a group of 10 students was asked how many hours they slept the night before. below are their responses: 0…

a group of 10 students was asked how many hours they slept the night before. below are their responses: 0, 7.5, 7.5, 8, 8.5, 8.5, 9, 9, 9, 9. what is the mean? what is the median? there is a low outlier in the list. if you remove the outlier, what are the revised mean and median? mean (without the outlier) (round to 2 decimal places.) median (without the outlier) which changed more by removing the outlier? mean median

a group of 10 students was asked how many hours they slept the night before. below are their responses: 0, 7.5, 7.5, 8, 8.5, 8.5, 9, 9, 9, 9. what is the mean? what is the median? there is a low outlier in the list. if you remove the outlier, what are the revised mean and median? mean (without the outlier) (round to 2 decimal places.) median (without the outlier) which changed more by removing the outlier? mean median

Answer

Explanation:

Step1: Calculate the original mean

The data set is (0, 7.5, 7.5, 8, 8.5, 8.5, 9, 9, 9, 9). The sum of the data is (0 + 7.5+7.5 + 8+8.5+8.5+9+9+9+9=76). The number of data - points (n = 10). The mean (\bar{x}=\frac{76}{10}=7.6).

Step2: Calculate the original median

Since (n = 10) (an even - numbered data set), the median is the average of the (\frac{n}{2})th and ((\frac{n}{2}+1))th ordered values. The (\frac{10}{2}=5)th and ((\frac{10}{2}+1) = 6)th values are (8.5) and (8.5). So the median (M=\frac{8.5 + 8.5}{2}=8.5).

Step3: Identify the outlier and recalculate mean and median

The outlier is (0). After removing the outlier, the new data set has (n=9) data - points: (7.5, 7.5, 8, 8.5, 8.5, 9, 9, 9, 9). The sum of the new data set is (7.5+7.5 + 8+8.5+8.5+9+9+9+9=76 - 0=76). The new mean (\bar{x}_{new}=\frac{76}{9}\approx8.44). Since (n = 9) (an odd - numbered data set), the median is the (\frac{n + 1}{2}=\frac{9+1}{2}=5)th ordered value, which is (8.5).

Step4: Determine which is changed more

The change in the mean is (|7.6-8.44| = 0.84). The change in the median is (|8.5 - 8.5|=0). So the mean is changed more by removing the outlier.

Answer:

What is the mean? 7.6 What is the median? 8.5 What are the revised mean and median (without the outlier)? Mean: 8.44, Median: 8.5 Which changed more by removing the outlier? mean