Question

Median

A group of students took a spelling test. After evaluation, the teacher

announced that " on an average" each of the five students’ mis-

spelled 18 words. Shown at the right is the actual number of words

mis-spelled by each student.

Is 18 the mean of these scores? (Yes). How many mis-spelled at least

18 words? (One). Does 18 satisfactorily represent the five scores? (No)

The five scores are arranged in order. Which score has the same

number of scores above it as below it? (10) Is 10 a more satisfactory

representative score? (Yes) Why or Why not? (Ans: It is more

representative of all of the scores than 18.

Why 10?

If a set of data contains a few very high scores or very low scores, the

mean does not satisfactorily represent the data. In situations such as

these it is often more desirable to use the middle score, called the

median, as the representative score.

The median of a set of numbers is the middle number when all the

numbers are arranged in order of size, i.e., in descending or

ascending order.

Student Number of words mis-spelled

Sunil 50

Manish 15

Ashok 10

Subodh 9

Rekha 6DATA HANDLING

13

To find the median for a set of numbers, arrange them in order of size

and select the middle number. If there is no middle number, that is

when the number of numbers in the data is even, then the mean of

the two middle scores is the median.

Ex. 1 : What is median weekly salary of workers in a firm whose salaries

are ₹84, ₹60, ₹50, ₹40, ₹45, ₹42, ₹38, ₹65, ₹71?

Sol:

1. First arrange data in ascending order:

₹38, ₹40, ₹42, ₹45, ₹50, ₹60, ₹38, ₹65, ₹71, ₹84

2. Next, count the number of salaries. It is 9. The fifth salary (₹50) has

four salaries which are less than it and four salaries above it.

Therefore ₹50 is the middle or median salary

Ex. 2 : Find the median salary of following salaries of workers:

₹56, ₹89, ₹121, ₹38, ₹98, ₹70, ₹70, ₹72

Sol: Arrange the salaries in ascending order:

₹38, ₹56, ₹70, ₹70, ₹72, ₹89, ₹98, ₹121

Count the number of salaries. It is 8.

Find the salary which has the same number of salaries above and

below it. In this case there is no single such salary so, median will be

mean of the fourth and fifth salary.

Median =

72+70

2 =

142

2 = ₹71 Ans.

Try and learn

Find median of the following

(a)2, 3, 5, 7, 9, 5

(b)4, 8, 12, 16, 20, 24, 28, 32, 18

(c)60, 33, 63, 61, 44, 48, 51, 61

(d)13, 22, 25, 8, 11, 19, 17, 31, 16, 10, 16.5
the last 4 lines are my questions and rest is for your help​

Answer 1

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Answer 2

Answer:

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