Question

the box - 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. Middleton has 25 data points and Westwood has 25 data points.

Step2: Calculate means

For Middleton: \((1\times1 + 2\times4+3\times6 + 4\times6+5\times4 + 6\times2+7\times1+9\times1)\div25=(1 + 8+18 + 24+20 + 12+7+9)\div25 = 109\div25 = 4.36\). For Westwood: \((1\times1+2\times3 + 3\times5+4\times7+5\times5+6\times3+7\times1)\div25=(1+6 + 15+28+25+18+7)\div25 = 100\div25 = 4\).

Step3: Find medians

Since \(n = 25\) (odd), for Middleton, arrange the data in ascending - order. The 13th value is 4. For Westwood, the 13th value is 4.

Step4: Calculate ranges

For Middleton, range \(=9 - 1=8\). For Westwood, range \(=7 - 1 = 6\).

Step5: Analyze variability

The spread of data in Westwood is less than in Middleton as the range of Westwood is smaller.

Answer:

A. Both have the same number of data points.
C. Both have the same median.
E. Westwood has less variability than Middleton.