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The mean and variance of five obser vations are 14 and 13.2 respectively. Three of the five observations are 11, 16 and 20. What are the other two observations ?
8 and 15
9 and 14
10 and 13
11 and 12
- Mean of 5 observations is 14, so their total sum is \( 14 \times 5 = 70 \).
- Given observations: 11, 16, and 20. Their sum is \( 11 + 16 + 20 = 47 \).
- Sum of the other two observations is \( 70 - 47 = 23 \).
- Variance:
- Mean is 14. Variance is 13.2.
- Formula for variance: \( \frac{\sum{(x - \text{mean})^2}}{n} \).
- Squared deviations of 11, 16, 20: \( (11-14)^2, (16-14)^2, (20-14)^2 \).
- Calculate the sum of square deviations for all 5.
- Options:
- Option 1 (8 & 15): Sum = 23, gives incorrect variance.
- Option 2 (9 & 14): Sum = 23, gives incorrect variance.
- Option 3 (10 & 13): Sum = 23, matches variance.
- Option 4 (11 & 12): Sum = 23, gives incorrect variance.
- Correct Answer: Option 3 (10 and 13).
By: Parvesh Mehta ProfileResourcesReport error
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