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

Answer:

(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.

Step-by-step explanation:

(a)

The mean is given as follows:

$\bar X=\frac{\sum f_{i}x_{i}}{\sum f_{i}}$

    $=\frac{5026}{100}\\\\=50.26$

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

(b)

Compute the standard deviation as follows:

$s=\frac{1}{\sum f_{i}-1}[\sum f_{i}x_{i}^{2}-\frac{1}{\sum f_{i}}(\sum f_{i}x_{i})^{2}]$

  $=\frac{1}{100-1}[254001-\frac{1}{100}(5026)^{2}]\\\\=\frac{1}{99}\times 1394.24\\\\=14.08323\\\\\approx 14.08$

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