Question

Ten experts rated a newly developed chocolate chip cookie on a scale of 1 to 50. Their ratings were:

Answer 1

Answer:

Option B.

Step-by-step explanation:

The given data set is

34, 35, 41, 28, 26, 29, 32, 36, 38, 40

We need to find the mean deviation of the given data.

Number of observations, n = 10

Mean of the data is

$Mean=\dfrac{\sum x}{n}$

$Mean=\dfrac{34+35+41+28+26+29+32+36+38+40}{10}$

$Mean=\dfrac{339}{10}$

$Mean=33.9$

Formula for mean deviation is

$\text{Mean deviation}=\dfrac{\sum |x-mean|}{n}$

$\sum |x-mean|=|34-33.9|+|35-33.9|+|41-33.9|+|28-33.9|+|26-33.9|+|29-33.9|+ |32-33.9|+|36-33.9|+|38-33.9|+|40-33.9|=41.2$

$\text{Mean deviation}=\dfrac{41.2}{10}$

$\text{Mean deviation}=4.12$

The mean deviation of the ratings is 4.12.

Therefore, the correct option is B.

Answer 2

Answer:

b. 4.12

Step-by-step explanation:

We have been given that 10 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.

First of all, we will find the mean of the ratings.

$\text{Mean of ratings}=\frac{34+35+41+28+26+29+32+36+38+40}{10}$

$\text{Mean of ratings}=\frac{339}{10}$

$\text{Mean of ratings}=33.9$

Let us find absolute deviation of each point from mean.

$|34-33.9|=0.1$

$|35-33.9|=1.1$

$|41-33.9|=7.1$

$|28-33.9|=5.9$

$|26-33.9|=7.9$

$|29-33.9|=4.9$

$|32-33.9|=1.9$

$|36-33.9|=2.1$

$|38-33.9|=4.1$

$|40-33.9|=6.1$

Now we will use mean deviation formula.

$\text{Absolute mean deviation}=\frac{\Sigma |x-\mu|}{N}$, where,

$\mu=\text{Mean}$ and N = Number of data points.

$MD=\frac{0.1+1.1+7.1+5.9+7.9+4.9+1.9+2.1+4.1+6.1}{10}$

$MD=\frac{41.2}{10}$

$MD=4.12$

Therefore, the mean deviation of the ratings is 4.12 and option 'b' is the correct choice.