MEAN & MEDIAN OF UNGROUPED DATA AND FREQUENCY POLYGON
Arithmetic Mean –
The average of numbers in arithmetic is known as the Arithmetic Mean or simply the mean or average of these given numbers in statistics. So, the arithmetic mean in equation is described as –
Sum of Observation
Mean = -----------------------
Number Of Observation
Mean of Un-Grouped Data –
The mean of ‘n’ observations x₁, x₂, x₃,………………., xᵣ is given by
(x₁ + x₂ + x₃ + ............+ xᵣ) Ʃ xᵢ
Mean, x = ------------------------------ = ----------
r r
where the symbol Ʃ, called sigma stands for the summation of the terms.
There are some examples are given below for your better understanding -
Example.1) The heights of 10 boys in a group are 167 cm, 123 cm, 250 cm, 170 cm, 180 cm, 125 cm, 250 cm, 325 cm, 130 cm, 120 cm. find the mean height per boy.
Sum of The Height of The Boys
Ans.) Mean Height = ------------------------------
Number of Boys
(167 + 123 + 250 + 170 + 180 + 125 + 150 + 225 + 130 + 120) cm
= ----------------------------------------------------------
10
1640 cm
= ------------- = 164 cm
10
Hence the mean height is 164 cm (Ans.)
Example.2) Find the mean of the first eight multiple of 5
Ans.) As per the given condition, first eight multiple of 5 are 5, 10, 15, 20, 25, 30, 35, 40
5 + 10 + 15 + 20 + 25 + 30 + 35 + 40
So, the required mean = --------------------------------------
8
180
= ------- = 22.5
8
The required mean is 22.5 (Ans.)
Example.3) If the mean of 7, 9, 11, 13, x, 21 is 13. Find the value of x
7 + 9 + 11 + 13 + x + 21
Ans.) As per the given condition, 13 = -------------------------
6
Or, 78 = 61 + x
Or, x = 78 – 61 = 17
So, the required value of x is 17 (Ans.)
Example.4) If the mean of the six observation x, x + 2, x + 4, x + 6, x + 8, x + 10 is 12, find the value of x.
Ans.) As per the given condition –
Mean of the given observation ;
x + (x + 2) + (x + 4) + (x + 6) + (x + 8) + (x + 10)
----------------------------------------------- = 12
6
6x + 30
Or, ----------- = 12
6
Or, 6 (x + 5) = (12 X 6)
Or, x + 5 = 12
Or, x = 7
Hence, x = 6 (Ans.)