Statistics

 x? = (2+4+10+12+14+x+y)/7 = 8
⇒ 42+x+y = 56 ⇒ x+y = 14
σ² = (Σx? ²/n) - (x? )²
16 = (4+16+100+144+196+x²+y²)/7 - (8)²
⇒ 16+64 = (460+x²+y²)/7
⇒ 560 = 460+x²+y² ⇒ x²+y² = 100
⇒ xy=48
(x-y)² = (x+y)² - 4xy = 4
|x-y| = 2

x? = Σf? x? / Σf? = (10 + 15x + 50) / (4+x)
= (60+15x)/ (4+x) = 15
σ² = 50 = Σf? x? ²/Σf? - (x? )²
50 = (50+225x+1250)/ (4+x) - (15)²
50 = (1300+225x)/ (4+x) - 225
⇒ 275 (4+x) = 1300 + 225x
⇒ 50x = 200 ⇒ x = 4

 x? = 10
⇒ x? = (63 + a + b)/8 = 10
⇒ a + b = 17
Since, variance is independent of origin.
So, we subtract 10 from each observation.
So, σ² = 13.5 = (79 + (a-10)² + (b-10)²)/8
⇒ a² + b² - 20 (a+b) = -171
⇒ a² + b² = 169
From (1) and (2) ; a = 12 and b = 5

The placement details of 2026 batch are yet to be released on the college page of St. John's National Academy of Health Sciences. However, the institute has released the NIRF report 2025 which includes the placement details for the batch 2024. The key highlights of St. John's National Academy of Health Sciences placements for the Class of 2023 and 2024 are tabulated below:

Let's take a look at the key highlights of St. John's National Academy of Health Sciences placements for the PG Class of 2024 in the table below:

∴ σ² ≤ 1/4 (M - m)²
Where M and m are upper and lower bounds of values of any random variable.
∴ σ² < 1/4 (10 - 0)
⇒ 0 < < 5
∴ σ ≠ 6

σ²=variance
µ=mean
σ² = Σ (x? -µ)²/n
µ=17
⇒ Σ (ax+b)/17 = 17
⇒ 9a+b=17
σ²=216
⇒ Σ (ax+b-17)²/17 = 216
⇒ Σa² (x-9)²/17 = 216
⇒ a² (81-18*9+3*35) = 216
⇒ a² (24) = 216 ⇒ a²=9 ⇒ a=3 (a>0)
⇒ From (1), b=-10
So, a+b=-7

Mean = 10 = (3+7+9+12+13+20+x+y)/8
16 = x + y
Variance σ² = 25 = (Σx?²/8) - (mean)²
25 = (3²+7²+9²+12²+13²+20²+x²+y²)/8 = 100
x² + y² = 148
(x+y)² = x² + y² + 2xy
256 = 148 + 2xy
x . y = 54