Question

Mrs. Hall records the height of 50 students in a spreadsheet the mean height is 68 inches after looking at the data again she realize that two of the 50 observations were outliers that must have been typos 82 and 86 inches she deleted these two observations what is the new mean rounded to the nearest hundredth

Answer 1

the answer is 67.33. Multiply 68 by 50, subtract 82 and 86 from that, then divide by 48

Answer 2

The new mean rounded to the nearest hundredth is:

67.33

Explanation:

The mean height of 50 students is: 68 inches.

Let
`a_1,a_2,.....,a_(50)` be the height of 50 students.

Let us suppose that:

`a_(49)=82\ inches\\\\and\ a_(50)=86\ inches`

Hence, we have:

`(a_1+a_2+.....+a_(49)+a_(50))/(50)=68\\\\\\i.e.\\\\\\a_1+a_2+a_(49)+a_(50)=68* 50\\\\\\a_1+a_2+.....+82+86=3400\\\\\\a_1+a_2+...+a_(48)=3400-168\\\\\\a_1+a_2+....+a_(48)=3232\\\\\\Hence\ mean\ of\ 48\ students\ is:\\\\\\(a_1+a_2+a_3+....a_(48))/(48)=(3232)/(48)\\\\\\(a_1+a_2+a_3+....a_(48))/(48)=67.33`

Hence, after deleting the outlier the mean of the remaining students is:

67.33