Question

Which of the accompanying boxplots likely has the data with the larger standard deviation? Why?

Choose the correct answer below.
O A. Boxplot I likely has the data with the larger standard deviation because the values associated with Boxplot I are larger than the values associated with Boxplot It, which likely results in a larger standard deviation
O B. Boxplot I likely has the data with the larger standard deviation because the IQR is smaller than that of Boxplot It, which likely results in a larger standard deviation.
O C. Boxplot Il likely has the data with the larger standard deviation because the median is less than the median of Boxplot I, which likely results in a larger standard deviation
OD. Boxplot II likely has the data with the larger standard deviation because the boxplot appears to have a greater spread, which likely results in a larger standard deviation

Answer 1

Standard deviation illustrates how the data elements of a dataset differ from the mean of the dataset.

The true statement is:

D. Boxplot II likely has the data with the larger standard deviation because the boxplot appears to have a greater spread, which likely results in a larger standard deviation

From the given boxplots, we have the following observation

Boxplot 1

Minimum = 9

Maximum = 26

Boxplot II

Minimum = 4

Maximum = 25

Calculate the range of both plots

$\mathbf{Range = Maximum - Minimum}$

So, we have:

$\mathbf{Box1 = 26- 9 = 17}$

$\mathbf{Box2 = 25- 4 = 21}$

The above shows that boxplot II has a greater range

Range is a measure of the spread of the dataset.

The higher the range, the higher the spread

This means that box II has a greater spread

Because box II has a greater spread, it will have a greater standard deviation.

Hence, (d) is correct

Read more about standard deviation and boxplots at:

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