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# Stets on solving some questions on descriptive statistics

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1) Calculate arithmetic mean of:
a. Wages: 75, 100, 120, 150, 200 Total
b. Workers: 5, 12, 20, 14, 9 60

2) Calculate the median age:
a. Age Years (Less than): 10, 20, 30, 40, 50, 60, 70, 80
b. No. of persons: 4, 16, 40, 76, 96, 112, 120, 125

3) Calculate Spearman's Rank Correlation:
a. Trainees: A, B, C, D, E, F, G, H, I, J
b. X Rank: 1, 6, 3, 9, 5, 2, 7, 10, 8, 4
c. Y Rank: 6, 8, 3, 7, 2, 1, 5, 9, 4, 10

4) Calculate Standard Deviation:
a. Roll No: 101, 102, 103, 104, 105
b. Marks: 10, 30, 20, 25, 15

5) From a bag containing 3 yellow and 2 blue balls, 2 balls are picked randomly. Find probability that they are of the same colour?

6) Find the missing frequency from the following if Mean is 38
a. Marks: 10, 20, 30, 40, 50, 60, 70
b. No. of Students: 8, 11, 20, 25, ?, 10, 3

7) Calculate mode :
a. Central Value: 70, 90, 110, 130, 150
b. Frequency: 43, 78, 83, 125, 87

8) Find the coefficient of correlation for the data:
a. X: 11, 12, 18, 24, 23, 27
b. Y: 13, 18, 12, 25, 30, 10

9) Fit a Linear Trend Equation by the method of Least Squares:
a. Year: 2000, 2001, 2002, 2003, 2004, 2005, 2006
b. Net profit Rs. In crores: 32, 36, 44, 37, 71, 72, 109

##### Solution Summary

The solution gives detailed steps on solving some questions on descriptive statistics: regression line, mean, standard deviation, correlation coefficient, rank coefficient.

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Sample questions we need step by step solutions for.

1) Calculate arithmetic mean of:
a. Wages: 75, 100, 120, 150, 200 Total
b. Workers: 5, 12, 20, 14, 9 60
Mean=(75*5+100*12+120*20+150*14+200*9)/60=131.25

2) Calculate the median age:
a. Age Years (Less than): 10, 20, 30, 40, 50, 60, 70, 80
b. No. of persons: 4, 16, 40, 76, 96, 112, 120, 125
Median is the middle value of data. Now there are 4+16+40+76+96+112+120+125=589 persons. The middle value occurs at 589/2 which the average of 294 and 295. Look at original data, median=60 because both 294th and 295th values are of age 60.

3) Calculate Spearman's Rank Correlation:
a. Trainees: A, B, C, D, E, F, G, H, I, J
b. X Rank: 1, 6, 3, 9, 5, 2, 7, 10, 8, 4
c. Y Rank: 6, 8, 3, 7, 2, ...

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