Box And Whisker Plot 5 Number Summary

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

30

45

20

The median of a data set is the middle value when the data is arranged in ascending order. In the given box and whisker plot, the box represents the interquartile range, with the median falling within the box. The line inside the box represents the median, which is the value at the center of the box. In this case, the line is at 30, indicating that the median of the data is 30.

Explanation

The median of a data set is the middle value when the data is arranged in ascending order. In the given box and whisker plot, the box represents the interquartile range, with the median falling within the box. The line inside the box represents the median, which is the value at the center of the box. In this case, the line is at 30, indicating that the median of the data is 30.

2. What is the upper quartile for the data set5, 5, 8, 10, 13, 13, 14, 18, 19, 19, 19, 24, 28

The upper quartile is a measure of central tendency that divides the data set into four equal parts. In this case, the data set is already sorted in ascending order. The upper quartile is the median of the second half of the data set. Since the second half of the data set starts with the number 19 and ends with the number 28, the upper quartile is 19.

Explanation

The upper quartile is a measure of central tendency that divides the data set into four equal parts. In this case, the data set is already sorted in ascending order. The upper quartile is the median of the second half of the data set. Since the second half of the data set starts with the number 19 and ends with the number 28, the upper quartile is 19.

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

42

25

30

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Explanation

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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 consists of the minimum value (0), the first quartile (5), the median (15), the third quartile (25), and the maximum value (30). This summary provides a concise description of the distribution of the data, indicating the range and the middle values.

Explanation

The 5 number summary consists of the minimum value (0), the first quartile (5), the median (15), the third quartile (25), and the maximum value (30). This summary provides a concise description of the distribution of the data, indicating the range and the middle values.

6. 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 of a set of data when arranged in order. In this case, when the data is arranged in ascending order, the median is 63. Since there are 6 values higher than 63 (88, 72, 67, 72, 77, 55) and 6 values lower than 63 (53, 48, 25, 34, 46, 63), it means that 50% of the data is higher than the median.

Explanation

The median is the middle value of a set of data when arranged in order. In this case, when the data is arranged in ascending order, the median is 63. Since there are 6 values higher than 63 (88, 72, 67, 72, 77, 55) and 6 values lower than 63 (53, 48, 25, 34, 46, 63), it means that 50% of the data is higher than the median.

7. 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. In this case, the upper quartile is 72. To determine the percentage of data higher than the upper quartile, we count the number of data points higher than 72, which is 3 (88, 77, and 72). Since there are a total of 12 data points, the percentage of data higher than the upper quartile is 3/12 = 25%.

Explanation

The upper quartile is the median of the upper half of the data. In this case, the upper quartile is 72. To determine the percentage of data higher than the upper quartile, we count the number of data points higher than 72, which is 3 (88, 77, and 72). Since there are a total of 12 data points, the percentage of data higher than the upper quartile is 3/12 = 25%.

8. 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 provides a summary of the distribution of the data. It includes the minimum value (30), the first quartile (50), the median (75), the third quartile (100), and the maximum value (150). These values give an overview of the spread and central tendency of the data.

Explanation

The 5 number summary provides a summary of the distribution of the data. It includes the minimum value (30), the first quartile (50), the median (75), the third quartile (100), and the maximum value (150). These values give an overview of the spread and central tendency of the data.

9. 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, specifically the range between the first quartile (Q1) and the third quartile (Q3). In this case, the first quartile is 15 and the third quartile is 25. To find the interquartile range, subtract Q1 from Q3: 25 - 15 = 10. However, the given answer of 20 is incorrect and does not represent the interquartile range.

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). In this case, the first quartile is 15 and the third quartile is 25. To find the interquartile range, subtract Q1 from Q3: 25 - 15 = 10. However, the given answer of 20 is incorrect and does not represent the interquartile range.

10. 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 higher than 48. Out of the 12 values given, there are 9 values higher than 48 (88, 53, 72, 67, 63, 55, 72, 77). Therefore, the percentage of data higher than the lower quartile is 9/12 or 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 higher than 48. Out of the 12 values given, there are 9 values higher than 48 (88, 53, 72, 67, 63, 55, 72, 77). Therefore, the percentage of data higher than the lower quartile is 9/12 or 75%.