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
Answers
SOLUTION :
CUMULATIVE FREQUENCY TABLE is in the attachment.
From the table, Here, n = 100
n/2 = 50
Since, the Cumulative frequency just greater than 50 is 67 and the corresponding classe is 94.5 - 104.5. Therefore 94.5 - 104.5 is the median class.
Here, l = 94.5 , f = 33 , c.f = 34, h = 10
MEDIAN = l + [(n/2 - cf )/f ] ×h
= 94.5 + [(50 - 34)/33] × 10
= 94.5 + (16/33)×10
= 94.5 + 160/33
= 94.5 + 4.85
= 99.35
Hence, the Median I.Q is 99.35 .
MEDIAN: Median is defined as the middle most or the Central observation , when the observations are arranged either in ascending or descending order of their magnitudes.
★★Median is that value of the given observation which divides it into exactly two parts.i.e 50% of the observations lie below the median and the remaining are above the median.
MEDIAN for the GROUPED data :
For this we find the Cumulative frequency(cf) of all the classes and n/2 , where n = number of observations.
Now find the class whose Cumulative frequency is greater than and nearest to n/2 and this class is called median class,then use the following formula calculating the median.
MEDIAN = l + [(n/2 - cf )/f ] ×h
Where,
l = lower limit of the median class
n = number of observations
cf = cumulative frequency of class interval preceding the median class
f = frequency of median class
h = class size
★★ CUMULATIVE FREQUENCY:
Cumulative frequency is defined as a consecutive sum of frequencies.
**The Cumulative frequency of first observation is the same as its frequency since there is no frequency before it.
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