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

A dataset has values 5, 5, 5, 5, 5. What is the standard deviation of this dataset?

Answer: 0

When all values are identical, there is no spread from the mean, so the standard deviation is 0.

Which of the following datasets has the greatest range?

Answer: {5, 15, 25, 35, 100}

The range is max minus min: Set B has 100 − 5 = 95, which is larger than 40, 40, or 40 for the others.

The median of the dataset {3, 7, 9, 12, 15, x} is 10.5. What is the value of x?

Answer: 12

With 6 values sorted, the median is the average of the 3rd and 4th values: (9 + x) / 2 = 10.5 gives x = 12.

A dot plot shows quiz scores for 12 students. The scores cluster around 85 with one score of 20. If the outlier is removed, which of the following will change the most?

Answer: Mean

The mean is sensitive to outliers; removing the score of 20 will increase the mean substantially more than it shifts the median.

Dataset: {4, 6, 8, 10, 12}. Each value is multiplied by 3. What happens to the mean and standard deviation?

Answer: Mean triples; standard deviation triples

Multiplying every value by 3 scales both the mean and the standard deviation by a factor of 3.

A symmetric, bell-shaped distribution has a mean of 50 and a standard deviation of 5. Approximately what percentage of data falls between 40 and 60?

Answer: 95%

The values 40 and 60 are each 2 standard deviations from the mean, so approximately 95% of data falls in this range.

The five-number summary for a dataset is: Min=3, Q1=10, Median=18, Q3=26, Max=40. A value of 60 is added to the dataset. Which summary statistic is most affected?

Answer: Max

Adding 60 replaces the maximum with a new, larger value; all other summary statistics remain unchanged.