5 9 10 9 17 Compute the sample standard deviation, CV and 65th percentile of the

Question

5 9 10 9 17 Compute the sample standard deviation, CV and 65th percentile of these data. B. Compute the Inter quartile range for these data. C. Develop a frequency distribution for these data using 4 classes each Make the lower limit of the first class 1. with a class width of 5. Determine the shape of these data using measures of central tendency. Sketch -- the diagram accordingly D. E. Develop a cumulative frequency histogram for the frequency distribution. F. Briefly explain key concepts of probability. V

Explanation / Answer

1)

S=(xi-x)^2/n-1

S=192.9/9

S=4.63

x=Ex/n=69/10=6.9

CV=S/X*100=4.63/6.9*100=67.1

2)

Q1=(n+1)/4=11/4=2.75th position and we get the value as 3.5

Q3=3(n+1)/4=8.25th position and we get the value as 9

IQR=9-3.5=5.5

3)

Data

Freq

1-5

5

6-10

4

11-15

0

16-20

1

4)

Data (xi)

Mean

6.9

Standard Error

1.46401275

Median

6

Mode

3

Standard Deviation

4.629614815

Sample Variance

21.43333333

Kurtosis

1.474851104

Skewness

1.037004874

Range

16

Minimum

1

Maximum

17

Sum

69

Count

10

As we can see that mean>median>mode and hence the data is right skewed.

Data (xi) (xi-x) (xi-x)^2 3 -66 4356 5 -64 4096 7 -62 3844 5 -64 4096 9 -60 3600 1 -68 4624 3 -66 4356 9 -60 3600 17 -52 2704 10 -59 3481 Sum Sum Sum 69 0 192.9

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