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. For Middleton, there are 25 dots. For Westwood, there are 25 dots. So, "Both have the same number of data points" is true.

Step2: Calculate means

For Middleton:
\[

$$\begin{align*} \text{Sum}&=(1\times1)+(2\times3)+(3\times5)+(4\times7)+(5\times5)+(6\times3)+(7\times1)+(10\times1)\\ &=1 + 6+15 + 28+25+18+7+10\\ &=100 \end{align*}$$

\]
Mean of Middleton $=\frac{100}{25}=4$.
For Westwood:
\[

$$\begin{align*} \text{Sum}&=(2\times1)+(3\times3)+(4\times5)+(5\times7)+(6\times5)+(7\times3)+(8\times1)\\ &=2+9 + 20+35+30+21+8\\ &=125 \end{align*}$$

\]
Mean of Westwood $=\frac{125}{25}=5$. So, "Both means are between 3 and 4" is false.

Step3: Find medians

Since there are 25 data - points (an odd number), the median is the 13th ordered value.
For Middleton: Arranging the data in ascending order, the 13th value is 4.
For Westwood: Arranging the data in ascending order, the 13th value is 5. So, "Both have the same median" is false.

Step4: Calculate ranges

Range = Maximum value - Minimum value.
For Middleton: Range $=10 - 1=9$.
For Westwood: Range $=8 - 2=6$. So, "Both have the same range" is false.

Step5: Analyze variability

The spread of data in Westwood is from 2 to 8, while in Middleton it is from 1 to 10. The data in Westwood is more clustered around the middle values, so Westwood has less variability than Middleton. So, "Westwood has less variability than Middleton" is true.

Answer:

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