5.28 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICSMeasures of Central Tendency and Measures of Dispersion
Solution :
Table : Calculation of Median
Marks f c.f
10–20 3 3
20–30 5 8
30–40 f 3 8 + f 3
40-–50 3 11 + f 3
50–60 1 12 + f 3
Here Median = 32.5 (given), so median class is (30–40).
Let f 3 be the missing frequency, N 2 =12 f 2 +^3 = 6 + f 3 /2 = m , c = 8, l 1 = 30 1 2 =40, fm = f 3From the formula, med. =^12 m^1
l l l
f
+ −
(m – c)We get, 32.5 = 30 + 3 34 0 30 6 f 8
f 2− + −
or, 2.5 = 3 310 f 2
f 2 −
or, 2.5 f 3 = 5 f 3 – 20 or f 3 =2.5^20 =8.Advantages of Median :
(i) The median, unlike the mean, is unaffected by the extreme values of the variable.
(ii) It is easy to calculate and simple to understand, particularly in a series of individual observations a
discrete series.
(iii) It is capable of further algebraic treatment. It is used in calculating mean deviation.
(iv) It can be located by inspection, after arranging the data in order of magnitude.
(v) Median can be calculated even if the items at the extreme are not known, but if we know the central
items and the total number of items.
(vi) It can be determined graphically.
Disadvantage of Median :
(i) For calculation, it is necessary to arrange the data; other averages do not need any such arrangement.
(ii) It is amenable to algebraic treatment in a limited sense, Median cannot be used to calculate the
combined median of two or more groups, like mean.
(iii) It cannot be computed precisely when it lies between two items.
(iv) Process involved to calculate median in case of continuous series is difficult to follow.
(v) Median is affected more by sampling fluctuations than the mean.
SELF EXAMINATION QESTIONS :- Define median, Mention merits and demerits of median.
- Find median of the following numbers :
(i) 38, 56, 31, 70, 41, 62, 53, 57 [Ans. 54.5]
(ii) 14, 15, 30, 40, 10, 25, 20, 35 [Ans. 22.5]
(iii) 25, 1275, 748, 162, 967, 162 [Ans. 455] - Of the numbers 78, 82, 36, 38, 50, 72, 68, 70, 64 find median. [Ans. 68]