUWMLV/2+VavAlVejA0KCnry5AkhpLy8fPLkyZaWlkOHDp0+ffqjR4+YLg8AXmkvXKb4tdde2759++LFiydMmLB48WJDQ8OOu2AR485UuaK/ePEivdL/+vXrHRwcEhIS9PT0IiMj165dS/+FBQDQQyosU0wIWbt27dq1a+nHS5cuJYR4eXllZ2cTLGL8ImpN3WRlZcXFxdG/TiMjI52cnBiqCgAAGKPiffQVFRUKhcLV1bW4uJhuyc3NHTZsGGN1AQAAQ1S5ovfz8wsPD6+srOTz+SUlJYGBgWlpaSEhIbt27WK8PgAAUJMqQZ+amkoIaW5uLikpkUqlhBA+nx8bG+vr68twdQAAoDbV5+h5PJ6TkxM9L+/t7f3S7bOysjZu3KjUKJfLjY2NVa4BAABeSnNvmPL29k5MTFRqvH37tlgs1lgNAACvIFWCvps7k1xcXNQoBgAAmKdK0H/44Yfx8fGDBg0yNTVV+lZZWRkTVQEAAGNUCfq4uLjly5fr6+sfPHiQ8YIAQGPq6+sXLFig7Sr6hadPn/r4+Gi7ir6i4hx9eHi4RCJhthQA0LBff/21ublZ21X0F0pLKbCJikEfEBAQEBDAbCkAoGGGhoYsTjdoh0+YAgBgOQQ9AADLIegBAFgOQQ8AwHIIegAAlkPQAwCwHIIeAIDlEPQAACyHoAcAYDkEPQAAyyHoAQBYDkEPAMByCHoAAJZD0AMAsByCHgCA5RD0AAAsh6AHAGA5BD0AAMsh6AEAWA5BDwDAcgh6AACWQ9ADALAcgh4AgOUQ9AAALIegBwBgObWCnqKo2tratrY2pqoBAADGqRL09fX1O3bsGDFihIGBgbGxMY/Hc3Z23rZtW1NTE+P1AQCAmlQJ+jVr1iQnJ4vF4oqKiubm5idPnkRFReXk5KxZs4bx+gAAQE26KuwTExNz9+5da2tr+kszMzNfX193d3eRSHTkyBFGywMAAHWpckUvEoni4+OVGi9cuDB8+HAmSgIAACapckUvFovnz5+/d+9eNzc3gUAgl8tzc3Orqqp++eUXxusDAAA1qRL0Xl5eBQUFqampxcXFMpnM1NR0xYoVU6ZM0dXt7mhtbW01NTVKjSrctNPU1FRfX9/rotUwaNAgfX19TfYIA11TU1NVVZXGutPR0TE2NtZYdzDgqBL0hBBdXd2AgIBe7ZKTk7Nnzx6lxpqaGh2d3k0frV69WiqV8vn8Xu2lsubmZn19/X/84x+a6Q5YoLCw8MSJEzKZTGM9Zmdnp6SkYO4UuqJi0KvA29v71KlTSo23b98Wi8W9Ok5LS8vXX39ta2vLXGndqaqqevfddzXTF7CDQqEQiUSdz/a+s2zZspaWFo11BwOOKkGfl5fX1bdcXFzUKAYAAJinStB/+OGH8fHxgwYNMjU1VfpWWVkZE1UBAABjVAn6uLi45cuX6+vrHzx4kPGCAACAWSqudRMeHm5vb89oJQAA0CdUfDE2ICCgt3fdAACAVmCZYgAAlkPQAwCwHIIeAIDlEPQAACyHoAcAYDkEPQAAyyHoAQBYDkEPAMByCHoAAJZD0AMAsByCHgCA5RD0AAAsh6AHAGA5BD0AAMsh6AEAWA5BDwDAcip+8AiAyq5du/bRRx8xdbS9N29GzJjR/TZ37txhqrv+6d69e//zP//D5/M11uPUqVMZ/CFCX0PQg6YVFRXNmzdv9erVzBxu2rTExMTuN+n8KfYsI5PJvvnmm2nTpmmmu/r6+jfffFMzfQEjMHUDAMByCHoAAJZD0AMAsByCHgCA5RD0AAAsh6AHAGA5BD0AAMsh6AEAWA5BDwDAcgh6AACWQ9ADALAcA0EvlUqrq6vVPw4AAPQFVYI+KCjoyZMnhJDy8vLJkydbWloOHTp0+vTpjx49Yro8AABQlyqrV168eLGhoYEQsn79egcHh4SEBD09vcjIyLVr1/70009d7dXc3Hz79m2lxoKCgqamJhVqAACAHlJrmeKsrKy4uDhDQ0NCSGRkpJOTUzcb5+fnnz59WqmxoaHBzs5OnRoAAKB7KgZ9RUWFra2tq6trcXHxyJEjCSG5ubnDhg3rZhdXV9fPPvtMte4AAEBlqgS9n59feHh4ZWUln88vKSkJDAxMS0sLCQnZtWsX4/UBAICaVAn61NRUQkhzc3NJSYlUKiWE8Pn82NhYX19fhqsDAAC1qT5Hz+PxnJyc6Hl5b29v5koCAAAm4Q1TAAAsh6AHAGA5BD0AAMsh6AEAWA5BDwDAcgh6AACWQ9ADALAcgh4AgOUQ9AAALIegBwBgObWWKYa+kJycfPLkSU32WFhY6OjoqMnuvLy8NNYdACDo+51Lly69/vrrr732msZ6HDdu3N///neNdffJJ588fPhQY90BAIK+P7KysnJwcNBYdzo6OprsztjYuLGxUWPdAQDm6AEAWA5BDwDAcgh6AACWQ9ADALAcgh4AgOVw181LNDY2Jicnz5gxQ2M93r1718rKSmPdAUBnwcHBDQ0NGuuuvr5+3bp1b775Zh8dH0H/Eo2NjYMGDUpMTNRYjwEBAdXV1RrrDgA6e/78eXJyssa6O3v27G+//dZ3x8fUDQAAyyHoAQBYDkEPAMByCHoAAJZD0AMAsBzuugGAXlMoFFVVVZrs0cTEhMPhaLJHNkHQA0DvNDU1paWlrVy5UmM93r9/f+/evZp8OwvLIOgBoHfa2toEAsGpU6c01uPu3btbWlo01h37YI4eAIDlEPQAACyHoAcAYDkEPQAAyyHoAQBYbuDddZOTk7NkyRJDQ0PNdFdfX//06dM5c+ZopjtCyM2bNx89epSSktLbHcvLy62trVW417iurk6TTzA3N7e5uZmpHj+9ffujlx3q+fPnnbt79Mi3pUVw/nw8I2X895EfFRYWanJIy8vLN27caGZm1tsdy8rKbG1te7tXc3NzTU2NJp/ggwcPTExMvvrqK431KJFIkpKSNNbdzZs3BQJB3x1/4AX90KFDR40a1aeD0hFFUVZWVir8Y1DZsGHDBg0aNGjQoN7umJeXN3LkSD09vd7uOHjwYDs7u97upbLhw4crFApTU1NGjhbj6OhqYND9NtnZ2a6urkqNI0c+pyi5np5yu/qcnZ3HjBljaWnJ+JG7MmTIEAsLC13dXv9zvnXrVmBgoAo9mpuba/KcsbS0NDAw0NjlHSEkOzs7JydHY90ZGBj84Q9/6LvjcyiK6ruj94UlS5bs3LlTk8k7UMydO/fEiRNGRkbaLqTfmTZtmibXFh9AMDJdYdnIYI4eAIDlEPQAACyHoAcAYDkEPQAAyyHoAQBYjrt161Zt19A7Dg4OIpGIy+Vqu5B+Z8SIEUKhEGt2d+bq6mpjY6PtKvojjExXWDYyA+/2SgAA6BVM3QAAsByCHgCA5RD0AAAsh6AHAGA5BD0AAMsh6AEAWA5BDwDAcgh6AACWG0hBn52d7enpaWpqunTp0oaGBm2Xo1FTpkzh/C4oKIhufOGA9LxxoJs1a1ZeXl77l2qOBpuGSGlkcPIQQpKSkjw8PAwNDX19fXNzc+nGV+icoQaIlpYWoVAoFovLysoCAgI+/fRTbVekUXZ2dpcvXy4qKioqKnr8+DHVxYD0vHFAS0pKWrZsGSHk3r17dIuao8GaIeo8MhROHoqqqKgwMjI6depUdXX1pk2bRo8eTb1i58yACfqkpCQXFxf6cXJysrOzs3br0aSmpiZ9fX2FQtGx8YUD0vPGAW3Pnj3vvffeoEGD2uNMzdFgzRB1HhmcPBRFnTx5ctKkSfTjpqYmDofz7NmzV+qcGTBTN8XFxW5ubvRjNze3hw8fUq/MKj0lJSV8Pj80NNTJyWnx4sXl5eWkiwHpeaNWnghTIiIiDh482PFTZ9UcDdYMUeeRwclDCJk1a9bZs2fpx5mZmfb29iYmJq/UOTNggl4mk7V/IPjgwYObm5ufP3+u3ZI0RiqVCoXC1atXnzt3jsvlLly4kHQxID1v1MoT6TtqjgaLhwgnDyFEIBAMHTqUoqizZ88uXrz4wIEDHA7nlTpnev2x8dpiamoql8vpx7W1tbq6uq/Op2D7+PjcuHGDfvz1118bGxvLZLIXDkjPGzX/LPqUmqPB4iHCyUN7+vTp8uXLS0pKYmJivLy8yCt2zgyYK3oHB4f218rv3btnb2+vozNgildTVlZWWloa/ZjH43G5XF1d3RcOSM8bNf8s+pSao8HiIcLJQwhpamqaOXPmqFGjrl69Sqc8edXOGc2/LKCalpYWa2vr06dPP3/+PDg4eOvWrdquSHPS09NNTExSU1NlMtn69esDAgKoLgak540sYGNj0/GuG3VGg2VD1HFkcPJQFHXy5El3d/eiDhQKxSt1zgyYoKcoKisry93dfciQIe+8805jY6O2y9Gctra2b775xtnZefDgwaGhoRUVFXT7Cwek540DXcc4o9QeDTYNUceRwclDUdSGDRuULnClUin1Kp0z+IQpAACW68eTSgAAwAQEPQAAyyHoAQBYDkEPAMByCHpgs1u3bs2cOdPY2NjMzCw4ODg/P59u19XVVSgU2q0NQGMQ9MBara2ts2fPnjBhgkQiuXPnzsiRI0NDQ3GbGbyCEPTAWuXl5WVlZX/5y18cHBysrKw+++wzkUhUU1Mzc+bM1tZWR0fHurq69PT0cePGGRoaBgUF0Qt+HT9+fPny5X/84x9NTEwmT558//59QohCoVi9erWpqam5ufknn3yi7WcG0DsIemAta2vrMWPGvPnmmxcuXGhoaOByubGxsSYmJgkJCVwut7CwsLGxMTQ0dPv27WVlNULV9QAAAjdJREFUZU5OTm+//Ta949GjR318fPLz8319fRcuXEhR1M8//5ycnCyRSBITEz/99NPCwkLtPjWAXkHQA2vp6upmZ2e/8cYbBw4csLOzCwoKysrK6rjBuXPnpk6dOnfuXFNT07179167dq21tZUQMnr06NWrV1tYWPztb38rLS0tKCgghLS0tFRWVnp4eJSVldnZ2WnnKQGoBEEPrNXc3ExR1OrVq+Pj48vLy8PDw19//fWOWV9aWpqQkGBvb29vb+/i4sLj8SorKwkhIpGI3kBPT8/e3r68vHzevHkbN25csWKFtbX1N998Q/8+ABgoEPTAWqdPn549ezb9WF9f/5133vHx8ZFIJO0bWFlZzZgxo7i4uLi4uLCwMDEx0dLSkhBSVFREb6BQKEpKSqysrH777Td/f/8bN25cvXo1Njb2yJEjmn86ACpD0ANrzZgx4/r161u2bMnPz79///7XX3+dk5Mzbdo0+rtyuXz27Nnp6elxcXEymeyvf/3runXrOBwOIeTWrVvffvutTCb7+OOPra2tnZ2df/nll0WLFj158qS1tbWpqYnP52v1mQH0DoIeWGvo0KHXrl3Lycl5/fXXvb29jx07durUKWdnZ0JIWFjY8OHDBQLB8ePHN2zYIBQKc3Jyvv/+e3rHWbNmJSUlOTg4pKSknDx5UkdHZ+XKlVZWVo6Ojl5eXj4+Pn/84x+1+swAegerVwL8l+PHj587d+7kyZPaLgSAMbiiBwBgOQQ9AADL/X/2BAVnNIyBjQAAAABJRU5ErkJggg==" alt="plot of chunk unnamed-chunk-19"/> </p>

