Question

For ten school days, the numbers of bikes parked at a school bike rack are 10, 12, 8, 11, 13, 9, 2, 1, 9, and 12. a. What is the mean number of bikes per day b. Identify two outliers for the data. Describe how the outliers affect the mean.

Answer 1

The number of bikes parked for 10 school days are given below as

`10,12,8,11,13,9,2,1,9,12`

Step 1:

Calculate the mean:

To calculate the mean of the set of data, we will add up all the values of the data and then divide by the number of data given

`mean=\frac{sumofnumbers}{number\text{ of data}}`

By substituting the values, we will have

`\begin{gathered} mean=\frac{sumofnumbers}{number\text{ofdata}} \\ mean=(10+12+8+11+13+9+2+1+9+12)/(10) \\ mean=(87)/(10) \\ mean=8.7 \end{gathered}`

Hence,

The mean number of bikes per day is 8.7

Step 2:

Identify two outliers for the data. Describe how the outliers affect the mean.

An outlier is an extreme value in a data set that is either much larger or much smaller than all the other values.

Hence,

In the set of values given below, the outliers are 1 and 2

To calculate the mean without the outliers

`\begin{gathered} mean=(10+12+8+11+13+9+9+12)/(8) \\ mean=(84)/(8) \\ mean=10.5 \end{gathered}`

The mean without the outliers is higher than the mean with the outliers

Hence,

The outliers (decreases the mean) so that the mean is a bit too low to be a representative measure of this student's typical performance. This makes sense because when we calculate the mean, we first add the scores together, then divide by the number of scores. Every score therefore affects the mean.