One-Variable Data: Distributions and Measures of Center and Spread Flashcards

A dataset of 6 values has a mean of 10 and a median of 9. If the largest value is removed, which is most likely?

Answer: Mean decreases; median stays the same or decreases slightly

The largest value is likely above the mean, so removing it decreases the mean; the median, based on middle values, may shift only slightly.

The standard deviation of {3, 6, 9, 12, 15} compared to {30, 60, 90, 120, 150} is:

Answer: 10 times smaller for the first dataset

The second dataset is the first multiplied by 10, so its standard deviation is 10 times larger; equivalently, the first has a standard deviation 10 times smaller.

A data set is: 14, 14, 16, 17, 19, 21, 22, 23, 25, 30. What is the IQR?

Answer: 7

Lower half {14,14,16,17,19} has median 16 (Q1); upper half {21,22,23,25,30} has median 23 (Q3); IQR = 23 − 16 = 7.

A researcher collects income data from a neighborhood. She finds the mean income is $90,000 but the median is $55,000. A newcomer with an income of $1,000,000 moves in. This would most likely:

Answer: Increase the mean substantially but barely affect the median

The million-dollar income is an extreme outlier that dramatically raises the mean, while the median—resistant to extremes—barely moves.

A symmetric distribution has mean 50. The values 45, 50, and 55 each appear equally often. This distribution has standard deviation closest to:

Answer: 5

The values are all within 5 units of the mean of 50, so the standard deviation is approximately 5 (the average deviation from the mean).

A histogram shows customer wait times in minutes: most customers wait 3–5 minutes, but a few wait over 20 minutes. The distribution is right-skewed. Which statement is correct?

Answer: The mean is greater than the median

The long right tail (customers waiting 20+ minutes) pulls the mean above the median in a right-skewed distribution.

The scores on a 10-point quiz for 5 students are: 6, 7, 8, 9, and x. If the mean is 8, what is x?

Answer: 10

Sum = 8 × 5 = 40; 6 + 7 + 8 + 9 + x = 40; 30 + x = 40; x = 10.