Question

Ten experts rated a newly developed chocolate chip cookie on a scale of 1 to 50. Their ratings were: 34, 35, 41, 28, 26, 29, 32, 36, 38, and 40. What is the mean deviation of the ratings?

Answer 1

The mean deviation of the ratings is  4.12

Explanation

The ratings of the ten experts are:  34, 35, 41, 28, 26, 29, 32, 36, 38 and 40

So, the mean of all ratings $=\frac{34+35+41+28+26+29+32+36+38+40}{10}= \frac{339}{10}=33.9$

The formula for Mean deviation $= \sum \frac{|x_{i}- \mu|}{N}$ , where $x_{i}$ is the given data from $i=1$ to $i=10$ , $\mu$ is the mean of the data and $N$ is the total number of data. So.....

$|x_{1}-\mu |= |34-33.9|=0.1\\ |x_{2}-\mu|=|35-33.9|=1.1\\ |x_{3}-\mu |=|41-33.9|=7.1\\ |x_{4}-\mu |=|28-33.9|=5.9\\ |x_{5}-\mu |=|26-33.9|=7.9\\ |x_{6}-\mu |=|29-33.9|=4.9\\|x_{7}-\mu |=|32-33.9|=1.9\\ |x_{8}-\mu |=|36-33.9|=2.1\\ |x_{9}-\mu |=|38-33.9|=4.1\\ |x_{10}-\mu |=|40-33.9|=6.1$

So, the Mean deviation $=\sum \frac{|x_{i}-\mu |}{N}=\frac{0.1+1.1+7.1+5.9+7.9+4.9+1.9+2.1+4.1+6.1}{10} = \frac{41.2}{10}=4.12$