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

A data set has 11 values. If the smallest value is removed, which of the following is most likely to change significantly?

Answer: Mean

Removing an extreme low value has a greater effect on the mean (which sums all values) than on the median or IQR, which depend on middle values.

A dataset has values 6, 8, 10, 12, 14. Each value is doubled. What happens to the standard deviation?

Answer: It is doubled.

Multiplying all values by a constant k multiplies the standard deviation by k; doubling all values doubles the standard deviation.

A dataset of 5 values has a mean of 10 and a range of 12. The minimum is 4. What is the maximum?

Answer: 16

Maximum = Minimum + Range = 4 + 12 = 16.

The dot plot shows daily high temperatures (°F) for 10 days: 72, 74, 74, 75, 76, 77, 77, 78, 80, 85. What is the interquartile range?

Answer: 4

Sorted: 72,74,74,75,76,77,77,78,80,85. Q1 = median of lower half {72,74,74,75,76} = 74; Q3 = median of upper half {77,77,78,80,85} = 78; IQR = 78 − 74 = 4.

A researcher reports that the median household income in a city is $52,000 while the mean is $78,000. Which explanation best accounts for this difference?

Answer: A small number of very high incomes pull the mean upward.

A few very wealthy households create extreme high values (outliers) that pull the mean up well above the median, which is unaffected by those extremes.

A data set is {4, 6, 8, 10, 12}. A value of 4 is replaced by 20. Which measures change?

Answer: Mean, range, and standard deviation

Replacing 4 with 20 changes the sum (affecting mean), extends the maximum (affecting range), and increases the spread (affecting standard deviation); the median remains 8.

Twelve students scored the following on a test: 60, 65, 70, 70, 72, 75, 78, 80, 82, 85, 90, 95. What is the median score?

Answer: 76.5

With 12 values, the median is the average of the 6th and 7th values: (75 + 78) ÷ 2 = 76.5.