Question

forty people were randomly sampled and surveyed as to the number of pets in their household. the results are listed below.
1 1 0 4 1 0 1 2
3 5 2 0 2 0 3 1
2 0 0 1 0 4 0 0
3 1 0 0 2 1 0 0
4 0 1 3 5 0 2 1
what is the mean, median, and mode of the household pet data?
a. 1.4, 2, 1 c. 1.5, 1, 0
b. 1.5, 2, 1 d. 1.4, 1, 0
please select the best answer from the choices provided

Explanation:

Step1: Calculate the mean

First, find the sum of all data values.
Count the number of \(0\)s: \(14\) times, \(1\)s: \(11\) times, \(2\)s: \(6\) times, \(3\)s: \(4\) times, \(4\)s: \(3\) times, \(5\)s: \(2\) times.
Sum \(S=(0\times14)+(1\times11)+(2\times6)+(3\times4)+(4\times3)+(5\times2)=11 + 12+12 + 12+10=57\).
The number of data points \(n = 40\).
Mean \(\bar{x}=\frac{S}{n}=\frac{57}{40}=1.425\approx1.4\).

Step2: Calculate the median

Arrange the data in ascending order (already \(0\)s, \(1\)s, etc. as counted).
Since \(n = 40\) (even), the median is the average of the \(\frac{n}{2}=20^{th}\) and \((\frac{n}{2}+1)=21^{st}\) values.
Counting the cumulative frequencies: \(14\) (for \(0\)) then \(14 + 11=25\) (for \(1\)). So the \(20^{th}\) and \(21^{st}\) values are \(1\).
Median \(M=\frac{1 + 1}{2}=1\).

Step3: Calculate the mode

The mode is the value that appears most frequently.
The value \(0\) appears \(14\) times, which is more frequent than other values.

Answer:

d. \(1.4,1,0\)