1. What is the median of this data set? 2. Assume that you test a sample and det

Question

1. What is the median of this data set?

2. Assume that you test a sample and determine that its Rockwell B hardness is 58. What percentile does this correspond to?

3. Calculate the 1st Quartile.

4. Calculate the 3rd Quartile.

5. What is the Inter Quartile Range?

6. What is the Xmin in your data?

7. What is the Xmax in your data?

8. Is there any outliers in your data collection? If so, what value(s) is the outlier? (enter 0 if there is none)

A materials science engineer would like to determine the hardness of an aluminum alloy. (S)he performed a series of hardness testing and collected the Rockwell B hardness of that particular alloy. The data from his/her experiments are given below: 58, 57, 70, 57, 53, 64, 50, 57, 56, 69, 66, 52, 54, 85, 66, 64 Use this information and answer Question 1 Question 8.

Explanation / Answer

above sret can be written by putting into ascendfing order as follows

1)median =(n+1)/2 th value =8.5 th value =(57+58)/2 =57.5

2)as 58 is 9th value

hence percentile correspods to it =(9/(n+!))*100 =52.94 percentile

3)1st quartile =(n+1)/4 th value 4.25 th value =54+0.25*(56-54)=54.5

4)3rd quartile =(n+1)*3/4 th value =12.75 th value =66

5)IQR=Q3-Q1 =66-54.5=11.5

6)Xmin=50

7)Xmax=85

8) for lower fence =Q1-1.5*IQR =54.5-1.5*11.5 =37.25

upper fence =Q3+1.5*IQR =66+1.5*11.5=83.25

as 85 falls outside fence range it is outlier

S. No X 1 50 2 52 3 53 4 54 5 56 6 57 7 57 8 57 9 58 10 64 11 64 12 66 13 66 14 69 15 70 16 85

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