The weights (in grams) of the contents of several small bottles are 4, 2, 5, 4, 5, 2 and 6. What is the sample variance?
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A. B. C. D. E.Explanation
Sample variance is given by: (Sum of squared deviation from the mean)/(n-1). Mean is 4. Sample variance = 14/6 = 2.33 xx-mean(x-mean)^2
2-24
2-24
To calculate the sample variance, you need to follow these steps:
Step 1: Calculate the mean (average) of the data set. Step 2: Subtract the mean from each data point, and square the result. Step 3: Sum all the squared differences. Step 4: Divide the sum by the number of data points minus 1 (this is the sample variance formula).
Let's calculate the sample variance for the given data set.
Step 1: Calculate the mean: Mean = (4 + 2 + 5 + 4 + 5 + 2 + 6) / 7 Mean = 28 / 7 Mean = 4
Step 2: Subtract the mean from each data point, and square the result: (4 - 4)^2 = 0 (2 - 4)^2 = 4 (5 - 4)^2 = 1 (4 - 4)^2 = 0 (5 - 4)^2 = 1 (2 - 4)^2 = 4 (6 - 4)^2 = 4
Step 3: Sum all the squared differences: 0 + 4 + 1 + 0 + 1 + 4 + 4 = 14
Step 4: Divide the sum by the number of data points minus 1: Sample Variance = 14 / (7 - 1) Sample Variance = 14 / 6 Sample Variance = 2.33
Therefore, the sample variance of the given data set is 2.33.
The correct answer is D. 2.33.