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Question
If the mean of the following data is 20.2, find the value of p:
| x | 10 | 15 | 20 | 25 | 30 |
| f | 6 | 8 | p | 10 | 6 |
Solution
We know that,
Mean of the data `(barx) = (sum_(i = 1)^5 f_i x_i)/(sum_(i = 1)^5 f_i) = 20.2` ...[Given]
⇒ `(f_1x_1 + f_2x_2 + f_3x_3 + f_4x_4 + f_5x_5)/(f_1 + f_2 + f_3 + f_4 + f_5) = 20.2`
⇒ `((6)(10) + (8)(15) + (p)(20) + (10)(25) + (6)(30))/(6 + 8 + p + 10 + 6) = 20.2`
⇒ `(60 + 120 + 20p + 250 + 180)/(30 + p) = 20.2`
⇒ 20p + 610 = 606 + 20.2p
⇒ 610 – 606 = 0.2p
⇒ `(2p)/10 = 4`
∴ p = 10 × 2 = 20
Hence, the value of p is 20.
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