Statistics Mathematics

1. Mean
Median
Mode

2. 2
Mean

3. What is Arithmetic Mean?
 The Arithmetic Mean is the average of the numbers a
calculated central value of a set of numbers. And add up all
the numbers, then divide by how many numbers there are.
3

4. Equation
 Direct Method 𝑥 =
𝑥ⅈ
𝑁
 Shortcut Method 𝑥 = 𝐴+
fⅈdⅈ
𝑁
× h
4

5. Example 5

6. Real Life Use
 In our class test exam result
 For result of any average equation
 Baseball game it use to find batman’s batting average
 Any kind of equation that use average there we use
mean
6

7. 7

8. WHAT IS GEOMETRIC MEAN ?
Geometric mean is defined as the N th positive root of the product of N
variables symbolically,
G.M. =
𝑁
𝑥1 ∗ 𝑥2 ∗ 𝑥3 … . 𝑥𝑁 = (𝑥1 ∗ 𝑥2 ∗ 𝑥3 ∗ ⋯ . 𝑥𝑁)
1
𝑁
Formula:
For ungrouped data:
G.M. = Antilog (
log 𝑥
𝑁
)
For grouped data:
G.M. = Antilog (
f log 𝑥
𝑁
)

9. EXAMPLE:

10. 10
Harmonic
Mean

11. What is Harmonic Mean? 11

12. Example of Ungrouped data:
Calculate the harmonic mean of the number 3,27,9.
Solution:
Total numbers = 3
Take reciprocal of the given number, = (1/3,1/27,1/9)
Now find total numbers/(sum of reciprocal)
= 3/(1/3+1/27+1/9)
= 3/((9+1+3)/27)
= 3*27/13
= 78/13
= 6
Therefore Result of the given data set is 6
12

13. Application of Harmonic Mean:
 Average speed
 Density
 Electricity
 In finance
 In geometry
 In other sciences
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14. Median

15. WHAT IS MEDIAN ?
The median is the middle value of a set of data.
Formula:
For ungrouped data:
If number of observation N is odd then
𝑁+1
2
th observation is median.
If number of observation N is even then the average of
𝑁
2
th and (
𝑁
2
+1) th
observation is median.
For grouped data:
Median = 𝐿 +
𝑁
2
− 𝑃.𝐶.𝐹
𝑓
∗ ℎ
Where,
L = Lower limit of median class.
N = Total frequency.
f = Frequency of median class.
P.C.F = Preceding cumulative frequency.
h = The size of interval.

16. EXAMPLE:

17. 17
Mode

18. WHAT IS
MODE
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19. FORMULA WITH
EXAMPLE
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20. APPLICATION
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21. Reference:
 https://en.wikipedia.org/wiki/Harmonic_mean
 https://www.researchgate.net/post/what_are_areas_of_application_of_Harmonic_Mean
 https://www.answers.com/Q/What_is_the_application_of_harmonic_mean
 https://www.investopedia.com/terms/h/harmonicaverage.asp
 https://www.tutorialspoint.com/statistics/harmonic_mean.htm
 https://en.wikipedia.org/wiki/Harmonic_mean#Examples
 https://www.quora.com/How-useful-is-the-harmonic-mean
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Thank You