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?

Answer 1

Remember how the mean is calculated:\[\frac{\text{sum of values}}{\text{number of values}}\]Therefore, you know that:\[\frac{\text{sum of values}}{\text{75}}=34\]Now you must add in 5 more values. Isolate the sum of values to left first:\[\text{sum of values} = (34)(75)=2550\]Now add in the new values and recalculate the mean:\[\frac{2550+23+26+32+33+40}{80}=?\]