Читать книгу Statistics and Probability with Applications for Engineers and Scientists Using MINITAB, R and JMP - Bhisham C. Gupta, Irwin Guttman - Страница 100

1 If the second quartile (median) is close to the center of the box and each of the whiskers is approximately of equal length, then the distribution is symmetric.

2 If the right box is substantially larger than the left box and/or the right whisker is much longer than the left whisker, then the distribution is right‐skewed.

3 If the left box is substantially larger than the right box and/or the left whisker is much longer than the right whisker, then the distribution is left‐skewed.

Example 2.8.1 (Noise levels) The following data gives the noise level measured in decibels (a usual conversation by humans produces a noise level of about 75 dB) produced by 15 different machines in a very large manufacturing plant:

85 80 88 95 115 110 105 104 89 87 96 140 75 79 99

Construct a box plot and examine whether the data set contains any outliers.

Figure 2.8.2 Box plot for the data in Example 2.8.1.

Solution: First we arrange the data in the ascending order and rank them.

Data values	75	79	80	85	88	89	95	96	97	99	104	105	110	115	140
Ranks	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15

We then find the ranks of the quartiles , , and . Thus, we have ()

Rank of = (25/100)(15+1) = 4

Rank of = (50/100)(15+1) = 8

Rank of = (75/100)(15+1) = 12

Therefore, the values of , , and are 85, 96, and 105, respectively, and the interquartile range is

Figure 2.8.2 shows the box plot for these data. Figure 2.8.2 shows that the data include one outlier. In this case, action should be taken to modify the machine that produced a noise level of 140 dB. Use MINITAB to create a box plot: