the two dot plots represent a sample of the number of people in households in two towns. which statements…

Explanation:

Step1: Count data - points

Count the number of dots in each dot - plot. Middleton has 1 + 3+ 5+ 5+ 3+ 1+ 1=19 data - points. Westwood has 2+ 4+ 6+ 4+ 2 = 18 data - points. So, "Both have the same number of data points" is false.

Step2: Calculate means

For Middleton: $\sum_{i = 1}^{n}x_{i}f_{i}=1\times1 + 2\times3+3\times5 + 4\times5+5\times3+6\times1+10\times1=1 + 6+15 + 20+15+6 + 10=73$. Mean of Middleton is $\frac{73}{19}\approx3.84$. For Westwood: $\sum_{i = 1}^{n}x_{i}f_{i}=2\times2+3\times4 + 4\times6+5\times4+6\times2=4 + 12+24+20+12 = 72$. Mean of Westwood is $\frac{72}{18}=4$. Both means are between 3 and 4.

Step3: Find medians

For Middleton (19 data - points, odd number of data - points), the median is the 10th - ordered value. Arranging the data, the median is 4. For Westwood (18 data - points, even number of data - points), the median is the average of the 9th and 10th ordered values. Arranging the data, the median is 4. So, both have the same median.

Step4: Calculate ranges

Range = Maximum value - Minimum value. For Middleton, range = 10 - 1=9. For Westwood, range = 6 - 2 = 4. They do not have the same range.

Step5: Analyze variability

The spread of data in Westwood is from 2 to 6, while in Middleton it is from 1 to 10. Westwood has less variability.

Answer:

Both means are between 3 and 4, Both have the same median, Westwood has less variability than Middleton.