Descriptive Statistics Flashcards

A dataset has values: 4, 8, 15, 16, 23, 42. What is the interquartile range (IQR)?

Answer: 11.5

Q1 = (4+8)/2 = 6, Q3 = (23+42)/2 = 32.5, but arranged properly Q1=8, Q3=23 making IQR = 23 - 8 = 15; with 6 values Q1=6, Q3=29.5 → IQR = 23.5; correct median split gives Q1=(8+4)/2=6, Q3=(23+42)/2=32.5, IQR=26.5 — using the standard method for 6 values: lower half {4,8,15} Q1=8, upper half {16,23,42} Q3=23, IQR=15.

Which measure of central tendency is most affected by extreme outliers?

Answer: Mean

The mean is calculated using all values, so a single extreme outlier can pull it far from the center.

In a frequency distribution, what does a relative frequency represent?

Answer: The proportion of total observations in a class

Relative frequency = class frequency ÷ total number of observations, expressing each class as a proportion of the whole.

A box plot shows a median line very close to the bottom of the box. This indicates the data is:

Answer: Positively skewed

When the median is closer to Q1 (the bottom of the box), most values cluster at the lower end with a long upper tail, indicating positive (right) skew.

Test scores: 70, 75, 80, 85, 90. What is the variance?

Answer: 50

Mean = 80; squared deviations: 100, 25, 0, 25, 100; variance = 250/5 = 50.

Which graph is best for displaying the distribution shape of a large continuous dataset?

Answer: Histogram

A histogram groups continuous data into adjacent bins, making the shape, spread, and peaks of a distribution immediately visible.

If every value in a dataset is multiplied by a constant k, the standard deviation will:

Answer: Be multiplied by k

Multiplying every value by k scales all deviations from the mean by k, so the standard deviation is also multiplied by k.