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

1 Populations, samples, and bias / 3 pts

A town has 5,000 households. A city worker wants to know how many of them have a vegetable garden.

1. What is the population? (0.5 pt)
2. She stands outside a garden supply store and asks 60 shoppers. Is the sample likely to be representative? Explain. (1.5 pt)
3. Describe a better way to choose the sample. (1 pt)

2 Making inferences / 4 pts

The town has 2,400 residents. A random sample of 80 residents is asked about recycling, and 28 say they recycle every week. A second random sample of 10 residents recorded their weekly trash, in pounds: 12, 15, 14, 13, 16, 14, 15, 13, 14, 14.

1. Estimate how many residents recycle every week. (2 pt)
2. Find the mean weekly trash of the sample and use it to estimate the total weekly trash of all 2,400 residents. (2 pt)

3 Mean absolute deviation / 4 pts

Six students did these numbers of push-ups: 8, 10, 12, 12, 14, 16.

1. Find the mean and the median. (2 pt)
2. Find the mean absolute deviation. (2 pt)

4 Five-number summary / 4 pts

A lemonade stand had these numbers of customers over 12 days: 14, 15, 17, 18, 20, 21, 23, 25, 26, 28, 30, 34.

1. Find the median, \(Q_1\), and \(Q_3\). (2 pt)
2. Find the range and the IQR. (1 pt)
3. Say how you would draw the box plot. (1 pt)

5 Comparing two classes / 3 pts

The box plots show quiz scores for two classes.

1. Find the median and IQR of each class. (1.5 pt)
2. Do the two distributions overlap a lot? Justify. (1.5 pt)

6 Tagging turtles / 2 pts

A biologist tags 25 turtles in a pond and releases them. Later she captures a random sample of 40 turtles, and 5 are tagged. Estimate the number of turtles in the pond.