If the median I Q of the students is 135, find the missing frequencies f1 and f2 in the following - Maths - Statistics

Question

If the median I Q of the students is 135, find the missing
frequencies f1 and f2 in the following frequency distribution for
220 students:

I Q 100-110 110-120 120-130 130-140 140-150 150-160 160-170
170-180
Number of students 15 35 f1 f2 33 23 19 8

Manbar Singh · Accepted Answer

CLASS INTERVALS
FREQUENCY
CUMULATIVE FREQUENCY

100-110
15
15

110-120
35
50

120-130
f1

50+f1â€‹

130-140
f2

50+f1â€‹+f2

140-150
33

83+f1â€‹+f2

150-160
23

106+f1â€‹+f2

160-170
19

125+f1â€‹+f2

170-180
8

133+f1â€‹+f2

N=133+f1â€‹+f2

Now, N = 220⇒133 + f1 + f2 = 220⇒ f1 + f2 = 87   
1Now, median is 135
So, median class = 130-140lower limit of median class, l = 130cumulative frequency of class preceeding median class, F = 50+f1frequency of median class, f = f2class size, h = 10Median = l + N2-Ff×h⇒135 = 130 + 110-50-f1f2×10⇒2f1 + f2 = 120     
2Subtracting 1 from 2, we getf1 = 33Now, from 1, f2 = 54

CLASS INTERVALS	FREQUENCY	CUMULATIVE FREQUENCY
100-110	15	15
110-120	35	50
120-130	f₁	50+f₁
130-140	f₂	50+f₁+f₂
140-150	33	83+f₁+f₂
150-160	23	106+f₁+f₂
160-170	19	125+f₁+f₂
170-180	8	133+f₁+f₂
	N=133+f₁+f₂

If the median I.Q of the students is 135, find the missing frequencies f1 and f2 in the following frequency distribution for 220 students: I.Q 100-110 110-120 120-130 130-140 140-150 150-160 160-170 170-180 Number of students 15 35 f1 f2 33 23 19 8

If the median I.Q of the students is 135, find the missing frequencies f1 and f2 in the following frequency distribution for 220 students:

I.Q 100-110 110-120 120-130 130-140 140-150 150-160 160-170 170-180
Number of students 15 35 f1 f2 33 23 19 8