AP Statistics Mean, Median, Standard Deviation and Outliers Test Solutions and Scoring (PDF)

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

Cover of the book AP Statistics Math Tests with Answer Keys (PDF)

Download as a PDFThe AP Statistics tests book with answer keysPrintable PDFSee the book ›

Sommaire

This summary statistics test answers 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.

Each solution is followed by a scoring guide. Give credit for a correct method even when an arithmetic slip changes the final number, and require a context sentence where one is requested.

AP Statistics · Common Core State Standards: AP STAT 1.6, AP STAT 1.7, HSS-ID.A.2, HSS-ID.A.3

Summary statistics test answers: worked solutions

Question 1 – Mean and median [3 pts]

Visits per month.

(a) Sum 48, $\frac{48}{10}=4.8$.

(b) 4 and 4, so median 4.

4.8; 4; mean larger.

Scoring: 1 point per part.

Question 2 – Five-number summary [2 pts]

Median 16; lower half 11, 13, 14 so $Q_1=13$; upper half 18, 19, 22 so $Q_3=19$.

11, 13, 16, 19, 22; IQR 6.

Scoring: 1 point for the five numbers, 1 point for IQR 6.

Question 3 – Standard deviation [3 pts]

Mean 5. Deviations: -3, -1, 1, 3. Squares: 9, 1, 1, 9 = 20.

$s=\sqrt{\frac{20}{3}}\approx 2.58$.

2.58.

Scoring: 1 point for the mean, 1 point for the sum of squares 20, 1 point for 2.58.

Question 4 – Outlier rule [3 pts]

Fences and the outlier.

$Q_1=33.5$, $Q_3=40$, $IQR=6.5$. Upper fence: $40+1.5(6.5)=49.75$.

80 is above the upper fence 49.75, so it is an outlier.

Scoring: 1 point for the quartiles, 1 point for the fence, 1 point for the conclusion.

Question 5 – Resistance [2 pts]

The mean includes every value, so it increases greatly. The median depends on the middle position only.

The mean increases; the median does not (if 70 was above the median).

Scoring: 1 point for naming the mean, 1 point for the reason.

Question 6 – Linear transformation [2 pts]

Mean: $66\times 2.54=167.64$. Standard deviation: $3\times 2.54=7.62$.

167.64 cm and 7.62 cm.

Scoring: 1 point for each.

Question 7 – Interpret the standard deviation [2 pts]

The standard deviation is the typical distance of a wait from the mean.

Wait times typically differ from the mean of 8 minutes by about 2.5 minutes.

Scoring: 1 point for typical distance, 1 point for context (8 minutes, waits).

Question 8 – Choose the summary [3 pts]

(a) Mean: $\frac{2825000}{5}=565000$. Median: $240,000.

(b) The median, because the $1,900,000 home skews the mean.

Mean $565,000; median $240,000; use the median.

Scoring: 1 point each for mean and median; 1 point for median with the outlier reason.

Total score

Total

20 points

Key facts behind this summary statistics test answers

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 answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All AP Statistics chapters: AP Statistics math.

Voter.. post

Free printable PDF