Question

The mouse weights​ (in grams) of a random sample of 100 mice involved in a nutrition experiment​ are: Interval 41.5----43.5 43.5-----45.5 45.5------47.5 47.5--------49.5 49.5--------51.5 51.5----53.5 53.5----55.5 55.5---- 57.5 57.5--------59.5 Frequency Interval 3 7 13 24 15 16 13 7 2Required:a. Find the mean of the weight of the mice. (Round to two decimal places.)b. Find the standard deviation of the weight of the mice. (Round to two decimal places.)

Answer 1

(a) The mean of the weight of the mice is 50.26 grams.

(b) The standard deviation of the weight of the mice is 14.08 grams.

Explanation:

(a)

The mean is given as follows:

`\bar X=(\sum f_(i)x_(i))/(\sum f_(i))`

`=(5026)/(100)\\\\=50.26`

Thus, the mean of the weight of the mice is 50.26 grams.

(b)

Compute the standard deviation as follows:

`s=(1)/(\sum f_(i)-1)[\sum f_(i)x_(i)^(2)-(1)/(\sum f_(i))(\sum f_(i)x_(i))^(2)]`

`=(1)/(100-1)[254001-(1)/(100)(5026)^(2)]\\\\=(1)/(99)* 1394.24\\\\=14.08323\\\\\approx 14.08`

Thus, the standard deviation of the weight of the mice is 14.08 grams.