A box plot is symmetric if the lengths of each box and whisker are the same.
B
A measure of center is a statistic that summarizes a data set by finding a central value. A measure of spread is a way of quantifying how spread out, or different, the points in a data set are.
A
Example Solution: The distribution is not symmetric since the lengths of each box and each whisker are not the same. There are no outliers.
B
Example Solution: The distribution is not symmetric, so the median and interquartile range are appropriate measures to use. The data values are centered around the median of about 19 visitors. The spread of the data around the center is about 22.
Practice makes perfect
A box plot illustrates the distribution of a data set by displaying it along a number line. It consists of three parts: a box and two whiskers.
The left whisker extends from the minimum to the first quartile.
The box extends from the first to the third quartile and has a vertical line through the median.
The right whisker extends from the third quartile to the maximum.
Let's look at our box plot.
The right side of the box is longer than the left side, and the right whisker is longer than the left one. This means that the left side of the box plot does not look like the right side. Therefore, the distribution is not symmetric. Now let's identify any outliers in the data set. Let's recall the definition of an outlier.
An outlier is a data point that is significantly different from the other values in the data set.
Now we can find any outliers on our graph.
Notice that there are no points on the graph that are far away from other points in the data set. This means that there are no outliers in the data set. Note that outliers are found by observing a graph, so they are somewhat subjective. Our solution is just an example solution.
We want to describe the center and spread of the distribution. Let's start by recalling some facts about measures of center and spread.
We determined in Part A that the distribution is non-symmetric, so we should use the median to describe the center and interquartile range to describe the spread of the distribution. We will find these measures one at a time.
Center of Distribution
When the data are arranged in numerical order, the median is the middle value — or the mean of the two middle values — in a set of data. To find the median, we will start by looking at the given box plot again.
We know that the box has a vertical line through median. This means that the data values are centered around the median of about 19 visitors.
Spread of Distribution
The interquartile range, or IQR, is a measure of spread that measures the difference between Q3 and Q1, the upper and lower quartiles. Let's start by identifying the quartiles on our box plot.
We can see that the lower quartile Q1 is about 16 and that the upper quartile Q3 is about 38. Now we can calculate the interquartile range.
IQR: 38−16=22
The interquartile range is about 22. This means that the spread of the data around the center is about 22.
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