Random Sampling and Comparing Populations: math test solutions, Grade 7 – download the PDF

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Test solutions with the detailed point scale. Add up your points and spot what to review.

Suggested time: 45 minutes. Out of 20 points. Calculator allowed only when the problem says so.

Sommaire

a) The population is all 5,000 households in the town. (0.5 pt)

b) No. Shoppers at a garden store are more likely than other residents to have a garden, so the sample is biased. (1.5 pt)

c) Number the households and use a random number generator to choose households to survey; every household then has the same chance. (1 pt)

a) Sample proportion \(\dfrac{28}{80}=0.35\). Estimate: \(0.35\times 2400=840\) residents. (2 pt: 1 for the proportion, 1 for the estimate)

b) Sum 140, so the mean is \(\dfrac{140}{10}=14\) lb. Estimated total: \(14\times 2400=33,600\) lb per week. (2 pt: 1 for the mean, 1 for the total)

a) Sum 72, so the mean is \(\dfrac{72}{6}=12\). The middle values are 12 and 12, so the median is 12. (2 pt)

b) Distances: 4, 2, 0, 0, 2, 4, which add to 12. \(\text{MAD}=\dfrac{12}{6}=2\). (2 pt)

a) Median: \(\dfrac{21+23}{2}=22\). \(Q_1=\dfrac{17+18}{2}=17.5\). \(Q_3=\dfrac{26+28}{2}=27\). (2 pt)

b) Range: \(34-14=20\). IQR: \(27-17.5=9.5\). (1 pt)

c) Draw a box from 17.5 to 27 with a line at 22, and whiskers to 14 and to 34. (1 pt)

a) Class A: median 70, IQR \(78-62=16\). Class B: median 72, IQR \(80-68=12\). (1.5 pt)

b) Yes. The medians differ by only 2 points, much less than either IQR, and the middle halves of the data (62 to 78 and 68 to 80) overlap. (1.5 pt)

The sample proportion tagged is \(\dfrac{5}{40}=\dfrac{1}{8}\). (1 pt)

So the 25 tagged turtles are about \(\dfrac{1}{8}\) of the pond: \(25\times 8=200\) turtles. (1 pt)

Test yourself: quick challenge for Grade 7