The owner of two fast-food restaurants has recorded customer satisfaction rating

Question

The owner of two fast-food restaurants has recorded customer satisfaction ratings for both locations on a scale of 1 to 5

(5equals=Most

satisfied). The table linked below summarizes the data.

a. Calculate the mean satisfaction rating at each location.

b. Calculate the standard deviation of each distribution.

c. What conclusions can be drawn from these results?

Number of Customers

Rating

Restaurant A

Restaurant B

1

6

14

2

11

16

3

9

15

4

39

14

5

15

11

Number of Customers

Rating

Restaurant A

Restaurant B

1

6

14

2

11

16

3

9

15

4

39

14

5

15

11

Explanation / Answer

RESTAURENT A
a.
Mean of following data,
Mean =(sum set of N numbers)/N
Mean = ( 6+11+9+39+15)/5 = 16
b.
standard deviation of following data
6,11,9,39,15
Step 1:Add them up:
6+11+9+39+15=80

Step 2: Square your answer:
80*80=6400
divide by number of items
6400/5=1280
Set this number aside for a moment.

Step 3: Take your set of original numbers from Step 1, and square them individually this time:
6^2+11^2+9^2+39^2+15^2=1984

Step 4: Subtract the amount in Step 2 from the amount in Step 3.
6400-1984=4416
Set this number aside for a moment.

Step 5: Subtract 1 from the number of items in your data set. For our example:
5-1=4

Step 6: Divide the number in Step 4 by the number in Step 5. This gives you the variance:
4416/4=1104
How to find the sample variance and standard deviation: Standard Deviation

Step 7: Take the square root of your answer from Step 6. This gives you the standard deviation:

squar root of 1104= 33.2264
RESTAURENT B
a.
Mean of following data,
Mean =(sum set of N numbers)/N
Mean = (14+16+15+14+11)/5 = 14

b.
standard deviation of following data,
14,16,15,14,11
Step 1:Add them up:
14+16+15+14+11=70

Step 2: Square your answer:
70*70=4900
divide by number of items
4900/5=980
Set this number aside for a moment.

Step 3: Take your set of original numbers from Step 1, and square them individually this time:
14^2+16^2+15^2+14^2+11^2=994

Step 4: Subtract the amount in Step 2 from the amount in Step 3.
4900-994=3906
Set this number aside for a moment.

Step 5: Subtract 1 from the number of items in your data set. For our example:
5-1=4

Step 6: Divide the number in Step 4 by the number in Step 5. This gives you the variance:
3906/4=976.5
How to find the sample variance and standard deviation: Standard Deviation

Step 7: Take the square root of your answer from Step 6. This gives you the standard deviation:

squar root of 976.5= 31.2489

c.
CONCLUSIONS:
bOTH Mean,Standard deviation RESTAURENT A is more than the RESTAURENT B

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