Find the value of p,if the mean of the following distribution is 7.5
X:3,5,7,9,11,13
Y:6,8,15,p,8,4
Answers
Question
Find the value of p, if the mean of the follow distribution is 7.5
X: 03, 05, 07,09, 11, 13
Y: 06, 08,15, p, 08, 04 (frequency)
Solution
X ------- Frequency (f) ---------- fX
3 ------------- 6 ------------------------ 18
5 ------------- 8 ------------------------ 40
7 ------------- 15 ---------------------- 105
9 ------------- p ------------------------ 9p
11 ----------- 8 ------------------------ 88
13 ----------- 4 ------------------------ 52
-------------------------------------------------------
Total ...... 41 + p ................ 303 + 9p
-------------------------------------------------------
We have to find the mean of the above data.
We know that, Mean = Sum of all observations/Total number of observations
We have, sum of all observations = fX = 303 + 9p
and Total number of observations = Frequency (f) = 41 + p
Also, given that mean of the above data is 7.5
Substitute these values to find the value of p.
→ 7.5 = (303 + 9p)/(41 + p)
→ 7.5(41 + p) = 303 + 9p
→ 307.5 + 7.5p = 303 + 9p
→ 322.5 - 303 = 9p - 7.5p
→ 4.5 = 1.5p
→ 4.5/1.5 = p
→ p = 3
Therefore, value of p is 3
||✪✪ QUESTION ✪✪||
Find the value of p,if the mean of the following distribution is 7.5..
X:3,5,7,9,11,13
Y:6,8,15,p,8,4
|| ✰✰ ANSWER ✰✰ ||
❁❁ Refer To Image First .. ❁❁
The mean is equal to the sum of all the values in the data set divided by the number of values in the data set.
From image we can see That :-
➻ Sum of data (Fixi) = (303 + 9P)
➻ Total Number of Values = (41 + P) .
So, Mean is :-
☛ Mean = [ (303 + 9P) / (41 + P) ]
Given That, Mean of data is 7.5.
So, Putting This value now, we get, ,
☛ 7.5 = [ (303 + 9P) / (41 + P) ]
Cross - Multiply,
☛ 7.5(41 + P) = (303 + 9P)
☛ 307.5 + 7.5P = 303 + 9P
☛ 307.5 - 303 = 9P - 7.5P
☛ 4.5 = 1.5 P
Dividing both sides by 1.5 now,
☛ P = 3.