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

Answer:

$\bar x = 3.545$

$Median = 3.435$

Step-by-step 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:

$\bar x = \frac{\sum x}{n}$

So, we have:

$\bar x = \frac{3.89 +3.51 +3.97 +3.31 +3.21 +3.36 +3.67 +3.24 +3.27+4.02}{10}$

$\bar x = \frac{35.45}{10}$

$\bar x = 3.545$

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:

$Median = \frac{n + 1}{2}th$

$Median = \frac{10 + 1}{2}th$

$Median = \frac{11}{2}th$

$Median = 5.5th$

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

$Median = \frac{3.36 + 3.51}{2}$

$Median = \frac{6.87}{2}$

$Median = 3.435$