IXL | Choose appropriate measures of center and variation for line plots

In Neil's science lab, each student added vinegar to baking soda until a reaction occurred. This line plot shows the distribution of the amount of vinegar each student needed to make a reaction.

Science experiment

0.75

1.25

1.75

2.25

2.75

3.25

Amount of vinegar (teaspoons)

Complete the sentences.

The distribution of the amount of vinegar needed for a reaction is best described as . So, the mean absolute deviation an appropriate measure of variation.

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Learn with an example

question

Lily only has one sibling, her older sister. When she discovered that one of her friends came from a family of 8 kids, she got curious and asked all of her other friends how many siblings they had. This line plot shows Lily's findings.

Lily's friends

Number of siblings

Complete the sentences.

The distribution of the number of siblings 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

One data value is far above all the other values. So, the distribution has an outlier.

Lily's friends

Number of siblings

These sentences are correct.

The distribution of the number of siblings is best described as symmetric with a high

outlier.

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

mean.

$Confetti$

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JJ.11Describe distributions in line plots

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