solutions for math problems

1. Probability and Statistics
Module 1

2. Measures of Central Tendency
Problems
Mean
Median
Geometric Mean
Mode
Harmonic Mean

3. 3
MEAN
11:02:00 AM
 Statistics is a study on collection of data.
 Mean, Median and mode are called Measures of Central Tendency
 Mean = X/n
 Mean =

4. 4
Median
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 Median : Middle value of the collection
 Find the cumulative frequency
 Find N/2 = f / 2
 See the cumulative the frequency just greater than N/2
 Corresponding value of x is the median class
 Apply the formula
 Median = L + [(N/2 – c)/f]*h
 L – Lower limit of the median class
 f- frequency of the median class
 c- cumulative frequency of the preceding to median class
 h- width of the class interval

5. 5
Mode
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 Mode : is the value which present most frequently in a set of
observations
 Mode =
 Maximum frequency is the modal class
 f_1 is the frequency of the modal class
 f_0 is the frequency of the class preceding the modal class
 f_2 is the frequency of the class succeeding the modal class

6. Problems

7. Problems

8. Problems

9. Problems

10. Problems

11. Problems

12. Problems

13. Problems

14. Problems

15. Problems

16. Problems

17. Problems

18. Problems

19. 19
Geometric Mean
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 It is the nth root of the product in N given items denoted by
g =
log g = + )
log g = )
g = antilog( ))

20. 20
Harmonic Median
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 It is the reciprocal of the arithmetic mean of the reciprocal of the
given items
HM =

21. 21
Problems
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22. 22
Problem
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23. Thank you