Question

The median of the following data is 16. Find the missing frequencies a and b,
if the total of the frequencies is 70.
Class Frequency
0-5 12
5-10 a
10-15 12
15-20 15
20-25 b
25-30 6
30-35 6
35-40 4

Answer 1

Step-by-step explanation:

cumulative frequency

12

12+a

24+a

39+a

39+a+b

45+a+b

51+a+b

55+a+b

now we know that,

55+a+b= 70

a+b=70-55

a+b= 15

a and b can't be equal as they are denoted by different variable.

wkt, median is 16

class interval is 15-20

so, m= (n/2-cf÷f)*h

16 = (35-(24+a)/15)*5

16= (35-24-a/15)*5

16= (11-a/15)*5

16=11-a/3

16*3=11-a

48=11-a

48-11=-a

37=-a

therefore, a=-37

then we know that,

55+a+b=70

we know a=-37,

55-37+b=70

b=70-55+37

b=107-55

therefore, b=52

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