AP Statistics 1.6 B Justify a Claim Using Distributions of Quantitative One Variable Graphical Representations Questions

Practise defending contextual claims from quantitative graphs by citing the relevant bars, intervals, frequencies and comparison that make the conclusion valid.

Exam points

identify a contextual pattern by comparing the relevant bars with neighbouring groups
convert mean ± standard deviation to a data interval, sum histogram counts and divide by the total

The following histograms summarize the teaching year for the teachers at two high schools, A and B.

High School A

High School B

Teaching year is recorded as an integer, with first-year teachers recorded as 1, second-year teachers recorded as 2, and so on. Both sets of data have a mean teaching year of 8.2, with data recorded from 200 teachers at High School A and 221 teachers at High School B. On the histograms, each interval represents possible integer values from the left endpoint up to but not including the right endpoint.

The standard deviation of the teaching year for the 221 teachers at High School B is 7.2. If one teacher is selected at random from High School B, what is the probability that the teaching year for the selected teacher will be within 1 standard deviation of the mean of 8.2 ? Justify your answer.

Part (c):
The interval mean plus or minus 1 standard deviation on either side of the mean is $8.2 \pm 7.2$ , or from 1.0 year to 15.4 years. Because teaching year is recorded as an integer, the interval includes teaching years 1 to 15. The number of teachers in that interval can be found by adding the heights of the five bars in the histogram for the intervals from 1 to 16, which includes 79+34+28+29+19=189. Therefore the probability is $\frac{189}{221} \approx 0.8552$ .

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AP Statistics 1.6 B Justify a Claim Using Distributions of Quantitative One Variable Graphical Representations Questions question 1