Page 65 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 5: Application of Mean, Median and Mode

Calculation of Median in a Series of Individual Observations Notes
Example 5: Find the median of the following:

Marks obtained by 11 students 40 42 44 48 52 60 68 70 75 80 82

⎛ N1 ⎞ +
Solution: Median M= Size of ⎜ ⎟ th item.
⎝ 2 ⎠
N = 11.
+
⎛ 11 1 12 ⎞
⎟
∴ M = Size of ⎜ = = 6 th item.
⎝ 2 6 ⎠
The 6th item is 60.
∴ M = 60.
Answer: The median marks of the above data is 60.
Example 6: Find the value of median from the following:
Marks — 10, 9, 19, 21, 25, 32, 11.
Solution: The above data is first rearranged in the ascending order.
Marks — 9, 10, 11, 19, 21, 25, 32.
⎛ N1 ⎞ +
M= ⎜ ⎟ th item.
⎝ 2 ⎠

⎛ + 8 ⎞ 71
N= 7 ∴ M = ⎜ ⎝ = 2 ⎟ ⎠ 2 = 4th item.

∴ M = 19.
Answer: The median marks in the above data is 19.
Example 7: Compute median for the following:
X — 9, 19, 21, 6, 12, 18, 17, 20.
Solution: The data is first rearranged in ascending order:
6, 9, 12, 17, 18, 19, 20, 21
⎛ N1 ⎞ +
M= ⎜ ⎟ th item. N = 8.
⎝ 2 ⎠

⎛ + 9 ⎞ 81
∴ M= ⎜ = ⎟ = 4.5th item.
⎝ 2 ⎠ 2

Size of 4th item + Size of 5th item
∴ M=
2
4th item = 17, 5th item = 18.
17 + 18 35
M= = = 17.5
2 2
Answer: The median of the above data is 17.5.

LOVELY PROFESSIONAL UNIVERSITY 59