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Q.88

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Found in: Page 149

### Introductory Statistics

Book edition OER 2018
Author(s) Barbara Illowsky, Susan Dean
Pages 902 pages
ISBN 9781938168208

# Given the following box plots, answer the questions. a. In complete sentences, explain why each statement is false. i. Data 1 has more data values above two than Data 2 has above two.ii. The data sets cannot have the same mode. iii. For Data 1, there are more data values below four than there are above four. b. For which group, Data 1 or Data 2, is the value of “7” more likely to be an outlier? Explain why in complete sentences.

a)

i. The number of data values in the data sets is not specified. True, Data Set 1 has a higher proportion of values that are greater than two. Data Set 2, on the other hand, may be a considerably larger set with a greater number of data values greater than two.

ii. Individual data values are not displayed in the box plots. We have no information about the data sets' modalities. It's possible that both data sets are in the same mode.

iii. Data Set 2 has a higher proportion of values below four than Data Set 1. This, however, prevents us from comparing the number of values in each interval.

b) The value " 7 " is more likely to be an outlier in Data Set 2, where more than 75 % \text of the data falls below three.

See the step by step solution

## Part (a) - Step 1: To explain

Why the statements are false.

i. Data 1 has more values above two than Data 2 has above two.

ii. The data sets cannot have the same mode.

iii. For Data 1, there are more data values below four than there are above four.

## Part(a) - Step 2: Explanation

Box plots are a graphical tool used in statistics to show the concentration of data. They also demonstrate how far the extreme numbers differ from the majority of the data. The smallest value, the first quartile, the median, the third quartile, and the maximum value are used to create a box plot. These values are used to see how similar other data values are to them.

A box plot can be used to determine how skewed the data is. If the median is roughly in the middle of the box, the data is symmetric. The data is right skewed if the longer part of the box is to the right of the median. The data is left-skewed if the longer part of the box is to the left of the median.

i. The number of data values in the data sets is not specified. True, Data Set 1 has a higher proportion of values that are greater than two. Data Set 2, on the other hand, may be a considerably larger set with a greater number of data values greater than two.

ii. Individual data values are not displayed in the box plots. We have no information about the data sets' modalities. It's possible that both data sets are in the same mode.

iii. Data Set 2 has a higher proportion of values below four than Data Set 1. This, however, prevents us from comparing the number of values in each interval.

## Part (b) - Step 3: To determine

for which group, Data 1 or Data 2 , is the value " 7 " more likely to be an outlier?

## Part (b) - Step 4: Explanation

Box plots are a graphical tool used in statistics to show the concentration of data. They also demonstrate how far the extreme numbers differ from the majority of the data. The smallest value, the first quartile, the median, the third quartile, and the maximum value are used to create a box plot. These values are used to see how similar other data values are to them.

A box plot can be used to determine how skewed the data is. If the median is roughly in the middle of the box, the data is symmetric. The data is rightskewed if the longer part of the box is to the right of the median. The data is left-skewed if the longer part of the box is to the left of the median.

We can observe from the box plots that Data 2 has 75% of data below 3 and is more spread out in the ${4}^{th}$ quarter. As a result, the "7" in Data 2 is more likely to be an outlier than in Data 1.