Question

Table 1
18 15 17 22 12 20
19 15 20 25 16 13

Calculate the mean, the median, the mode, the standard deviation, the Pearson coefficient of skewness of assembling time.

Answer 1

Answer on Question #70662 – Math – Statistics and Probability

Question

Table 1

18 15 17 22 12 20

19 15 20 25 16 13

Calculate the mean, the median, the mode, the standard deviation, the Pearson coefficient of skewness of assembling time.

Solution

$$\text{mean:} \frac{18 + 15 + 17 + 22 + 12 + 20 + 19 + 15 + 20 + 25 + 16 + 13}{12} = \frac{53}{3} \approx 17.6667$$

median: 12, 13, 15, 15, 16, 17, 18, 19, 20, 20, 22, 25

$$\frac{17 + 18}{2} = \frac{35}{2} = 17.5$$

12 occurs in the set once

13 occurs in the set once

15 occurs in the set twice

16 occurs in the set once

17 occurs in the set once

18 occurs in the set once

19 occurs in the set once

20 occurs in the set twice

22 occurs in the set once

25 occurs in the set once

Here 15 and 20 occur twice. This is higher than any of the other data values. Thus, we say that the data set is bimodal, meaning that it has two modes.

Variance: $\sigma^2 = \left(12 - \frac{53}{3}\right)^2 + \left(13 - \frac{53}{3}\right)^2 + \left(15 - \frac{53}{3}\right)^2 + \left(15 - \frac{53}{3}\right)^2 + \left(16 - \frac{53}{3}\right)^2 + \left(17 - \frac{53}{3}\right)^2 + \left(18 - \frac{53}{3}\right)^2 + \left(19 - \frac{53}{3}\right)^2 + \left(20 - \frac{53}{3}\right)^2 + \left(22 - \frac{53}{3}\right)^2 + \left(25 - \frac{53}{3}\right)^2 = \frac{1410}{9} = \frac{470}{3} \approx 156.6667$

Standard deviation: $\sigma = \sqrt{\sigma^2} = \sqrt{\frac{470}{3}} = \frac{\sqrt{1410}}{3} \approx 12.5167$

The Pearson coefficient of skewness using the median

$$S k_2 = \frac{3(\bar{X} - M d)}{\sigma}$$ $$S k _ {2} = \frac {3 \left(\frac {5 3}{3} - \frac {3 5}{2}\right)}{\frac {\sqrt {1 4 1 0}}{3}} \approx 0. 0 4 0$$

Answer: 17.6667; 17.5; 15 and 20; 12.5167; 0.040.

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