Question

When the outliers are removed, how does the mean change? dot plot with 1 on 18, 2 on 38, 1 on 40, 3 on 44, 1 on 46, 1 on 48 The mean decreases by 2.75. The mean increases by 2.75. The mean increases by 3.25. There are no outliers.

Answer 1

Answer:

B. The mean increases by 2.75.

Step-by-step explanation:

We have been given that a dot plot has 1 dot on 18, 2 dots on 38, 1 dot on 40, 3 dots on 44, 1 dot on 46 and 1 dot on 48. We are asked to find how does the mean of given dot-plot will change,when the outliers are removed.

Upon using the given information we will get our data set as:

18, 38, 38, 40, 44, 44, 44, 46, 48.

Let us find mean of our given data set.  

$\text{Mean}=\frac{\text{ The sum of values of data points}}{\text{The total number of data points}}$

$\text{Mean of given data set}=\frac{18+38+38+40+44+44+44+46+48}{9}$

$\text{Mean of given data set}=\frac{360}{9}$

$\text{Mean of given data set}=40$

We can see that 18 is an outlier of given data set, so upon removing 18 from our data set total number of data points will be 8 and mean of new data set will be:

$\text{Mean of new data set}=\frac{38+38+40+44+44+44+46+48}{8}$

$\text{Mean of new data set}=\frac{342}{8}$

$\text{Mean of new data set}=42.75$  

We can see that mean of data set after removing outlier is 42.75, while the mean of data set including outlier was 40.

Since 42.75 is more than 40 by 2.75 points, therefore, after removing the outlier the mean increases by 2.75 and option B is the correct choice.