The weights (in grams) of the contents of several small bottles are 8, 4, 3, 6, 7, 1 and 5. What is the sample variance?
5.81
4.33
5.67
2.22
To find the sample variance, you need to follow these steps:
Step 1: Calculate the mean
To start, find the mean (average) of the weights. To do this, add up all the weights and divide by the total number of weights.
8 + 4 + 3 + 6 + 7 + 1 + 5 = 34 (total sum of weights)
34 / 7 = 4.857 (mean)
Step 2: Calculate the deviations
Next, find the deviation of each weight from the mean. Subtract the mean from each weight.
8 - 4.857 = 3.143
4 - 4.857 = -0.857
3 - 4.857 = -1.857
6 - 4.857 = 1.143
7 - 4.857 = 2.143
1 - 4.857 = -3.857
5 - 4.857 = 0.143
Step 3: Square the deviations
Now, square each of the deviations calculated in Step 2.
3.143^2 = 9.855649
-0.857^2 = 0.735649
-1.857^2 = 3.437649
1.143^2 = 1.305649
2.143^2 = 4.592649
-3.857^2 = 14.882649
0.143^2 = 0.020449
Step 4: Sum the squared deviations
Add up all the squared deviations.
9.855649 + 0.735649 + 3.437649 + 1.305649 + 4.592649 + 14.882649 + 0.020449 = 34.830243
Step 5: Calculate the variance
Finally, calculate the variance by dividing the sum of squared deviations by the total number of weights minus 1 (for the sample variance).
34.830243 / (7 - 1) = 34.830243 / 6 = 5.8050405
The sample variance is approximately 5.81 grams.
Therefore, the correct answer is: 5.81.