If the mean of the following frequency distibution is 24, find the value of p.
Class0−1010−2020−3030−4040−50Frequency34p32
The given data is shown as follows:
Class | Frequency (fi) | Class mark (xi) | (fixi) |
0 - 10 | 3 | 5 | 15 |
10 - 20 | 4 | 15 | 60 |
20 - 30 | p | 25 | 25p |
30 - 40 | 3 | 35 | 105 |
40 - 50 | 2 | 45 | 90 |
Total | ∑fi=12+p | ∑fixi=270+25p |
The mean of given data is given by
¯x=∑fixi∑fi
⇒ 24 = 270+25p12+p
⇒ 24(12 + p) = 270 + 25p
⇒288 + 24p = 270 + 25p
⇒ 25p - 24p = 288 - 270
⇒ p = 18
Hence, the value of p is 18.