Question

The mean of the following data is 52.5. find the value of p class intervals and frequency
0-20 15
20-40 22
40-60 37
60-80 P
80-100 21

Answer 1

Given:

The mean of the following data is 52.5.

0-20 15

20-40 22

40-60 37

60-80 P

80-100 21

To find:

Find the value of p class intervals and frequency

Solution:

Consider the attached figure for aligned frequency table.

From given, we have,

Class        fi            xi                    fi × xi

0 - 20      15         (0+20)/2= 10    150

20 - 40    22           30                  660

40 - 60    37           50                  1850

60 - 80      P           70                  70P

80 - 100   21           90                  1890

∑ fi = 95 + P

∑ fi × xi = 4550 + 70P

now consider,

mean = ∑ fi × xi / ∑ fi

52.5 = (4550 + 70P) / (95 + P)

upon solving the above equation, we get,

$52.5=\dfrac{4550+70P}{95+P}\\\\52.5\left(95+P\right)=4550+70P\\\\49875+525P=45500+700P\\\\-175P=-4375\\\\P=25$

Therefore, the value of P is 25