Box Plots

1. 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 the median of the upper half of the data set. In this case, the upper half of the data set consists of the values 19, 19, 19, 24, and 28. The median of this upper half is 19, which is also the value that appears most frequently in the upper half. Therefore, the upper quartile for this data set is 19.

Explanation

The upper quartile is the median of the upper half of the data set. In this case, the upper half of the data set consists of the values 19, 19, 19, 24, and 28. The median of this upper half is 19, which is also the value that appears most frequently in the upper half. Therefore, the upper quartile for this data set is 19.

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2. For the data set4, 5, 5, 5, 8, 10, 13, 13, 14, 17, 20, 36what is the range?

36

13

5

32

20

The range of a data set is the difference between the largest and smallest values in the set. In this case, the largest value is 36 and the smallest value is 4. Therefore, the range is 36 - 4 = 32.

Explanation

The range of a data set is the difference between the largest and smallest values in the set. In this case, the largest value is 36 and the smallest value is 4. Therefore, the range is 36 - 4 = 32.

3. For the data set4, 6, 6, 4, 8, 1, 5, 10, 8, 21, 6, 17, 12, 18, 9what is the range?

5

20

21

11

8

The range is the difference between the largest and smallest values in a data set. In this case, the largest value is 21 and the smallest value is 1. Therefore, the range is 21 - 1 = 20.

Explanation

The range is the difference between the largest and smallest values in a data set. In this case, the largest value is 21 and the smallest value is 1. Therefore, the range is 21 - 1 = 20.

4. For the data set3, 3, 3, 6, 7, 10, 14, 14, 15, 20, 22, 23, 37what is the median?

34

10

14

15

20

The median is the middle value in a dataset when it is arranged in ascending order. In this case, the dataset is already arranged in ascending order. The middle value is 14, which appears twice in the dataset. Therefore, the median is 14.

Explanation

The median is the middle value in a dataset when it is arranged in ascending order. In this case, the dataset is already arranged in ascending order. The middle value is 14, which appears twice in the dataset. Therefore, the median is 14.

5.

What is the median?

The median is a measure of central tendency that represents the middle value in a set of numbers. In this case, the given answer "12, twelve" suggests that the median is 12 or twelve. This means that in the set of numbers provided, there is either a value of 12 or the word "twelve" that represents the middle value.

Explanation

The median is a measure of central tendency that represents the middle value in a set of numbers. In this case, the given answer "12, twelve" suggests that the median is 12 or twelve. This means that in the set of numbers provided, there is either a value of 12 or the word "twelve" that represents the middle value.

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

The lower quartile is the median of the lower half of the data set. To find it, we first arrange the data set in ascending order: 5, 5, 8, 10, 13, 13, 14, 18, 19, 19, 19, 24, 28. There are 13 numbers in total, so the lower half consists of the first 6 numbers. The median of this lower half is the average of the 3rd and 4th numbers, which are both 8. Therefore, the lower quartile is 8.

Explanation

The lower quartile is the median of the lower half of the data set. To find it, we first arrange the data set in ascending order: 5, 5, 8, 10, 13, 13, 14, 18, 19, 19, 19, 24, 28. There are 13 numbers in total, so the lower half consists of the first 6 numbers. The median of this lower half is the average of the 3rd and 4th numbers, which are both 8. Therefore, the lower quartile is 8.

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7.

What is the median?

The median is a measure of central tendency in statistics that represents the middle value of a set of numbers. In this case, the given set of numbers is "11" and "eleven." Since there are only two numbers in the set, the median is the average of these two values, which is 11.

Explanation

The median is a measure of central tendency in statistics that represents the middle value of a set of numbers. In this case, the given set of numbers is "11" and "eleven." Since there are only two numbers in the set, the median is the average of these two values, which is 11.

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8. What is the lower quartile for the data set6, 4, 4, 10, 8, 34, 12, 4, 19, 20, 20, 17, 31, 10, 2, 32, 16, 12

The lower quartile is a measure of central tendency that divides a dataset into four equal parts. To find the lower quartile, the data set needs to be arranged in ascending order. In this case, the data set is already provided in ascending order. The lower quartile is the median of the lower half of the data set. Since there are an odd number of data points (17 in total), the lower quartile will be the middle value of the lower half, which is 6.

Explanation

The lower quartile is a measure of central tendency that divides a dataset into four equal parts. To find the lower quartile, the data set needs to be arranged in ascending order. In this case, the data set is already provided in ascending order. The lower quartile is the median of the lower half of the data set. Since there are an odd number of data points (17 in total), the lower quartile will be the middle value of the lower half, which is 6.

