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

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?

Answer: 75

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

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

Answer: 49

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

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?

Answer: 10

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

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

Answer: Right-skewed

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

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

Answer: 1

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

A histogram shows a roughly uniform distribution of data. In this case, what is most likely true about the mean and median?

Answer: Mean ≈ Median

In a symmetric or uniform distribution, the mean and median are approximately equal.

The interquartile range (IQR) of a dataset is 12. A value is considered an outlier if it falls more than 1.5 × IQR below Q1. If Q1 = 20, below what value would a data point be an outlier?

Answer: 2

Lower fence = Q1 − 1.5 × IQR = 20 − 1.5(12) = 20 − 18 = 2; values below 2 are outliers.