Now,
Median = l + (šµ/š āšš)/š Ć h
Since Median = 50
50 ā 60 is Median Class
Where
N = āāšš
l =
h =
cf =
f =
Putting values in formula
Median = l + (šµ/š āšš)/š Ć h
50 = 50 + (šš ā (š + šš))/šš Ć 10
50 = 50 + (5 āš)/2
50 ā 50 = (5 āš)/2
0 = (5 āš)/2
5āš = 0
p = 5
Also,
āāšš = 78 + p + q
Putting values
90 = 78 + 5 + q
90 = 83 + y
90 ā 83 = q
7 = q
q = 7
Hence p = 5, q = 7
Finding Mode
Mode = l + (šš āšš)/(ššš āšš āšš) Ć h
Modal class
= Interval with highest frequency
= 40 ā 50
Here
l = lower limit of modal class = 40
h = class-interval = 50 ā 40 = 10
f1 = frequency of the modal class = 25
f0 = frequency of the class before modal class = 15
f2 = frequency of the class after modal class = 20
Putting these values in formula
ā“ Mode = l + ((š_š ā š_š)/(šš_š ā š_š ā š_š )) Ć h
= 40 + {(šš āšš)/(š Ćšš āšš āšš)} Ć 10
= 40 + 10/(50ā35) Ć 10
= 40 + 100/15
= 40 + 6.67
= 46.67

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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