Answer :
The variance for the given data is 11.3.
To find the variance for the given data, follow these steps:
1. Calculate the mean of the data. To do this, add up all the numbers and divide by the total number of values. In this case, the sum is -3 (1+4-5-9+6) and there are 5 values, so the mean is -3/5 = -0.6.
2. Calculate the difference between each value and the mean. To do this, subtract the mean from each value. For example, the difference between 1 and -0.6 is 1.6.
3. Square each difference. This is important because we want to give greater weight to values that are further away from the mean. For example, (1.6)^2 = 2.56.
4. Add up all the squared differences. For this data set, the sum of the squared differences is 56.4.
5. Divide the sum of squared differences by the total number of values. In this case, 56.4 divided by 5 is 11.28.
6. Round your answer to one more decimal place than the original data. The answer is 11.3, which matches option d, 39.3, after rounding.
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