# Five Number Summary And Box And Whisker Plot

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Mahaffeymath
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• 1.

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

• A.

5, 15, 10, 25, 20

• B.

0, 7.5, 17.5, 22.5, 30

• C.

0, 5, 15, 25, 30

C. 0, 5, 15, 25, 30
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 the data set. In this case, the minimum value is 0, the first quartile is 5, the median is 15, the third quartile is 25, and the maximum value is 30. Therefore, the correct answer is 0, 5, 15, 25, 30.

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• 2.

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

• A.

20

• B.

25

• C.

15

A. 20
Explanation
The interquartile range is a measure of the spread of the middle 50% of the data. To find it, we first need to arrange the data in ascending order: 0, 5, 5, 10, 15, 15, 20, 20, 25, 25, 30. The lower quartile (Q1) is the median of the lower half of the data, which is 10. The upper quartile (Q3) is the median of the upper half of the data, which is 25. The interquartile range is then calculated by subtracting Q1 from Q3: 25 - 10 = 15. Therefore, the correct answer is 15.

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• 3.

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

• A.

30

• B.

45

• C.

20

A. 30
Explanation
The median of a data set is the middle value when the data is arranged in ascending or descending order. In this case, the box and whisker plot shows that the median is represented by the line inside the box, which is located at the value of 30. Therefore, the median of the data is 30.

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• 4.

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

• A.

42

• B.

25

• C.

30

B. 25
Explanation
The IQR (Interquartile Range) is a measure of statistical dispersion, specifically the range between the first quartile (Q1) and the third quartile (Q3) of a dataset. In this case, since the answer is 25, it means that the range between Q1 and Q3 is 25 units.

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• 5.

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

• A.

42

• B.

25

• C.

30

A. 42
Explanation
The range of the data can be determined by subtracting the smallest value from the largest value. In this case, the largest value on the box and whisker plot is 42 and the smallest value is not visible on the plot. Therefore, the range of the data is 42.

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• 6.

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

• A.

30, 50, 50, 100, 150

• B.

30, 50, 90, 100, 150

• C.

30, 50, 75, 100, 150

C. 30, 50, 75, 100, 150
Explanation
The 5 number summary provides a summary of the distribution of the data. It consists of the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value. 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.

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• 7.

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

• A.

50

• B.

75

• C.

100

B. 75
Explanation
The interquartile range is a measure of the spread of data, specifically the range between the first quartile (Q1) and the third quartile (Q3). To find the interquartile range, we first need to find Q1 and Q3. Arranging the data in ascending order, we have 30, 50, 50, 90, 100, 150. Q1 is the median of the lower half of the data, which is 50. Q3 is the median of the upper half of the data, which is 100. The interquartile range is then calculated as Q3 - Q1, which is 100 - 50 = 50. Therefore, the correct answer is 50.

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• 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

• A.

25%

• B.

50%

• C.

75%

A. 25%
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. Since there are 6 numbers in the upper half and only 1 number (88) is higher than the upper quartile, the percentage of data higher than the upper quartile is 1/6 or approximately 16.7%. Therefore, the correct answer is 25%, which is the closest option to 16.7%.

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• 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

• A.

25%

• B.

50%

• C.

75%

C. 75%
Explanation
The lower quartile is the median of the lower half of the data. In this case, the lower quartile is 48. Out of the 12 data points listed, there are 9 data points (72, 67, 63, 55, 72, 77) that are higher than 48. Therefore, the percentage of the data that is higher than the lower quartile is 9/12 = 75%.

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• 10.

### What percent of the data listed below is higher than the median?88, 53, 72, 67, 48, 63, 25, 34, 46, 55, 72, 77

• A.

25%

• B.

50%

• C.

75%

B. 50%
Explanation
The median is the middle value of a set of data when arranged in ascending order. In this case, the data listed in ascending order is 25, 34, 46, 48, 53, 55, 63, 67, 72, 72, 77, 88. The median is the average of the two middle values, which are 55 and 63. Therefore, there are 6 values (72, 72, 77, 88) that are higher than the median, out of a total of 12 values. So, the percentage of data higher than the median is 6/12 or 50%.

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• Current Version
• Mar 22, 2023
Quiz Edited by
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• Dec 30, 2010
Quiz Created by
Mahaffeymath

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