Five-number Summary And Box-and-whisker Plot! Trivia Quiz

1) Based on the box and whisker plot below, what is the range of the data?

42

25

30

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Explanation

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2) Based on the box and whisker plot below, what is the median of the data?

30

45

20

The median is the middle value in a set of data when arranged in order. In this case, the box and whisker plot shows that the median is located at the middle of the box, which is at the value of 30. Therefore, the median of the data is 30.

Explanation

The median is the middle value in a set of data when arranged in order. In this case, the box and whisker plot shows that the median is located at the middle of the box, which is at the value of 30. Therefore, the median of the data is 30.

3) What percent of the data listed below is higher than the median?

88, 53, 72, 67, 48, 63, 25, 34, 46, 55, 72, 77

25%

50%

75%

The median is the middle value when the data is arranged in ascending order. In this case, the median is 63. To determine the percentage of data higher than the median, we count the number of values greater than 63, which is 6 (88, 72, 67, 72, 77, 55). Since there are a total of 12 values, the percentage of data higher than the median is 6/12 = 50%.

Explanation

The median is the middle value when the data is arranged in ascending order. In this case, the median is 63. To determine the percentage of data higher than the median, we count the number of values greater than 63, which is 6 (88, 72, 67, 72, 77, 55). Since there are a total of 12 values, the percentage of data higher than the median is 6/12 = 50%.

4) Based on the box and whisker plot below, what is the IQR of the data?

42

25

30

The IQR, or interquartile range, is a measure of statistical dispersion, specifically the range between the first quartile (Q1) and the third quartile (Q3) of the data. In this case, the box and whisker plot is not provided, so it is not possible to determine the IQR or provide an explanation.

Explanation

The IQR, or interquartile range, is a measure of statistical dispersion, specifically the range between the first quartile (Q1) and the third quartile (Q3) of the data. In this case, the box and whisker plot is not provided, so it is not possible to determine the IQR or provide an explanation.

5) Determine the 5 number summary for the set of data: 5, 20, 15, 25, 0, 10, 15, 5, 25, 30, 20

5, 15, 10, 25, 20

0, 7.5, 17.5, 22.5, 30

0, 5, 15, 25, 30

The 5 number summary provides a summary of the distribution of the data. It includes the minimum value (0), the first quartile (5), the median (15), the third quartile (25), and the maximum value (30). These values give an indication of the spread and central tendency of the data set.

Explanation

The 5 number summary provides a summary of the distribution of the data. It includes the minimum value (0), the first quartile (5), the median (15), the third quartile (25), and the maximum value (30). These values give an indication of the spread and central tendency of the data set.

6) What is the 5 number summary of the following data? 100, 150, 50, 30, 90, 50

30, 50, 50, 100, 150

30, 50, 90, 100, 150

30, 50, 75, 100, 150

The 5 number summary consists of the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value of a dataset. In this case, the minimum value is 30, the first quartile is 50, the median is 75, the third quartile is 100, and the maximum value is 150.

Explanation

The 5 number summary consists of the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value of a dataset. In this case, the minimum value is 30, the first quartile is 50, the median is 75, the third quartile is 100, and the maximum value is 150.

7) Determine the Interquartile range for the following set of data: 5, 20, 15, 25, 0, 10, 15, 5, 25, 30, 20

20

25

15

The interquartile range is a measure of the spread of data and is calculated by finding the difference between the upper quartile and the lower quartile. In this case, the upper quartile is 25, which is the third largest value in the data set, and the lower quartile is 5, which is the third smallest value. Therefore, the interquartile range is 25 - 5 = 20.

Explanation

The interquartile range is a measure of the spread of data and is calculated by finding the difference between the upper quartile and the lower quartile. In this case, the upper quartile is 25, which is the third largest value in the data set, and the lower quartile is 5, which is the third smallest value. Therefore, the interquartile range is 25 - 5 = 20.

8) What percent of the data listed below is higher than the upper quartile?

88, 53, 72, 67, 48, 63, 25, 34, 46, 55, 72, 77

25%

50%

75%

The upper quartile is the median of the upper half of the data. To find the upper quartile, we first need to arrange the data in ascending order: 25, 34, 46, 48, 53, 55, 63, 67, 72, 72, 77, 88. The upper half of the data is: 63, 67, 72, 72, 77, 88. The median of this upper half is the upper quartile. In this case, the upper quartile is 72. There are 6 data points higher than 72 in the given data set. Since there are a total of 12 data points, the percentage of data higher than the upper quartile is (6/12) * 100 = 50%. Therefore, the given answer of 25% is incorrect.

Explanation

The upper quartile is the median of the upper half of the data. To find the upper quartile, we first need to arrange the data in ascending order: 25, 34, 46, 48, 53, 55, 63, 67, 72, 72, 77, 88. The upper half of the data is: 63, 67, 72, 72, 77, 88. The median of this upper half is the upper quartile. In this case, the upper quartile is 72. There are 6 data points higher than 72 in the given data set. Since there are a total of 12 data points, the percentage of data higher than the upper quartile is (6/12) * 100 = 50%. Therefore, the given answer of 25% is incorrect.

9) What percent of the data listed below is higher than the lower quartile?

88, 53, 72, 67, 48, 63, 25, 34, 46, 55, 72, 77

25%

50%

75%

The lower quartile is the median of the lower half of the data set. In this case, the lower quartile is 48. To determine the percentage of data higher than the lower quartile, we need to count the number of values that are greater than 48. Out of the 12 values listed, 9 values (88, 53, 72, 67, 63, 55, 72, 77) are higher than 48. Therefore, the percentage of data higher than the lower quartile is 75%.

Explanation

The lower quartile is the median of the lower half of the data set. In this case, the lower quartile is 48. To determine the percentage of data higher than the lower quartile, we need to count the number of values that are greater than 48. Out of the 12 values listed, 9 values (88, 53, 72, 67, 63, 55, 72, 77) are higher than 48. Therefore, the percentage of data higher than the lower quartile is 75%.

10) What is the interquartile range of the following data? 100, 150, 50, 30, 90, 50

50

47.5

100

The interquartile range (IQR) measures statistical dispersion and is the difference between the first quartile (Q1) and the third quartile (Q3). For the data set [100, 150, 50, 30, 90, 50], Q1 is 50 and Q3 is 97.5. The IQR is calculated as Q3 - Q1, which equals 47.5. It represents the range within which the middle 50% of the data lies, providing insight into data spread.

Explanation

The interquartile range (IQR) measures statistical dispersion and is the difference between the first quartile (Q1) and the third quartile (Q3). For the data set [100, 150, 50, 30, 90, 50], Q1 is 50 and Q3 is 97.5. The IQR is calculated as Q3 - Q1, which equals 47.5. It represents the range within which the middle 50% of the data lies, providing insight into data spread.