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

A student's test scores are 78, 82, 91, 85, and 79. What score must the student earn on the 6th test to achieve a mean of exactly 85?

Answer: 95

Required total = 85 × 6 = 510; current sum = 78+82+91+85+79 = 415; needed score = 510 − 415 = 95.

A box plot has the following five-number summary: Min = 2, Q1 = 10, Median = 16, Q3 = 22, Max = 30. In which interval is approximately 25% of the data?

Answer: 2 to 10

Each quartile region (Min to Q1, Q1 to median, median to Q3, Q3 to max) contains approximately 25% of the data.

Dataset X has values {1, 3, 5, 7, 9} and Dataset Y has values {0, 0, 5, 10, 10}. Which statement about the means and standard deviations is correct?

Answer: The means are equal; Dataset Y has a greater standard deviation.

Both datasets have mean = 5; Dataset Y has values farther from the mean (0 and 10 vs. 1 and 9), so Dataset Y has the greater standard deviation.

The values in a dataset are tripled. What happens to the median and range?

Answer: Both the median and range are tripled.

Multiplying all values by 3 scales all measures proportionally — both the median and range are multiplied by 3.

A teacher drops the lowest score before calculating a student's average. A student scores 55, 70, 80, 85, and 90. What is the student's average after the lowest score is dropped?

Answer: 81.25

Dropping 55 leaves {70, 80, 85, 90}; mean = (70+80+85+90)/4 = 325/4 = 81.25.

The values in a dataset increase uniformly. A dot plot shows values at 10, 20, 30, 40, 50. If 30 is added a second time to the dataset, which measure of center changes?

Answer: Neither mean nor median

With the original dataset, mean = 30 and median = 30. Adding a second 30 gives {10,20,30,30,40,50}: new mean = 180/6 = 30, new median = (30+30)/2 = 30. Both remain 30, so neither changes.

A professor grades 5 papers with scores 68, 72, 75, 81, and 94. Which score, if changed to 100, would produce the largest increase in the mean?

Answer: 68

Replacing the smallest value (68) with 100 increases the total sum the most (by 32), producing the greatest increase in mean.