Advertisements
Advertisements
प्रश्न
Find the value of p, if the mean of the following distribution is 20.
| x: | 15 | 17 | 19 | 20+p | 23 |
| f: | 2 | 3 | 4 | 5p | 6 |
उत्तर
The given data in tabulated form is
| x | 15 | 17 | 19 | 20+p | 23 |
| f | 2 | 3 | 4 | 5p | 6 |
We have to find the value of p using the information that the mean of the data is 20.
Prepare the following frequency table of which the first column consists of the values of the variate and the second column the corresponding frequencies. Multiply the frequency of each row with the corresponding values of variable to obtain the third column containing `f_ix_i`.
| `x_i` | `f_i` | `f_ix_i` |
| 15 | 2 | 30 |
| 17 | 3 | 51 |
| 19 | 4 | 76 |
| 20+p | 5p | 5p(20+p) |
| 23 | 6 | 138 |
Find the sum of all entries in the second and third column to obtain N and `sum f_ix_I` respectively. Therefore,
` N = sum_(i=1)^5 f_i`
= 2+3+4+5p+6
=15+5p
` sum_(i=1)^5 f_ix`
=30+51+76+5p(20+p)+138
=5p2 + 100p +295
The mean is
`bar(X) = (sum_(i=1)^5 f_ix_i)/N`
`=(5p^2 +100p+295)/(15+5p)`
Hence, we have
`=(5p^2 +100p+295)/(15+5p)=20`
⇒5p2 + 100p +295=300+100p
⇒5p2 = 300-295
⇒ 5p2 = 5
⇒ p2 =`5/5`
⇒ p2 = 1
`⇒ p =+- 1`
If p is negative then the 4th frequency becomes negative. But frequency can’t be negative. Hence the possible value of p is 1
p = 1
APPEARS IN
संबंधित प्रश्न
The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.
29, 32, 48, 50, x, x + 2, 72, 78, 84, 95
The sums of the deviations of a set of n values 𝑥1, 𝑥2, … . 𝑥11 measured from 15 and −3 are − 90 and 54 respectively. Find the valùe of n and mean.
Find the mean of the following data:
| x : | 19 | 21 | 23 | 25 | 27 | 29 | 31 |
| f : | 13 | 15 | 16 | 18 | 16 | 15 | 13 |
Find the missing value of p for the following distribution whose mean is 12.58.
| x | 5 | 8 | 10 | 12 | p | 20 | 25 |
| f | 2 | 5 | 8 | 22 | 7 | 4 | 2 |
Find the median of the following data : 41, 43, 127, 99, 61, 92, 71, 58, 57 If 58 is replaced
by 85, what will be the new median.
If the mean of x + 2, 2x + 3, 3x + 4, 4x + 5 is x + 2, find x.
The mean of a, b, c, d and e is 28. If the mean of a, c, and e is 24, What is the mean of band d?
If `barx` is the mean of x1, x2, ..., xn, then for a ≠ 0, the mean of `ax_1, ax_2, ..., ax_n, x_1/a, x_2/a, ..., x_n/a` is ______.
A child says that the median of 3, 14, 18, 20, 5 is 18. What doesn’t the child understand about finding the median?
A class consists of 50 students out of which 30 are girls. The mean of marks scored by girls in a test is 73 (out of 100) and that of boys is 71. Determine the mean score of the whole class.
