The variance of five positive observa shy tions is 3 6 If four of the observations are 2 2 4 5 then ...........

Mathematics (NDA) Statistics

The variance of five positive observa tions is 3.6. If four of the observations are 2, 2, 4, 5 then what is the remaining observation ?

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2022 NDA -1 Math

- Let's say the five observations are 2, 2, 4, 5, and x.

- The mean = (2 + 2 + 4 + 5 + x)/5 = (13 + x)/5.

- Variance formula for 5 values = [S(xi – mean)²]/5 = 3.6

- So, the sum of squared deviations: 5 × 3.6 = 18

- Calculating: [(2-mean)² + (2-mean)² + (4-mean)² + (5-mean)² + (x-mean)²] = 18

- Substitute mean: (2-a)² + (2-a)² + (4-a)² + (5-a)² + (x-a)² = 18, where a = (13+x)/5

Test options:

- Option 1: 4 ? mean=17/5=3.4 ? variance not 3.6

- Option 2: 5 ? mean=18/5=3.6 ? variance not 3.6

- Option 3: 7 ? mean=20/5=4

(2-4)² = 4, (2-4)² = 4, (4-4)² = 0, (5-4)² = 1, (7-4)² = 9

Sum = 4+4+0+1+9=18 ? 18/5 = 3.6

- Option 4: 9 ? mean=22/5=4.4 ? variance not 3.6

Correct Answer:

Option 3, 7

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