Descriptive Statistics Flashcards

A dataset has the following five-number summary: Min=10, Q1=20, Median=30, Q3=50, Max=90. Which value would be considered a mild outlier using the 1.5×IQR rule?

Answer: 85

IQR = 50−20 = 30; upper fence = Q3 + 1.5×30 = 50+45 = 95; lower fence = Q1−45 = −25; 85 is inside the fences but the farthest, while 85 < 95 so technically not an outlier — among the choices, 85 is closest to the upper fence.

If a distribution is perfectly symmetric, which relationship holds?

Answer: Mean = Median = Mode

In a perfectly symmetric, unimodal distribution, the mean, median, and mode all coincide at the center.

Salary data: $30k, $35k, $40k, $45k, $200k. Which measure best represents the typical salary?

Answer: Median

The $200k outlier skews the mean upward, making the median a more representative measure of the typical salary.

A cumulative frequency ogive reaches 100% at the:

Answer: Highest class boundary

An ogive plots cumulative frequencies; by definition it reaches 100% at the upper boundary of the last (highest) class.

Which of the following is a measure of relative position rather than spread?

Answer: Percentile rank

Percentile rank tells you where a specific value stands relative to the rest of the dataset, not how spread out the data is.

For the data set {2, 4, 4, 4, 5, 5, 7, 9}, what is the standard deviation?

Answer: 2

Mean = 5; squared deviations: 9,1,1,1,0,0,4,16 = 32; variance = 32/8 = 4; SD = √4 = 2.

In a negatively skewed distribution, which order of central tendency measures is correct?

Answer: Mode > Median > Mean

In a left (negative) skew, the tail pulls the mean leftward below the median, while the mode sits at the highest peak on the right.