Question

Roberta has collected a set of data and calculated the mean to be 34. The set contains 75 numbers, but Roberta gets an email telling her to add the following 5 numbers to her data: {23, 26, 32, 33, 40}

To the nearest tenth, what is the new mean for her data?


A) 27.8


B) 30.8


C) 33.8


D) 36.8

Answer 1

30.8 add it all up and divided how ever many number there are

Answer 2

C) New Mean = 33.8

Explanation:

Mean of collected set of data = 34

Total number of observations = 75

Mean =
`\frac{\text{Sum of all observation}}{\text{Number of observations}}`

Thus, we can calculate the sum of observations as : Mean × Total number of observations = 2550

5 new numbers were added to data: 23, 26, 32, 33, 40

New sum of observations = 2550 + 23 + 26 + 32 + 33 + 40 = 2704

New total number of observations = 75 + 5 = 80

New Mean =
`\frac{\text{New sum of all observation}}{\text{New number of observations}}` =
`(2704)/(80)` = 33.8

Thus, option C) 33.8 is the new mean.