129k views
0 votes
Find the sample standard deviation. 12​, 12​, 12​, 15​, 18​,
18​, 18
show work pls

User Deandob
by
7.2k points

1 Answer

6 votes

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.

User Dasean
by
8.0k points

No related questions found