Question

question 3 (1 point) saved
what is the mean of this data?
20, 18, 17, 13, 21, 19, 17, 22, 16, 23
the mean is 18.3
the mean is 18.4
the mean is 18.6
the mean is 18.5
question 4 (1 point)
what is the variance of the same data from question 3?
the variance is 8.24
the variance is 8.64
the variance is 8.04
the variance is 8.44

Explanation:

Step1: Calculate the mean

Let the data set be \(x_1 = 20,x_2 = 18,x_3 = 17,x_4 = 13,x_5 = 21,x_6 = 19,x_7 = 17,x_8 = 22,x_9 = 16,x_{10}=23\). The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}\), where \(n = 10\).
\(\sum_{i=1}^{10}x_i=20 + 18+17+13+21+19+17+22+16+23=186\).
\(\bar{x}=\frac{186}{10}=18.6\).

Step2: Calculate the variance

The formula for the variance \(s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n}\).
\((20 - 18.6)^2=1.4^2 = 1.96\)
\((18 - 18.6)^2=(- 0.6)^2=0.36\)
\((17 - 18.6)^2=(-1.6)^2 = 2.56\)
\((13 - 18.6)^2=(-5.6)^2 = 31.36\)
\((21 - 18.6)^2=2.4^2 = 5.76\)
\((19 - 18.6)^2=0.4^2 = 0.16\)
\((17 - 18.6)^2=(-1.6)^2 = 2.56\)
\((22 - 18.6)^2=3.4^2 = 11.56\)
\((16 - 18.6)^2=(-2.6)^2 = 6.76\)
\((23 - 18.6)^2=4.4^2 = 19.36\)

\(\sum_{i = 1}^{10}(x_i - 18.6)^2=1.96+0.36 + 2.56+31.36+5.76+0.16+2.56+11.56+6.76+19.36=82.4\)

\(s^2=\frac{82.4}{10}=8.24\)

Answer:

Question 3: The mean is 18.6
Question 4: The variance is 8.24