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Summative Assessment on Mean, Median and Interquartile Range (IQR)
Using the data sets below, find the mean, median and interquartile range (IQR).
Round all decimal answers to the nearest tenths place.
1) This data set represents the amount of dollars paid by concert attendees:
(45,34,23,12,6,90,56,23,45,67)
Mean: 40.1
Median: 39.5
IQR: 33
2) This data set represents the ages of concert attendees: (43,32,32,32,12,15,15,7,3,4,6)
Mean: 18.3
Median: 15
IQR: 26
3) This data set represents the amount of emails received daily by students:
(5,6,3,2,8,12,12,9,7,8,5,4,3)
Mean: 6.5
Median: 6
IQR: 5
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4) Explain what the mean is and the steps that you need to take in order to find the mean of an unordered data set.
The mean is a measure of center of a set of data. In order to find the mean, you need to add all the data points of the data set and divide this sum by the number of data points in the data set.
5) Explain what the median is and the steps that you need to take in order to find the median of an unordered data set.
Median is another way to measure the center of a set of data. In order to find the median, first order the data points from smallest to largest (including duplicates). Then, look for the data point found in the middle. This will be the median. If you have an odd number of data points, the median will be the middle data point. If the number of data points is even, the median will be the average of the two middle data points.
6) Explain what the IQR is and the steps that you need to take in order to find the IQR of an unordered data set.
The IQR, or interquartile range, is a measure of the variability of a data set. In order to find the IQR, first order the data points from smallest to largest. Find the median of the data set; this will divide the dataset into two data sets—one upper and one lower. Look at the data points in the lower data set and find its median; this is called Q1. Look at the data points in the upper data set and find its median; this is called Q3. To find the IQR subtract Q1 from
Q3. IQR = Q3 – Q1
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