Question

a survey of 20 middleton residents was done to determine the number of people in each household. the numerical frequencies are shown in the dot plot. what is the outlier of this distribution? what is the mean of this data set? what is the range of this data set?

Explanation:

Step1: Identify the outlier

An outlier is a data - point that is far from other data - points. From the dot - plot, the value 9 is far from the cluster of data points which are mostly between 1 and 6. So the outlier is 9.

Step2: Calculate the sum of the data set

Count the number of dots at each value: 1 dot at 1, 3 dots at 2, 4 dots at 3, 4 dots at 4, 3 dots at 5, 2 dots at 6, 1 dot at 9. The sum is \(1\times1 + 3\times2+4\times3 + 4\times4+3\times5+2\times6+1\times9=1 + 6+12 + 16+15+12+9 = 71\).

Step3: Calculate the mean

The mean \(\bar{x}=\frac{\text{Sum of data points}}{\text{Number of data points}}\). There are 20 data points. So \(\bar{x}=\frac{71}{20}=3.55\).

Step4: Calculate the range

The range is the difference between the maximum and minimum values. The maximum value is 9 and the minimum value is 1. So the range is \(9 - 1=8\).

Answer:

Outlier: 9
Mean: 3.55
Range: 8