Answer:
the variance is approximately 26.96.
Explanation:
First, we need to find the mean (average) of the data:
mean = (12+13+15+16+24+15+22+10+9+13+13+18+16+25+23+24) / 16
mean = 17.06
Next, we find the difference between each data point and the mean:
(12 - 17.06)² = 27.23
(13 - 17.06)² = 16.47
(15 - 17.06)² = 4.26
(16 - 17.06)² = 1.12
(24 - 17.06)² = 47.11
(15 - 17.06)² = 4.26
(22 - 17.06)² = 24.01
(10 - 17.06)² = 49.58
(9 - 17.06)² = 64.97
(13 - 17.06)² = 16.47
(13 - 17.06)² = 16.47
(18 - 17.06)² = 0.87
(16 - 17.06)² = 1.12
(25 - 17.06)² = 63.35
(23 - 17.06)² = 35.43
(24 - 17.06)² = 47.11
Then, we add up all the squared differences:
27.23 + 16.47 + 4.26 + 1.12 + 47.11 + 4.26 + 24.01 + 49.58 + 64.97 + 16.47 + 16.47 + 0.87 + 1.12 + 63.35 + 35.43 + 47.11 = 404.34
Finally, we divide the sum of squared differences by the number of data points minus one (since we used the mean to calculate the differences) to get the variance:
variance = 404.34 / 15
variance ≈ 26.96
Therefore, the variance is approximately 26.96.