A line plot is symmetric if the left and right side of the distribution look 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. There is a cluster from 0 to 3 times and a gap from 3 to 5 times. There are peaks at 1 and 2 times. There are no outliers.
B
The data values are centered around the median of 2. The spread of the data around the center is 2.
Practice makes perfect
A line plot is a way of illustrating a data set in which each data point is represented with a mark above a number line. Marks representing the same elements are stacked above each other. We want to identify the shape of the distribution on the given line plot.
The left side of the distribution is taller than the right side, which means that the distribution is non-symmetric. Now let's identify any clusters, gaps, peaks, or outliers on the plot. Let's begin by recalling the definitions of these attributes.
Name
Definition
Cluster
Group of points that lie close together
Gap
Area of a graph that does not contain any data values
Peak
Most frequently occurring value or interval of values
Outlier
Data point that is significantly different from the other values in the data set
With these definitions in mind, we can draw some conclusions about the clusters, gaps, peaks, and outliers in our plot.
There appears to be a cluster from 0 to 3 times.
There is a gap from 3 to 5 times.
There are peaks at 1 and 2 times.
There do not appear to be any outliers.
Note that clusters and 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 know from Part A that the distribution is non-symmetric, which means that we should use the median to describe the center and interquartile range to describe the spread of a distribution. We will do these things 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 line plot.
We can see that there are 15 data values in the set. This means that the middle value is the 8th value. Let's write all the data values as a set and mark the median.
0,0,0,1,1,1,1,2,2,2,2,3,3,3,5
The data values are centered around the median of 2.
Spread of Distribution
The interquartile range, or IQR, is a measure of spread that calculates the difference between Q3 and Q1, the upper and lower quartiles.
The interquartile range is equal to 2. This means that the spread of the data around the center is 2.
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