Data Set 2B
Suppose that the height (in meters) of 6 fir trees in the garden department of a store are as follows:
1, 2, 2, 4, 4, 5
-What is the variance for Data Set 2B?
A) √2
B) 1.5
C) 2.5
D) 1
E) 2

Question

Quizplus · Accepted Answer

First, we need to find the mean of the data set:
(1 + 2 + 2 + 4 + 4 + 5) / 6 = 2.67

Next, we need to find the deviation of each value from the mean:
(1 - 2.67) = -1.67
(2 - 2.67) = -0.67
(2 - 2.67) = -0.67
(4 - 2.67) = 1.33
(4 - 2.67) = 1.33
(5 - 2.67) = 2.33

Next, we need to square each deviation:
(-1.67)^2 = 2.79
(-0.67)^2 = 0.44
(-0.67)^2 = 0.44
(1.33)^2 = 1.78
(1.33)^2 = 1.78
(2.33)^2 = 5.44

Next, we need to find the sum of the squared deviations:
2.79 + 0.44 + 0.44 + 1.78 + 1.78 + 5.44 = 12.67

Finally, we need to divide the sum of squared deviations by the number of observations (n) minus one, which is the sample size minus one:
12.67 / (6-1) = 2.534

Therefore, the variance is approximately 2.534, which is closest to the answer of E) 2.

Data Set 2B Suppose That the Height (In Meters) of 6 Fir Trees