If the mean of the following frequency distribution is 7.2. Find the value of p and k when total frequency is 5.
X:2 4 6 8 10 12
F:4 p 10 16 k 3
Answers
Question:
If the mean of the following frequency distribution is 7.2. Find the value of p and k when total frequency is 5.
Solution:
In question we have given that mean is 7.2
And we know that -
From above = 232 + 4p + 10k
= 33 + p + k
--- [1]
Total frequency is 5.
So,
Substitute value of p = - 28 - k in equation (1)
Substitute value of k = -14 in p
Given :-----
- x = 2, 4 ,6 ,8 , 10, 12
- F = 4, p , 10, 16, k , 3
Question :-----
- we have to Find value of p and k ..
Formula used :------
- Mean of ungrouped date is given by sum of fixi , divided by sum of fi ...
Calculation :-----
From image we can see that ,,,
→ sum of fi we get = 33 + p + k
→ sum of fixi we get = 232+4p+10k
so, above told formula we get,
→ 7.2 = (232+4p+10k)/(33+p+k)
cross - multiplying we get,,,,
→ 33×7.2 + 7.2k + 7.2p = 232 + 4p + 10k
→ 7.2k - 10k + 7.2p - 4p = 232 - 237.6
→ (-2.8)k + 3.2p = (- 5.6) ------ Equation (1)
Now since it is given ,
sum if frequency is 5 .
→ 33 + p + k = 5
→ p + k = - 28
→ p = (-28-k) --------------- Equation (2)
Putting value of this in Equation (1) we get,,
→(-2.8)k + 3.2(-28-k) = ( -5.6)
→ -2.8k - 89.6 -3.2k = -5.6
→ (-6k) = (-5.6) + 89.6
→ (-6k) = 84
dividing both side by (-6) we get,
→ k = (-14)
Now how is value of frequency in negative yar ,
kuch bhe matlab ,,,
saaf saaf dikh raha question galat hai, but u need answer with given date , ok ... fine .....
so,
putting value of k in Equation (2) we get,,,
→ p = [(-28) - (-14)]
→ p = [ -28 + 14]
→ p = (-14) ....
Very nice Question ,
so,
value of p is (-14) and value of k is also (-14) ....
Given data is only possible when both have same values (-14)..
Thank you so much for providing us such a great Question ...
___________________________
→ mean ( or simply average ) of simple data = sum of observation / No. of observation
→ mean of grouped data is same as mean of un-grouped data ...