Let the mean of the data x 1 3 5 7 9 Frequency (f) 4 24 28 α 8 be 5...

Given,

The mean of the below data is $5$

$x$	$1$	$3$	$5$	$7$	$9$
Frequency \left(f\right)$</td> <td style="text-align: center;">$4$</td> <td style="text-align: center;">$24$</td> <td style="text-align: center;">$28$</td> <td style="text-align: center;">$\alpha$</td> <td style="text-align: center;">$8$</td> </tr> </tbody></table><p>Now finding mean we get,</p><p>$\dfrac{4 + 72 + 28 \times 5 + 7\alpha + 72}{64 + \alpha} = 5$</p><p>$⇒ \alpha = 16$</p><p>So, total number of observation will be,$∑ {f}_{i} = 80$</p><p>Now finding, mean deviation we get,</p><p>$M . D = \dfrac{∑ {f}_{i}\left|{x}_{i} - 5\right|}{∑ {f}_{i}}$</p><p>$= \dfrac{4 \times 4 + 24 \times 2 + 0 + 16 \times 2 + 8 \times 4}{80}= \dfrac{8}{5}$</p><p>So,$m = \dfrac{8}{5}$</p><p>Now finding, variance we get, </p><p>${\sigma}^{2} = \dfrac{∑ {f}_{i}{\left|{x}_{i} - 5\right|}^{2}}{∑ {f}_{i}}$</p><p>$⇒ {\sigma}^{2} = \dfrac{4 \times 16 + 24 \times 4 + 0 + 16 \times 4 + 8 \times 16}{80}$</p><p>$⇒ {\sigma}^{2} = \dfrac{22}{5}$</p><p>Hence, the value of$\dfrac{3\alpha}{m + {\sigma}^{2}} = \dfrac{3 \times 16}{\dfrac{8}{5} + \dfrac{22}{5}} = 8 Practice Statistics on Quantrex Academy → More from Statistics Consider a data consisting of 10 observations x_1, x_2, …, x_ 10 , whose mean is 5 and… JEE Advanced 2026A set of four observations has mean 1 and variance 13 . Another set of six observations… JEE Main 2026Let the mean and the variance of seven observations 2, 4, α, 8, β, 12, 14 , α < β , be 8… JEE Main 2026A data consists of 20 observations x_1, x_2, …, x_ 20 . If ∑_ i=1 ^ 20 (x_i + 5)^2 = 2500… JEE Main 2026A variable X takes values 0, 0, 2, 6, 12, 20, …, n(n-1) with frequencies ^nC_0, ^nC_1… JEE Main 2026The mean deviation about the mean for the data x_i 5 7 9 10 12 15 f_i 8 6 2 2 2 6 is… JEE Main 2026For 10 observations x_1, x_2, …, x_ 10 , if ∑_ i=1 ^ 10 (x_i+2)^2=180 and ∑_ i=1 ^ 10… JEE Main 2026Suppose that the mean and median of the non-negative numbers 21, 8, 17, a, 51, 103, b… JEE Main 2026The mean and variance of n observations are 8 and 16 , respectively. If the sum of the… JEE Main 2026If the mean of the data Class 5-10 10-15 15-20 20-25 25-30 30-35 Frequency 2 k 28 54 k+1… JEE Main 2026The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these… JEE Main 2026Let X=\ x ∈ ~N: 1 ≤ x ≤ 19\ and for some a, b ∈ ℝ, Y=\ a x+b: x ∈ X\ . If the mean and… JEE Main 2026The mean and variance of a data of 10 observations are 10 and 2, respectively. If an… JEE Main 2026If the mean and the variance of the data Class 4-8 8-12 12-16 16-20 Frequency 3 λ 4 7 are… JEE Main 2026Let the mean and variance of 8 numbers -10,-7,-1, x, y, 9,2,16 be (7)/(2) and (293)/(4)… JEE Main 2026If the mean deviation about the median of the numbers k, 2 k, 3 k, …. ., 1000 k is 500… JEE Main 2026 Full Statistics list Statistics JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs