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1 vote
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.
1. What is the mean deviation of the ratings?
Select one:
a. 8.00
b. 4.12
c. 12.67
d. 0.75

2 Answers

6 votes

Answer:

b. 4.12

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}=(34+35+41+28+26+29+32+36+38+40)/(10)


\text{Mean of ratings}=(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}=(\Sigma |x-\mu|)/(N), where,


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


MD=(0.1+1.1+7.1+5.9+7.9+4.9+1.9+2.1+4.1+6.1)/(10)


MD=(41.2)/(10)


MD=4.12

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

User Gonjay
by
4.5k points
6 votes

Answer:

Option B.

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=(\sum x)/(n)


Mean=(34+35+41+28+26+29+32+36+38+40)/(10)


Mean=(339)/(10)


Mean=33.9

Formula for mean deviation is


\text{Mean deviation}=(\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}=(41.2)/(10)


\text{Mean deviation}=4.12

The mean deviation of the ratings is 4.12.

Therefore, the correct option is B.

User Hfrmobile
by
4.5k points