Find out missing frequencies in the following incomplete distribution:
Measurement 0-10 10-20 20-30 30-40 40-50
Frequency 3 ? 20 12 ?
The values of Median and Mode are 27 and 26 respectively.
Answers
Given : incomplete distribution:
Measurement 0-10 10-20 20-30 30-40 40-50
Frequency 3 ? 20 12 ?
The values of Median and Mode are 27 and 26 respectively.
To Find : Missing frequencies
Solution:
CI f cf
0 - 10 3 3
10 - 20 a 3+a
20 - 30 20 23+a
30 - 40 12 35+a
40 - 50 b 35+a+b
Mode = 26 hence lies in 20 - 30
f of modal class = 20
Mode = 20 + 10 * ( 20 - a) / (20 - a + 20 - 12)
⇒ 26 = 20 + 10 * (20 - a) / (28 - a)
⇒ 6 * (28 - a) = 10 ( 20 - a)
⇒ 168 -6a = 200 - 10a
⇒ 4a = 32
⇒ a = 8
CI f cf
0 - 10 3 3
10 - 20 8 11
20 - 30 20 31
30 - 40 12 43
40 - 50 b 43+b
Median = 27
⇒ 27 = 20 + 10 ( (43 + b)/2 - 11)/ 20
⇒7 = ( (21 + b)/ 4
⇒28 = (21 + b)
⇒ b = 7
a = 8 and b = 7
missing frequencies are 8 and 7
CI f cf
0 - 10 3 3
10 - 20 8 11
20 - 30 20 31
30 - 40 12 43
40 - 50 7 50
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Step-by-step explanation:
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