# Summation Notation, Percentile and Proportion

Please show your work. I am having trouble working out the problems. I would like as detailed an explaination for the answers as you can give.

1. A teacher gives a 20-point quiz to 10 students. The scores are listed below. What percentile corresponds to the score of 12?

20 8 10 7 15 16 12 19 14 9

A. 13

B. 40

C. 25

D. 12

My answer...

1) The ten values, in order, are:

7, 8, 9, 10, 12, 14, 15, 16, 19, 20

The value 12 is the fifth value:

5/10 = 0.5 = 50%

But this does not match any of the listed answer values,

2) A data set contains the observations 3, 6, 7, 2, 8. Find Σx 2 -Σx 25 .

A. 129.6

B. 297.2

C. 540.8

D. 26.8

I have no idea how to get this

3)Merchants are always interested in determining why a customer selected their store to make a purchase. Best Sportswear Boutique conducted a customer survey to determine why its customers shopped at the store. The results are shown in the figure. What proportion of customers responded that merchandise was the reason they shopped at the store?

A.27

B.37

C. 12

D. 30

**See number 30 on the picture enclosed**

My answer....

20 + 30 + 10 + 10 = 70 interviewed

30 chose "merchandise"

30/70 = 3/7 = 0.4285714286....

This does not match any of the listed options. Please help.

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#### Solution Preview

For #1:

Since there are 4 scores below 12, the percentile is: 4/10 x 100 = 40.

The answer is B.

For #2:

I think the problem is more of a typographical error. If the case is Σx^25, then the answers would have all been negative ...

#### Solution Summary

This posting contains the solution and step by step procedures on how the answers are obtained.