Question 1 Foundation
Find the mean of .
Answer.
The total is 50 and there are 5 values, so the mean is 10.
Describing Data
Original questions written at exam standard. Work each one before you open the solution.
Difficulty
Question 2 Foundation
Find the range of .
Answer.
. The range depends only on the two extreme values.
Question 3 Standard
Find the variance of .
Answer.
The mean is 5, and , so . The standard deviation is 2.
Question 4 Standard
The mean of a data set is greater than its median. What does this indicate?
Answer. Positive (right) skew
A long tail to the right pulls the mean above the median. Income data behaves this way.
Question 5 Stretch
Every value in a data set is multiplied by 3. What happens to the mean, the standard deviation and the variance?
Answer. Mean ×3, standard deviation ×3, variance ×9
Scaling multiplies the mean and the standard deviation by the same factor. Variance scales by the square of it.
Question 6 Stretch
For and , which values would be flagged as outliers?
Answer. Below 2 or above 50
IQR = 12, so the boundaries are and .