Question

Following is the distribution of I.Q. of 100 students. Find the median I.Q.

I.Q.:	55−64	65−74	75−84	85−94	95−104	105−114	115−124	125−134	135-144
No. of students:	1	2	9	22	33	22	8	2	1

Answer 1

Here, the frequency table is given in inclusive form. Transforming the given table into exclusive form and prepare the cumulative frequency table.

IQ	Frequency(fi)	Cummulative Frequency(c.f.)
54.5−64.5	1	1
64.5−74.5	2	3
74.5−84.5	9	12
84.5−94.5	22	34
94.5−104.5	33	67
104.5−114.5	22	89
114.5−124.5	8	97
124.5−134.5	2	99
134.5−144.5	1	100
	N = 100

Here,

So,

Thus, the cumulative frequency just greater than 50 is 67 and the corresponding class is 94.5−104.5.

Therefore, 94.5−104.5 is the median class.

Here, l = 94.5, f = 33, F = 34 and h = 9

We know that,

$$\begin{gathered} =94.5+\left(\frac{50-34}{33}\right)\times 10 \\ =94.5+\frac{160}{33} \\ =94.5+4.85 \\ =99.35 \end{gathered}$$

Hence, the median is 99.35.