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

A dataset contains the values 8, 11, 14, 14, 17, 20, 23. What is the mean of this dataset?

Answer: 15.3

8+11+14+14+17+20+23 = 107; mean = 107 ÷ 7 ≈ 15.3.

A dataset of 8 values has a mean of 16. If every value in the dataset is increased by 4, what is the new mean?

Answer: 20

Adding a constant k to every value increases the mean by k, so the new mean is 16 + 4 = 20.

The data values 3, 5, 7, 9, 11, 13, and 15 form an arithmetic sequence. What is the relationship between the mean and the median of this dataset?

Answer: The mean and median are equal.

In a symmetric distribution such as an arithmetic sequence, the mean and median are always equal; both equal 9 here.

A dataset of 10 test scores has a mean of 80. One score of 40 is removed. What is the new mean of the remaining 9 scores?

Answer: 84.4

Total sum = 80 × 10 = 800; after removing 40, the new sum = 760; new mean = 760 ÷ 9 ≈ 84.4.

Which of the following describes a dataset where the median is a more appropriate measure of center than the mean?

Answer: A dataset with a few extremely large values that skew the distribution

The median is preferred when outliers are present because it is resistant to extreme values, unlike the mean which is pulled toward them.

The five-number summary of a dataset is: Min = 4, Q1 = 12, Median = 19, Q3 = 28, Max = 50. What is the range?

Answer: 46

Range = Max − Min = 50 − 4 = 46.

A teacher records quiz scores for 6 students: 72, 75, 80, 80, 85, 88. What is the mode?

Answer: 80

The mode is the value that appears most frequently; 80 appears twice while all other values appear once.