AP Statistics Mean, Median, Standard Deviation and Outliers Test with Point Values (PDF)

AP Statistics math test: Mean, Median, Standard Deviation and Outliers – Maths PDF

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This summary statistics test for AP Statistics covers mean, median, standard deviation and outliers (Common Core AP STAT 1.6, AP STAT 1.7, HSS-ID.A.2, HSS-ID.A.3), with a free PDF to print.

This 45-minute test covers measures of center and spread, resistance, the 1.5 IQR rule, and linear transformations. Show your work and state each conclusion in context.

Time and points

About this test

Grade: AP Statistics
Chapter: Mean, Median, Standard Deviation and Outliers
Standards: AP STAT 1.6, AP STAT 1.7, HSS-ID.A.2, HSS-ID.A.3
Time: 45 minutes
Total: 20 points

Summary statistics test: questions

Question 1 – Mean and median [3 pts]

Visits per month.

(a) Find the mean. (1 point) (b) Find the median. (1 point) (c) Which is larger and why? (1 point)

Question 2 – Five-number summary [2 pts]

Number of pages read.

Find the five-number summary and IQR for 11, 13, 14, 16, 18, 19, 22.

Question 3 – Standard deviation [3 pts]

Four values.

Find the standard deviation of 2, 4, 6, 8 to two decimal places. (3 points)

Question 4 – Outlier rule [3 pts]

Fences for the data.

Use the 1.5 IQR rule to decide whether 80 is an outlier in 31, 33, 34, 35, 36, 38, 39, 41, 80. (3 points)

Question 5 – Resistance [2 pts]

A data set has mean 52 and median 51. The largest value 70 is replaced by 700. Which of the mean and median changes? Explain.

Question 6 – Linear transformation [2 pts]

Heights in inches have mean 66 and standard deviation 3. Find the mean and standard deviation in centimeters (1 inch = 2.54 cm).

Question 7 – Interpret the standard deviation [2 pts]

The mean wait for a bus is 8 minutes with standard deviation 2.5 minutes. Interpret the standard deviation in context.

Question 8 – Choose the summary [3 pts]

House prices in a neighborhood are $210,000, $225,000, $240,000, $250,000, and $1,900,000. (a) Find the mean and median. (2 points) (b) Which should a realtor report to describe a typical home and why? (1 point)

Key facts behind this summary statistics test

Key facts

Mean = sum divided by n; median = middle of the ordered list.
Skewed right: mean > median; skewed left: mean < median; symmetric: about equal.
s = sqrt( sum of squared deviations / (n – 1) ); IQR = Q3 – Q1.
1.5 IQR rule: outliers lie below Q1 – 1.5 IQR or above Q3 + 1.5 IQR.
Adding c shifts center but not spread; multiplying by k scales both by |k|.

How to use this summary statistics test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All AP Statistics chapters: AP Statistics math.

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