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Below is given frequency distribution of I.Q. (Intelligent Quotient) of 80 candidates. Find median I.Q. of candidates.

I.Q.
70 - 80
80 - 90
90 - 100
100 - 110
110 - 120
120 - 130
130 - 140
No. of Candidates
7
16
20
17
11
7
2

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100.5

98.5

94.5

None of these

answer is B.

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Detailed Solution

Given data,

I.Q.	70 - 80	80 - 90	90 - 100	100 - 110	110 - 120	120 - 130	130 - 140
No. of Candidates	7	16	20	17	11	7	2

There are total 80 candidates. Hence, the median will be the mean of 40th and 41st candidate. Both of which lie in the interval 90-100
The median of grouped data is given by:
Median=

L + (\frac{\frac{n}{2} - c f_{b}}{f_{m}}) \times w

where:
L is the lower class boundary of the group containing the median
n is the total number of data

c f_{b}

is the cumulative frequency of the groups before the median group

f_{m}

is the frequency of the median group
w is the group width
Hence,

\Rightarrow

Median =

90 + (\frac{\frac{80}{2} - 23}{20}) \times 10

\Rightarrow

Median =

90 + (\frac{17}{20}) \times 10

\Rightarrow

Median =

90 + 8.5

\Rightarrow

Median =

98.5

Thus, the median is 98.5.
Hence, the correct option is 2.

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Below is given frequency distribution of I.Q. (Intelligent Quotient) of 80 candidates. Find median I.Q. of candidates.I.Q.70 - 8080 - 9090 - 100100 - 110110 - 120120 - 130130 - 140No. of Candidates71620171172

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Below is given frequency distribution of I.Q. (Intelligent Quotient) of 80 candidates. Find median I.Q. of candidates.

I.Q.
70 - 80
80 - 90
90 - 100
100 - 110
110 - 120
120 - 130
130 - 140
No. of Candidates
7
16
20
17
11
7
2