FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 5.21- Places A, B and C are equidistant from each other. A person walks from A to B at 5 km.p.h.; from B to
C at 5 km.p.h. and from C to A at 4 km.p.h.. Determine his average speed for the entire trip.
[Ans.^4138 km.p.h. ] - A person covered a distance from X to Y at 20 km.p.h.. His average speed is 22 km.p.h.. Is the statement
correct? [Hints. Use H.M.] [Ans No.]
5.1.5. MEDIAN :
Definition
If a set of observation are arranged in order of magnitude (ascending or descending), then the middle
most or central value gives the median. Median divides the observations into two equal parts, in such a
way that the number of observations smaller than median is equal to the number greater than it. It is not
affected by extremely large or small observation. Median is, thus an average of position. In certain sense,
it is the real measure of central tendency.
So Median is the middlemost value of all the observations when they are arranged in ascending order of
magnitudes.
5.1.5.1. Calculation of Median :
(A) For simple data or Series of Individual Observations :
Individual observations are those observations (or variates) having no frequencies or frequency is unit
every case.
At first, the numbers are to arranged in order of magnitude (ascending or descending). Now for n (the total
number of items) odd.
Median = value of n 1 2 + th item
and for n even
Median = average value n 2 th item and
n 1
2
+
th item.or, median = value of n 1 2 + th item (n = odd or even)
[Note : n 1 2 + th item gives the location of median, but not its magnitude]
Steps to calculate Median
- Arrange the data in ascending or descending order. 2. Find n (odd or even). 3. Apply usual formula
and calculate.
Example 25 : To find the median of the following marks obtained by 7 students : 4, 12, 7, 9, 14, 17, 16.
(i) Arrangement of marks : 4, 7, 9, 12, 14, 16, 17.
(ii) n = 7 = an odd number
(iii) Median = value of n 1 2 + th item = value of 7 1 2 + th item = value of 4 th item = 12 (from the arranged
data
∴ median is 12 marks.
[Note : Unit of the result will be same as given in original variate.]