<pre><code class="r"># to save this plot:
#dev.copy(png, file =&#39;./figures/histogram_filled.png&#39;)
#dev.off()
</code></pre>

<h2>Are there differences in activity patterns between weekdays and weekends?</h2>

<ol>
<li>A new factor variable in the dataset is created with two levels -&ldquo;weekday&rdquo; and &ldquo;weekend&rdquo; indicating whether a given date is a weekday or weekend day.</li>
</ol>

<pre><code class="r"># convert formatted date as weekdays using weekdays()
activity$daytype[(weekdays(activity$dateformat) == &#39;Saturday&#39;)
                 |(weekdays(activity$dateformat) == &#39;Sunday&#39;)] = &#39;Weekend&#39;
activity$daytype[!((weekdays(activity$dateformat) == &#39;Saturday&#39;)
                 |(weekdays(activity$dateformat) == &#39;Sunday&#39;))] = &#39;Weekday&#39;
# convert the daytype to factor from character
activity$daytype = as.factor(activity$daytype)
</code></pre>

<ol>
<li>A panel plot is made containing a time series plot of the 5-minute interval (x-axis) and the average number of steps taken, averaged across all weekday days or weekend days (y-axis):</li>
</ol>

<pre><code class="r">meanDaily = with(activity, tapply(steps, list(interval, daytype), mean, na.rm=T))
par(mfrow = c(2, 1), mar = c(2, 2, 1 , 1), oma = c(1, 1, 0, 0))
plot(intervalDaily, meanDaily[, 1], type=&#39;l&#39;, main = &#39;Weekend&#39;, xlab= &#39;&#39;, ylim = c(0, 250))
plot(intervalDaily, meanDaily[, 2], type=&#39;l&#39;, main = &#39;Weekday&#39;, xlab=&#39;interval&#39;,
     ylim = c(0, 250))
mtext(&#39;Number of steps&#39;, outer=T, side=2)
mtext(&#39;Interval&#39;, outer=T, side=1)
</code></pre>

<p><img 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" alt="plot of chunk unnamed-chunk-21"/> </p>

<pre><code class="r">#dev.copy(png, file =&#39;./figures/weekdays.png&#39;)
#dev.off()
</code></pre>

<p>It appears that there is a difference between weekdays and weekends regarding the steps taken. During the weekends, average number of steps peaks around 9:00am. During the weekdays, the average steps are relatively more evenly distributed along the day time period. </p>

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