Question

The weight gain of beef steers were measured over a 140 day test period. the average daily gains (lb/day) of 10 steers on the same diet were as follows. The tenth steer had a weight gain of 4.02 lb/day.

3.89 3.51 3.97 3.31 3.21 3.36 3.67 3.24 3.27
determine the mean and median.

Answer 1

`\bar x = 3.545`

`Median = 3.435`

Explanation:

Given

`x:3.89, 3.51, 3.97, 3.31, 3.21, 3.36, 3.67, 3.24, 3.27`

`10th: 4.02`

Solving (a): The mean

This is calculated as:

`\bar x = (\sum x)/(n)`

So, we have:

`\bar x = (3.89 +3.51 +3.97 +3.31 +3.21 +3.36 +3.67 +3.24 +3.27+4.02)/(10)`

`\bar x = (35.45)/(10)`

`\bar x = 3.545`

Solving (b): The median

First, we sort the data; as follows:

`3.21, 3.24, 3.27, 3.31, 3.36, 3.51, 3.67, 3.89, 3.97, 4.02`

`n = 10`

So, the median position is:

`Median = (n + 1)/(2)th`

`Median = (10 + 1)/(2)th`

`Median = (11)/(2)th`

`Median = 5.5th`

This means that the median is the average of the 5th and 6th item

`Median = (3.36 + 3.51)/(2)`

`Median = (6.87)/(2)`

`Median = 3.435`