IXL | Choose appropriate measures of center and variation

On a field trip to the Stanbury Fire Department, Grayson asked how long it took the firefighters to respond to calls last week. This line plot shows the distribution of the response times.

Stanbury Fire Department response times

Time (minutes)

Complete the sentences.

The distribution of the response times is best described as . So, the mean absolute deviation an appropriate measure of variation.

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question

Lexi sews custom tote bags to sell at craft fairs. She measures the leftover pieces of fabric from each bag and records the different amounts. This line plot shows the distribution of leftover fabric.

Leftover fabric

2.5

3.5

Amount (square feet)

Complete the sentences.

The distribution of the leftover fabric is best described as . So, the mean an appropriate measure of center.

key idea

Mean and median are measures of center.

The mean is calculated by taking the average of all the values in a data set.
The median is found by ordering the values in a data set from least to greatest, then selecting the middle value.

Mean absolute deviation (MAD) and interquartile range (IQR) are measures of variation.

The MAD is calculated by taking the average distance between the data values and the mean.
The IQR is the range of the middle 50% of the data set.

The mean and MAD can be strongly affected by the shape of a distribution and by outliers. So, they are appropriate measures for symmetric distributions but may not be appropriate for skewed distributions or when there are outliers.

Since the median is the middle value in a data set, it is less affected by the shape of a distribution or by outliers. And, since the IQR is the range of the middle 50% of the data set, it is also less affected by the shape or by outliers. So, they are almost always appropriate measures.

solution

Most of the data values are on the left, and the "tail" of the graph extends to the right. So, the distribution is skewed to the right. It does not have a symmetric shape.

Leftover fabric

2.5

3.5

Amount (square feet)

These sentences are correct.

The distribution of leftover fabric is best described as not

symmetric.

So, the mean is not an appropriate measure of center.

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Not feeling ready yet? These can help:

JJ.11Describe distributions in line plots

II.13Interpret histograms

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