Question

Find the missing frequency p for the following frequency distribution whose mean is 28. 25. x = 15 , 20, 25 ,30 , 35, 40. y = 8, 7 , p , 14,15,6 ​

Answer 1

Answer:

p=10

Step-by-step explanation:

the mean of this data set containing  values and their frequencies is given by the sum of the product of the values and their respective frequencies divided by the sum of the frequencies, i.e.

if x= 15,20,25,30,35,40

and

y= 8,7,p,14,15,6

then,

the mean is given as

$mean =\frac{1}{\sum y_i} *\sum x_i *y_i$

but the sum of the frequencies is

8+7+p+14+15+6=50+p

sum of the product of values and their respective frequencies is

15*8+20*7+25*p+30*14+35*15+40*6= 1445+25p

Therefore mean is

$mean=\frac{1295+25p}{50+p} \\\\28.25=\frac{1445+25p}{50+p}\\ \\28.25(50+p)=1445+25p\\1412.5+28.25p=1445+25p\\28.25p-25p=1445-1412.5\\3.25p=32.5\\p=10$

p=10

Answer 2

Answer:

The missing frequency p is 10