Question

The ages of a group of teachers are listed. 25, 32, 33, 35, 41, 43, 45, 48, 52, 55, 60, 62 If another teacher with an age of 45 is added to the data, how would the mean be impacted? The value of the mean would remain the same at about 41. The value of the mean would remain the same at about 44. The mean would increase in value to about 47. The mean would decrease in value to about 42.

Answer 1

B) The value of the mean would remain the same at about 44.

Explanation:

The mean is a measure of central tendency. It is calculated by summing up all the values in a dataset and dividing the sum by the number of values.

The mean age of the original group of 12 teachers can be calculated by summing the ages and dividing that sum by 12:

`\begin{aligned}\textsf{Mean}&=(25+32+33+35+41+43+45+48+52+55+60+62)/(12)\\\\&=(531)/(12)\\\\&=44.25\end{aligned}`

If another teacher with an age of 45 is added to the data, the total number of teacher is now 13. Therefore, the new mean is:

`\begin{aligned}\textsf{New mean}&=(25+32+33+35+41+43+45+48+52+55+60+62+45)/(13)\\\\&=(576)/(13)\\\\&=44.31\;(\sf 2\;d.p.)\end{aligned}`

Therefore, if another teacher with an age of 45 is added to the data, the value of the mean would remain the same at about 44.