Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 13

Question 1

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?

Accepted Answer

95

Answer

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

Question 2

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?

Accepted Answer

2 to 10

Answer

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

Question 3

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?

Accepted Answer

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

Answer

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.

Question 4

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

Accepted Answer

Both the median and range are tripled.

Answer

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

Question 5

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?

Accepted Answer

81.25

Answer

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

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 13