Free UTMA Descriptive Statistics Questions and Answers

Question 1

What is the mean of the following data set: 5, 8, 12, 15, 20?

Accepted Answer

12

Answer

The mean of a data set is calculated by summing all the values and then dividing by the total number of values. For the data set 5, 8, 12, 15, 20, the sum is 5 + 8 + 12 + 15 + 20 = 60. Since there are 5 values, the mean is 60 / 5 = 12.

Question 2

What is the median of the following data set: 3, 7, 9, 14, 21?

Accepted Answer

9

Answer

The median is the middle value in a data set when the values are arranged in order. For the given data set 3, 7, 9, 14, 21, the numbers are already in ascending order. With five values, the middle value is the third one, which is 9.

Question 3

What is the mode of the following data set: 4, 4, 6, 8, 9, 9, 9, 10?

Accepted Answer

9

Answer

The mode of a data set is the value that appears most frequently. In the given data set (4, 4, 6, 8, 9, 9, 9, 10), the number 9 appears three times, which is more than any other number. Therefore, the mode is 9.

Question 4

Which measure of central tendency is most appropriate to use for a skewed data distribution?

Accepted Answer

Median

Answer

For a skewed data distribution, the median is the most appropriate measure of central tendency. Unlike the mean, which can be significantly pulled by extreme values or the skew, the median represents the true middle value and is more robust to outliers.

Question 5

What is the standard deviation of the following data set: 2, 4, 4, 4, 5, 5, 7, 9?

Accepted Answer

2

Answer

To find the standard deviation, first calculate the mean of the data set (2, 4, 4, 4, 5, 5, 7, 9), which is (2+4+4+4+5+5+7+9)/8 = 40/8 = 5. Then, calculate the variance by averaging the squared differences from the mean: ((2-5)^2 + 3*(4-5)^2 + 2*(5-5)^2 + (7-5)^2 + (9-5)^2)/8 = (9 + 3 + 0 + 4 + 16)/8 = 32/8 = 4. The standard deviation is the square root of the variance, which is sqrt(4) = 2.

UTMA - University of Toronto Math Assessment Practice Test

UTMA - University of Toronto Math Assessment Practice Test

Free UTMA Descriptive Statistics Questions and Answers