Mean, Median, and Skewness Quiz

1. A dataset has values: 2, 4, 6, 8, 10. What is the median?

4

6

8

10

To find the median, first arrange the dataset in ascending order: 2, 4, 6, 8, 10. Since there are five values (an odd number), the median is the middle value, which is the third number in this ordered list. Thus, the median is 6.

Explanation

To find the median, first arrange the dataset in ascending order: 2, 4, 6, 8, 10. Since there are five values (an odd number), the median is the middle value, which is the third number in this ordered list. Thus, the median is 6.

2. Which measure of central tendency is most affected by extreme outliers?

Median

Mode

Mean

Range

The mean is the arithmetic average of a set of values and is calculated by summing all values and dividing by the count. Extreme outliers can significantly skew this average, making it unrepresentative of the data set. In contrast, the median and mode are less affected by such extremes.

Explanation

The mean is the arithmetic average of a set of values and is calculated by summing all values and dividing by the count. Extreme outliers can significantly skew this average, making it unrepresentative of the data set. In contrast, the median and mode are less affected by such extremes.

3. In a right-skewed distribution, how do the mean and median compare?

Mean equals median

Mean is greater than median

Median is greater than mean

Cannot be determined

In a right-skewed distribution, the tail on the right side pulls the mean upward, making it greater than the median. The median, being the middle value, remains less affected by extreme values, while the mean is influenced by them, resulting in the mean being higher than the median.

Explanation

In a right-skewed distribution, the tail on the right side pulls the mean upward, making it greater than the median. The median, being the middle value, remains less affected by extreme values, while the mean is influenced by them, resulting in the mean being higher than the median.

4. Calculate the mean of: 5, 10, 15, 20, 25.

12

15

18

20

To calculate the mean, add all the numbers together (5 + 10 + 15 + 20 + 25 = 75) and then divide by the total count of numbers (5). Thus, 75 divided by 5 equals 15, which represents the average value of the given set.

Explanation

To calculate the mean, add all the numbers together (5 + 10 + 15 + 20 + 25 = 75) and then divide by the total count of numbers (5). Thus, 75 divided by 5 equals 15, which represents the average value of the given set.

5. Which dataset has a median of 7? (A) 3, 5, 7, 9, 11 (B) 2, 4, 6, 8, 10 (C) 1, 5, 7, 8, 15

Dataset A only

Dataset B only

Datasets A and C

All three datasets

To find the median, the data sets must be ordered. For dataset A (3, 5, 7, 9, 11), the median is 7, as it is the middle value. For dataset C (1, 5, 7, 8, 15), the median is also 7. Dataset B has a median of 6, so it does not qualify.

Explanation

To find the median, the data sets must be ordered. For dataset A (3, 5, 7, 9, 11), the median is 7, as it is the middle value. For dataset C (1, 5, 7, 8, 15), the median is also 7. Dataset B has a median of 6, so it does not qualify.

6. A left-skewed distribution has a long tail on the left. How does the mean compare to the median?

Mean is greater

Mean is less

Mean equals median

Relationship is undefined

In a left-skewed distribution, the tail extends towards the lower values, pulling the mean downwards. Since the median is less affected by extreme values, it remains higher than the mean. Thus, in this type of distribution, the mean is typically less than the median.

Explanation

In a left-skewed distribution, the tail extends towards the lower values, pulling the mean downwards. Since the median is less affected by extreme values, it remains higher than the mean. Thus, in this type of distribution, the mean is typically less than the median.

7. Find the median of: 12, 8, 15, 3, 20, 18, 5.

8

12

15

18

To find the median, first arrange the numbers in ascending order: 3, 5, 8, 12, 15, 18, 20. Since there are seven numbers (an odd count), the median is the middle number, which is the fourth number in this ordered list. Thus, the median is 12.

Explanation

To find the median, first arrange the numbers in ascending order: 3, 5, 8, 12, 15, 18, 20. Since there are seven numbers (an odd count), the median is the middle number, which is the fourth number in this ordered list. Thus, the median is 12.

8. Why is the median preferred over the mean when analyzing income data with billionaires?

It is easier to calculate

It is unaffected by extreme values

It represents mode better

It always equals the mode

The median is preferred over the mean in income data analysis because it is not influenced by extreme values, such as the high incomes of billionaires. This makes the median a more accurate representation of the typical income within a dataset, providing a clearer understanding of income distribution without distortion from outliers.

Explanation

The median is preferred over the mean in income data analysis because it is not influenced by extreme values, such as the high incomes of billionaires. This makes the median a more accurate representation of the typical income within a dataset, providing a clearer understanding of income distribution without distortion from outliers.

9. A symmetric distribution has a skewness coefficient of ____.

A symmetric distribution is one where the left and right sides of the distribution are mirror images of each other. This symmetry results in a skewness coefficient of zero, indicating that the data is evenly distributed around the mean, with no tail extending more to one side than the other.

Explanation

A symmetric distribution is one where the left and right sides of the distribution are mirror images of each other. This symmetry results in a skewness coefficient of zero, indicating that the data is evenly distributed around the mean, with no tail extending more to one side than the other.

Submit

10. If a dataset has mean = 50 and median = 45, the distribution is likely ____ skewed.

When the mean is greater than the median, it indicates that the distribution has a longer tail on the right side. This occurs because higher values are pulling the mean up, while the median, being the middle value, remains lower. Hence, the distribution is likely right skewed.

Explanation

When the mean is greater than the median, it indicates that the distribution has a longer tail on the right side. This occurs because higher values are pulling the mean up, while the median, being the middle value, remains lower. Hence, the distribution is likely right skewed.

Submit

11. The ____ is the value that divides a dataset into two equal halves.

The median is a statistical measure that represents the middle value of a dataset when it is ordered from least to greatest. If the dataset has an odd number of values, the median is the middle number; if even, it is the average of the two middle numbers, effectively dividing the dataset into two equal halves.

Explanation

The median is a statistical measure that represents the middle value of a dataset when it is ordered from least to greatest. If the dataset has an odd number of values, the median is the middle number; if even, it is the average of the two middle numbers, effectively dividing the dataset into two equal halves.

Submit

12. In a perfectly symmetric distribution, mean, median, and mode are ____ to each other.

In a perfectly symmetric distribution, the values of mean, median, and mode coincide at the center of the distribution. This symmetry ensures that the data is evenly distributed around the central point, leading to all three measures of central tendency being the same, reflecting a balanced dataset.

Explanation

In a perfectly symmetric distribution, the values of mean, median, and mode coincide at the center of the distribution. This symmetry ensures that the data is evenly distributed around the central point, leading to all three measures of central tendency being the same, reflecting a balanced dataset.

Submit