IXL | Choose appropriate measures of center and variation

Felix is learning to play the piano. This histogram shows the distribution of his daily practice time over the last two weeks.

0-10

11-20

21-30

31-40

41-50

51-60

61-70

Practice time (minutes)

Number of times

Piano practice times

Complete the sentences.

The distribution of practice times is best described as . So, the are both appropriate measures of variation.

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question

Rhianna is following a strict training schedule as she prepares to run her first half-marathon. This histogram shows the distribution of distances she has run during her training so far.

1-2

3-4

5-6

7-8

9-10

Distance (miles)

Number of runs

Training for a half-marathon

Complete the sentences.

The distribution of distances is best described as . So, the is a more appropriate measure of center than the .

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.

1-2

3-4

5-6

7-8

9-10

Distance (miles)

Number of runs

Training for a half-marathon

These sentences are correct.

The distribution of distances is best described as not

symmetric.

So, the median is a more appropriate measure of center than the

mean.

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Not feeling ready yet? These can help:

JJ.11Describe distributions in line plots

II.13Interpret histograms

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