Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 6

Question 1

The test scores for 11 students, listed in order, are: 60, 63, 67, 70, 72, 75, 78, 80, 84, 88, 92. What is the median score?

Accepted Answer

75

Answer

With 11 values, the median is the 6th value in the ordered list, which is 75.

Question 2

In a symmetric distribution, the mean is 40 and the standard deviation is 6. What value is 1.5 standard deviations above the mean?

Accepted Answer

49

Answer

1.5 standard deviations above the mean: 40 + 1.5(6) = 40 + 9 = 49.

Question 3

A dot plot shows these values: 3, 3, 4, 4, 4, 5, 5, 6, 6, 10. Which value is an outlier that most distorts the mean?

Accepted Answer

10

Answer

The value 10 is much larger than the rest of the data (which clusters between 3 and 6) and pulls the mean upward.

Question 4

A dataset of salaries has a mean of $65,000 and a median of $55,000. This suggests the distribution is:

Accepted Answer

Right-skewed

Answer

When mean > median, high-value outliers pull the mean upward, indicating right skew.

Question 5

For the dataset {2, 4, 4, 4, 5, 5, 7, 9}, what is the difference between the mean and the mode?

Accepted Answer

1

Answer

Mean = (2+4+4+4+5+5+7+9)/8 = 40/8 = 5; Mode = 4 (appears 3 times); Difference = 5 − 4 = 1.

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