Mean and Median: Central Tendency Quiz

1. What is the mean of the dataset: 8, 12, 15, 10, 5?

10

12

15

8

To find the mean, sum all the numbers in the dataset: 8 + 12 + 15 + 10 + 5 = 50. Then, divide the total by the number of values, which is 5. Thus, 50 ÷ 5 = 10, making 10 the mean of the dataset.

Explanation

To find the mean, sum all the numbers in the dataset: 8 + 12 + 15 + 10 + 5 = 50. Then, divide the total by the number of values, which is 5. Thus, 50 ÷ 5 = 10, making 10 the mean of the dataset.

2. Find the median of: 22, 18, 25, 20, 19.

18

20

22

25

To find the median, first arrange the numbers in ascending order: 18, 19, 20, 22, 25. Since there is an odd number of values (5), the median is the middle number, which is the third value in this ordered list. Thus, the median is 20.

Explanation

To find the median, first arrange the numbers in ascending order: 18, 19, 20, 22, 25. Since there is an odd number of values (5), the median is the middle number, which is the third value in this ordered list. Thus, the median is 20.

3. A dataset has values: 3, 7, 9, 11, 15. The mean is ____.

To find the mean, add all the values together: 3 + 7 + 9 + 11 + 15 = 45. Then, divide the sum by the number of values (5): 45 ÷ 5 = 9. Thus, the mean of the dataset is 9.

Explanation

To find the mean, add all the values together: 3 + 7 + 9 + 11 + 15 = 45. Then, divide the sum by the number of values (5): 45 ÷ 5 = 9. Thus, the mean of the dataset is 9.

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4. Which measure of central tendency is resistant to outliers?

Mean

Median

Mode

Range

The median is the middle value in a data set when arranged in order. Unlike the mean, which can be significantly affected by extreme values (outliers), the median remains stable because it only depends on the position of numbers, making it a more reliable measure of central tendency in skewed distributions.

Explanation

The median is the middle value in a data set when arranged in order. Unlike the mean, which can be significantly affected by extreme values (outliers), the median remains stable because it only depends on the position of numbers, making it a more reliable measure of central tendency in skewed distributions.

5. Dataset: 5, 6, 8, 10, 12. The median is ____.

To find the median, first arrange the dataset in ascending order: 5, 6, 8, 10, 12. The median is the middle value in a sorted list. With five numbers, the third number is the median, which is 8. Thus, the median of this dataset is 8.

Explanation

To find the median, first arrange the dataset in ascending order: 5, 6, 8, 10, 12. The median is the middle value in a sorted list. With five numbers, the third number is the median, which is 8. Thus, the median of this dataset is 8.

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6. If five students scored 70, 75, 80, 85, 90, what is the mean score?

75

80

82

85

To calculate the mean score, add all the scores together: 70 + 75 + 80 + 85 + 90 = 400. Then, divide the total by the number of students: 400 ÷ 5 = 80. Thus, the mean score of the five students is 80.

Explanation

To calculate the mean score, add all the scores together: 70 + 75 + 80 + 85 + 90 = 400. Then, divide the total by the number of students: 400 ÷ 5 = 80. Thus, the mean score of the five students is 80.

7. How many values are below the median in a dataset with 9 values?

3

4

5

6

In a dataset with 9 values, the median is the 5th value when arranged in order. Therefore, there are 4 values below the median, which are the first four values in the ordered list. This is because half of the values will be below and half will be above the median in an odd-numbered dataset.

Explanation

In a dataset with 9 values, the median is the 5th value when arranged in order. Therefore, there are 4 values below the median, which are the first four values in the ordered list. This is because half of the values will be below and half will be above the median in an odd-numbered dataset.

8. Dataset: 12, 14, 18, 22, 28. The mean is ____.

To find the mean of the dataset, sum all the values: 12 + 14 + 18 + 22 + 28 = 94. Then, divide the total by the number of values (5): 94 ÷ 5 = 18.8. Thus, the mean of the dataset is 18.8.

Explanation

To find the mean of the dataset, sum all the values: 12 + 14 + 18 + 22 + 28 = 94. Then, divide the total by the number of values (5): 94 ÷ 5 = 18.8. Thus, the mean of the dataset is 18.8.

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9. True or False: The mean is always equal to the median.

True

False

The mean is not always equal to the median, as they represent different measures of central tendency. The mean can be influenced by extreme values (outliers), while the median is the middle value in a sorted dataset. In skewed distributions, these two measures can differ significantly, making the statement false.

Explanation

The mean is not always equal to the median, as they represent different measures of central tendency. The mean can be influenced by extreme values (outliers), while the median is the middle value in a sorted dataset. In skewed distributions, these two measures can differ significantly, making the statement false.

10. For dataset 4, 6, 6, 8, 10, the median is ____.

To find the median, first arrange the dataset in ascending order: 4, 6, 6, 8, 10. The median is the middle value of a sorted list. Since there are five numbers, the median is the third number, which is 6.

Explanation

To find the median, first arrange the dataset in ascending order: 4, 6, 6, 8, 10. The median is the middle value of a sorted list. Since there are five numbers, the median is the third number, which is 6.

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11. A teacher recorded test scores: 60, 65, 70, 75, 100. Which is most affected by the outlier 100?

Median

Mean

Mode

Both median and mean equally

The mean is significantly influenced by extreme values, such as the outlier of 100 in this set of test scores. When calculating the mean, this high score raises the average considerably compared to the other scores. In contrast, the median and mode remain less affected by outliers, making the mean the most impacted statistic in this case.

Explanation

The mean is significantly influenced by extreme values, such as the outlier of 100 in this set of test scores. When calculating the mean, this high score raises the average considerably compared to the other scores. In contrast, the median and mode remain less affected by outliers, making the mean the most impacted statistic in this case.

12. If the mean of four numbers is 25, what is their sum?

25

50

100

6.25

To find the sum of four numbers when their mean is 25, you multiply the mean by the number of values. Since there are four numbers, the calculation is 25 (mean) × 4 (numbers) = 100. Thus, the sum of the four numbers is 100.

Explanation

To find the sum of four numbers when their mean is 25, you multiply the mean by the number of values. Since there are four numbers, the calculation is 25 (mean) × 4 (numbers) = 100. Thus, the sum of the four numbers is 100.