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New answer posted
4 months agoContributor-Level 10
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
New answer posted
4 months ago
Contributor-Level 10
The placement details of 2025 batch are yet to be released on the official website 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:
Particulars | MBBS Placement Statistics (2023) |
|---|---|
Median package (MBBS) | INR 5.5 LPA |
Total students graduated (MBBS) | 124 |
Total students placed (MBBS) | 99 |
Students opted for higher studies | 18 |
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:
Particulars | Placement Statistics (2023) | Placement Statistics (2024) |
|---|---|---|
Median package PG 2-year (MSc, MHA) | INR 3.6 LPA | INR 3.8 LPA |
Median package PG 3-year | INR 12 LPA | INR 13.5 LPA |
Total students graduated (PG 2-year) | 42 | 124 |
Total students placed (PG 2-year) | 41 | 46 |
Total students graduated (PG 3-year) | 99 | 113 |
Total students placed (PG 3-year) | 89 | 100 |
Note: The above-mentioned data are gathered from the St. John's National Academy of Health Sciences NIRF
New answer posted
4 months agoContributor-Level 10
∴ 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
New answer posted
4 months agoContributor-Level 10
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
New answer posted
4 months agoContributor-Level 10
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
New answer posted
4 months agoContributor-Level 10
5+3+7+a+b = 25 ⇒ a+b=10
S.D. = √(((5²+3²+7²+a²+b²)/5) - 5²) = 2
√((a²+b²+83)/5) - 25 = 4 ⇒ a²+b² = 62
⇒ (a+b)² - 2ab = 62 ⇒ ab = 19
So equation whose roots are a and b is x² - 10x + 19 = 0
New answer posted
4 months agoContributor-Level 10
Mean = (6+10+7+13+a+12+b+12)/8 = (60+a+b)/8 = 9 ⇒ a+b=12.
Variance = (Σx? ²/n) - (mean)² = 37/4.
Σx? ²/8 - 81 = 37/4.
Σx? ² = 8 (81+9.25) = 8 (90.25) = 722.
Σx? ² = 36+100+49+169+a²+144+b²+144 = 642+a²+b².
642+a²+b²=722 ⇒ a²+b²=80.
(a+b)²=144 ⇒ a²+b²+2ab=144 ⇒ 80+2ab=144 ⇒ 2ab=64.
(a-b)² = a²+b²-2ab = 80-64 = 16.
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