Over a nine-month period, OutdoorGearLab tested hardshell jackets designed for ice climbing, mountaineering, and backpacking. Based on the breathability, durability, versatility, features, mobility, and weight of each jacket, an overall rating ranging from 0 (lowest) to 15 (highest) was assigned to each jacket tested. The following data show the results for 10 top-of-the line jackets (OutdoorGearLab website, February 27, 2013). Answer questions 10-14. Table 2. 5 12 6 8 5 6 7 5 12 4   1.The 75th percentile is __________.  2.Compute the first quartile. (Please show your calculation process.) 3.Interpret the first quartile that you calculate from question 14.

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Over a nine-month period, OutdoorGearLab tested hardshell jackets designed for ice climbing, mountaineering, and backpacking. Based on the breathability, durability, versatility, features, mobility, and weight of each jacket, an overall rating ranging from 0 (lowest) to 15 (highest) was assigned to each jacket tested. The following data show the results for 10 top-of-the line jackets (OutdoorGearLab website, February 27, 2013). Answer questions 10-14.

Table 2.

5

12

6

8

5

6

7

5

12

4

 

1.The 75th percentile is __________. 

2.Compute the first quartile. (Please show your calculation process.)

3.Interpret the first quartile that you calculate from question 14.

 

 

 

Expert Solution
Step 1

The given data is as follows.

5
12
6
8
5
6
7
5
12
4

The formula for the percentile rank is as follows.

r=p(n-1)100+1

n is the sample size.

If the r is an integer then ith percentile is at Xr

If the r=rf+rl is not an integer then ith percentile is 

p=Xrl+Xrf×(Xrl+1-Xrl)

The formula for the quartile is as follows.

The rank of ith quartile is

r=i(n+1)4 

If the rank is not an integer then the quartile is

Q=Xrl+Xrf×(Xrl+1-Xrl)

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