Answer:
Sample standard deviation = 3
Explanation:
We can use the following steps to calculate the sample standard deviation for the given data set:
Step 1: First, calculate the mean of the data set by adding all the values and dividing by the total number of values:
(12 + 12 + 12 + 15 + 18 + 18 + 18) / 7 = 15.
Thus, the mean is 15.
Step 2: Next, subtract the mean from each value in the data set to get the deviation of each value from the mean.
(12 - 15) = -3
- We can simply write -3 thrice since 12 appears thrice in the data set.
(15 - 15) = 0
(18 - 15) = 3
- Similarly, we can write 3 thrice since 18 appears thrice in the data set.
Thus, the deviations are -3, -3, -3 0, 3, 3, and 3.
Step 3: Square each deviation:
(-3)^2 = 9
- We can write 9 thrice since -3 appears as a deviation thrice.
0^2 = 0
(3)^2 = 9
- We can again write 9 thrice since 3 appears as a deviation thrice.
Thus, the squares of all our deviations are 9, 9, 9, 0, 9, 9, and 9.
Step 4: Add up all the squared deviations:
9 + 9 + 9 + 0 + 9 + 9 + 9 = 54.
Thus, the sum of the squared deviations is 54.
Step 5: Find the variance by dividing the sum of squared deviations by one less than the number of values in the data set:
54 / (7 - 1) = 9
54 / 6 = 9
Thus, the variance is 9
Step 6: Finally, find the sample standard deviation by taking the square root of the variance:
√9 = 3
So, the sample standard deviation for this data set is 3.