Here is a stem-and-leaf display of the escape time data introduced in Exercise 36 of this chapter. a. Determine the value of the fourth spread. b. Are there any outliers in the sample? Any extreme outliers? c. Construct a boxplot and comment on its features. d. By how much could the largest observation, currently 424, be decreased without affecting the value of the fourth spread? Reference exercise- 36 A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape (“Oxygen Consumption and Ventilation During Escape from an Offshore Platform,” Ergonomics, ?1997: 281–292): a. ?Construct a stem-and-leaf display of the data. How does it suggest that the sample mean and median will compare? b?. ?Calculate the values of the sample mean and median. [?Hint:?x?i? = 9638 ?.] c. ?By how much could the largest time, currently 424, be increased without affecting the value of the sample median? By how much could this value be decreased without affecting the value of the sample median? d.? ?What are the values of and when the observations are reexpressed in minutes?
Answer Step 1 of 4 a)Lower fourth=359 Upper fourth=391.25 Fourth spread=Upper fourth-Lower fourth =391.25-359=32.25 Step 2 of 4 b) Minimum value=325 Maximum value=424 Lower outlier bound is = lower fourth value - 1.5(fourth spread) = 359 - 1.5(32.25) = 310.625 There are no outlier in the low end of the distribution Upper outlier bound is = upper fourth value + 1.5(fourth spread) = 359 + 1.5(32.25) = 407.375 (424 is an outlier) There is one outlier in the high end of the distribution c)Step 3 of 4 Step 4 of 4 d)The largest observation, currently 424, be decreased without affecting the value of the fourth spread is 424-407.375=16.625 Problem2 answer a)Step 1 of 4 32/55 33/49 34/ 35/6699 36/34469 37/03345 38/9 39/2347 40/23 41/ 42/4 Step 2 of 4 x 9638 b) Mean= n = 26 =370.69 Median =( n+1 ) value 2 =369.5