IXL - Choose appropriate measures of center and variation (Algebra 1 practice)

When Hazel plays the video game Turbo Galactic

Travels,

she earns points for dodging space aliens and avoiding black holes. This histogram shows the distribution of total points scored in each game Hazel played last month.

0-25

26-50

51-75

76-100

101-125

126-150

151-175

176-200

Total points

Number of games

Points scored each game

Complete the sentences.

The distribution of total points is best described as . So, the standard deviation an appropriate measure of variation.

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Learn with an example

question

Jason is keeping track of how much flour he uses per batch of bread in his bread-making class. This histogram shows the distribution of the amounts of flour Jason has used so far in the class.

0-0.5

1-1.5

2-2.5

3-3.5

4-4.5

5-5.5

Amount of flour (cups)

Number of batches

Making bread

Complete the sentences.

The distribution of the amounts of flour used is best described as . So, the is a more appropriate measure of variation 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.

Standard deviation and interquartile range (IQR) are measures of variation.

The standard deviation measures how much data values typically vary from the mean.
The IQR is the range of the middle 50% of the data set.

The mean and standard deviation 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

The distribution has a high number of batches centered around 3–3.5 cups of flour, but the left and right sides are not at all mirror images. So, the distribution does not have a symmetric shape.

0-0.5

1-1.5

2-2.5

3-3.5

4-4.5

5-5.5

Amount of flour (cups)

Number of batches

Making bread

These sentences are correct.

The distribution of the amounts of flour used is best described as not

symmetric.

So, the interquartile range is a more appropriate measure of variation than the standard

deviation.

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Work it out

Not feeling ready yet? These can help:

JJ.11Describe distributions in line plots

II.6Variance and standard deviation

HH.4Interpret histograms

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