Question

the two dot plots represent a sample of the number of people in households in two towns. which statements are true about the data sets? check all that apply. both have the same number of data points. both means are between 3 and 4. both have the same median. both have the same range. westwood has less variability than middleton.

Explanation:

Step1: Count the number of data points

Middleton: \(1 + 4+4 + 4+6+1=20\)
Westwood: \(1+4 + 5+5+5=20\)
So, both have the same number of data points.

Step2: Calculate the mean for Middleton

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Calculate the mean for Westwood

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So, the statement "Both means are between 3 and 4" is false.

Step3: Calculate the median for Middleton

Arrange the data: \(1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,10\)
The median (average of 10th and 11th terms) is \(\frac{4 + 4}{2}=4\)
Arrange the data for Westwood: \(2,3,3,3,3,4,4,4,4,4,5,5,5,5,5,6,6,6,6,6\)
The median (average of 10th and 11th terms) is \(\frac{4+5}{2} = 4.5\)
So, the statement "Both have the same median" is false.

Step4: Calculate the range for Middleton

Range \(=10 - 1=9\)
Calculate the range for Westwood
Range \(=6 - 2=4\)
So, the statement "Both have the same range" is false.

Step5: Analyze the variability

The spread of data (variability) can be seen from the range or the distribution. Since Westwood has a smaller range and the data is more clustered around the center compared to Middleton (which has an out - lier at 10), Westwood has less variability.

Answer:

Both have the same number of data points; Westwood has less variability than Middleton.