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

A class of 30 students has a mean exam score of 80. A second class of 20 students has a mean score of 70. What is the combined mean for all 50 students?

Answer: 76

Combined mean = (30×80 + 20×70) ÷ 50 = (2400 + 1400) ÷ 50 = 3800 ÷ 50 = 76.

The data values 1, 4, 9, 16, 25 represent perfect squares. The mean is 11. Which value is farthest from the mean?

Answer: 25

Distances from mean 11: |1−11|=10, |4−11|=7, |9−11|=2, |16−11|=5, |25−11|=14; the value 25 is farthest.

A data set has a mean of 50 and a standard deviation of 8. A data point has a value of 66. How many standard deviations above the mean is this value?

Answer: 2

Z-score = (66 − 50) ÷ 8 = 16 ÷ 8 = 2 standard deviations above the mean.

A dot plot shows the number of hours 9 students practiced guitar each week: 1, 2, 3, 3, 4, 5, 5, 6, 7. If the outlier 1 is removed, which of the following changes?

Answer: The range decreases, and the mean increases.

Removing the minimum (1) decreases the range from 6 to 5, and removing a below-mean value increases the mean.

A bimodal distribution has two peaks at 20 and 60 with a valley in between. Which statement best describes the mean?

Answer: The mean is approximately 40, between the two peaks.

If both peaks are roughly symmetric and equal in size, the mean falls in the middle of the two peaks, approximately at 40.

The values in a dataset have a mean of 30. If 5 is subtracted from each value and then all values are multiplied by 2, what is the new mean?

Answer: 50

First, subtracting 5 changes mean to 30 − 5 = 25; then multiplying by 2 gives 25 × 2 = 50.

A dataset: 10, 20, 30, 40, 50. The mean and median are both 30. A value of 100 is added. Which statement is true about the updated measures?

Answer: The mean increases more than the median.

New mean = (10+20+30+40+50+100)/6 = 250/6 ≈ 41.7 (increase of ~11.7); new median = (30+40)/2 = 35 (increase of 5); mean increases more.