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 data - points

Count the number of dots in each dot - plot. In Middleton, there are 25 dots. In Westwood, there are 25 dots. So, both have the same number of data points.

Step2: Calculate means

For Middleton: $(1\times1 + 2\times3+3\times5 + 4\times7+5\times4+6\times3+7\times1+10\times1)\div25=(1 + 6+15 + 28+20+18+7+10)\div25 = 105\div25 = 4.2$. For Westwood: $(2\times1+3\times4 + 4\times6+5\times7+6\times4+7\times2+8\times1)\div25=(2 + 12+24+35+24+14+8)\div25 = 119\div25 = 4.76$. So, the means are not between 3 and 4.

Step3: Find medians

For Middleton (25 data points, median is 13 - th ordered value). Arranging in order, median is 4. For Westwood (25 data points, median is 13 - th ordered value), median is 5. So, they don't have the same median.

Step4: Calculate ranges

For Middleton, range = 10 - 1=9. For Westwood, range = 8 - 2 = 6. So, they don't have the same range.

Step5: Analyze variability

The data in Westwood is more clustered around the middle values compared to Middleton. So, Westwood has less variability than Middleton.

Answer:

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