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?

Answer 1

The answers are:
1.4
1
0

Answer 2

Answer : The mean, median, and mode of the household pet data is, 1.4, 1 and 0 respectively.

Step-by-step explanation :

Mean : It is determine by adding all the numbers then divided by how many numbers there are.

$Mean=\frac{\text{Sum of outcomes}}{\text{Number of outcomes}}$

Median : It is the middle term that is sorted by the list of numbers. It is determine by placing the numbers in increasing order.

For odd observations the formula will be: $\frac{n+1}{2}$

For even observations:

First find the value at position $\frac{n}{2}$

Second find the value at position $\frac{n+1}{2}$

Then find that average of two values to get the median.

Mode : It is defined as the value that appears most in a set of data.

As we are given that the set of data:

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

First we have to placing the numbers in increasing order.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5

Now we have to determine the mean.

$Mean=\frac{\text{Sum of outcomes}}{\text{Number of outcomes}}$

Sum of outcomes = 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 = 56

$Mean=\frac{56}{40}=1.4$

The mean of the household pet data is, 1.4

Now we have to determine the median.

For even data:

$\frac{n}{2}$ and $\frac{n+1}{2}$

Here, n = 40

$\frac{40}{2}$ and $\frac{40+1}{2}$

20 and 20.5

The number of pets at 20th position and 21th position is, 1 and 1 respectively.

Then we have to take an average of two values.

$\frac{1+1}{2}=1$

The median of the household pet data is, 1

Now we have to determine the mode.

In the given set of data, 0 appears 15 times, 1 appears 10 times, 2 appears 6 times, 3 appears 4 times, 4 appears 3 times and 4 appears 2 times.

The value that appears most in a set of data is, 0

The mode of the household pet data is, 0