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9. For the data set4, 4, 4, 6, 10, 13, 14, 18, 20, 24, 24, 28, 30, 31what is the median?

27

16

14

17

18

The median is the middle value in a data set when it is arranged in ascending order. In this case, the data set is already arranged in ascending order. Since there are 14 numbers in the data set, the middle value would be the 7th number. The 7th number in the data set is 14. Therefore, the correct answer is 14.

Explanation

The median is the middle value in a data set when it is arranged in ascending order. In this case, the data set is already arranged in ascending order. Since there are 14 numbers in the data set, the middle value would be the 7th number. The 7th number in the data set is 14. Therefore, the correct answer is 14.

10.

what is the range?

The range refers to the set of all possible values that a variable can take. In this case, the given options for the range are 45, fortyfive, forty five, and forty-five. These options represent different ways of expressing the same value, which is 45.

Explanation

The range refers to the set of all possible values that a variable can take. In this case, the given options for the range are 45, fortyfive, forty five, and forty-five. These options represent different ways of expressing the same value, which is 45.

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12. What is the upper quartile for the data set6, 4, 4, 10, 8, 34, 12, 4, 19, 20, 20, 17, 31, 10, 2, 32, 16, 12

20

8

12

34

10

The upper quartile is the median of the upper half of the data set. To find the upper quartile, we first need to arrange the data set in ascending order: 2, 4, 4, 4, 6, 8, 10, 10, 12, 12, 16, 17, 19, 20, 20, 31, 32, 34. Since there are 18 numbers in the data set, the median is the 9th number, which is 12. Therefore, the upper quartile is the median of the upper half of the data set, which is 20.

Explanation

The upper quartile is the median of the upper half of the data set. To find the upper quartile, we first need to arrange the data set in ascending order: 2, 4, 4, 4, 6, 8, 10, 10, 12, 12, 16, 17, 19, 20, 20, 31, 32, 34. Since there are 18 numbers in the data set, the median is the 9th number, which is 12. Therefore, the upper quartile is the median of the upper half of the data set, which is 20.

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14.

Which data set has the high median?

White

Grey

Both

Neither

The data set "white" has the high median.

Explanation

The data set "white" has the high median.

15. What is the median for the data set6, 4, 4, 10, 8, 34, 12, 4, 19, 20, 20, 17, 31, 10, 2, 32, 16, 12

12

17

4

20

18

The median is the middle value of a data set when it is arranged in ascending or descending order. In this case, when the data set is arranged in ascending order, we have 2, 4, 4, 4, 6, 8, 10, 10, 12, 12, 16, 17, 19, 20, 20, 31, 32, 34. Since there are 18 numbers in total, the middle value is the 9th number, which is 12. Therefore, the correct answer is 12.

Explanation

The median is the middle value of a data set when it is arranged in ascending or descending order. In this case, when the data set is arranged in ascending order, we have 2, 4, 4, 4, 6, 8, 10, 10, 12, 12, 16, 17, 19, 20, 20, 31, 32, 34. Since there are 18 numbers in total, the middle value is the 9th number, which is 12. Therefore, the correct answer is 12.

16.

What is the upper quartile?

9

6

12

30

19

The upper quartile is a measure of central tendency that divides a dataset into two halves, with the upper quartile representing the upper 25% of the data. In this case, the given numbers are arranged in ascending order: 6, 9, 12, 19, 30. The upper quartile is the value that separates the upper 25% of the data, which is 19.

Explanation

The upper quartile is a measure of central tendency that divides a dataset into two halves, with the upper quartile representing the upper 25% of the data. In this case, the given numbers are arranged in ascending order: 6, 9, 12, 19, 30. The upper quartile is the value that separates the upper 25% of the data, which is 19.

17.

what is the lower quartile?

7

5

11

23

19

The lower quartile is the median of the lower half of a data set. In this case, the data set is {7, 5, 11, 23, 19}. To find the lower quartile, we first arrange the numbers in ascending order: {5, 7, 11, 19, 23}. Since there are an odd number of values, the median is the middle value, which is 11. Therefore, the lower quartile is 11.

Explanation

The lower quartile is the median of the lower half of a data set. In this case, the data set is {7, 5, 11, 23, 19}. To find the lower quartile, we first arrange the numbers in ascending order: {5, 7, 11, 19, 23}. Since there are an odd number of values, the median is the middle value, which is 11. Therefore, the lower quartile is 11.