Question

The following stem and leaf diagram show the number of days in a year a team of thirty technicians were absent from their work on medical grounds. Stem and Leaf Diagram of Number of Days Absent from Work Stem (tens) Leaf (ones) 01 1 23 2 017 3 1358 4 23678889 5 01345778 6 0123 a. Calculate the median number of days of absenteeism in the company. b. Calculate the interquartile range of the number of days of absenteeism in the company. c. You are presenting the dispersion of absenteeism rates to your manager who is not trained in statistics. Would you consider using quartiles to present dispersion information or the variance? Explain. d. The human resources manager of the company mentions that the company has always used median to present the absenteeism level of its workers. Based on the stem and leaf diagram, is his choice of measure of central tendency/location justified? Explain.

Answer 1

Values from stem and leaf graph are 1,12,13,20,21,27,31,33,35,38
42,43,46,47,48,48,48,49,50,51
53,54,55,57,57,58,60,61,62,63

So the median is (n/15 + n/16)/2 = (48+48)/2 = 48

Population size:30
Lower quartile (x_L): 32.5
Upper quartile (x_U): 55.5

Interquartile range (x_U-x_L): 23

Mean (μ): 42.766666666667

Variance (σ²): 261.04555555556

Standard deviation (σ): 16.156904268936
Variance will be a better estimate because of no outliers present in the data set as median>mean , so it is fairly a normally distributed graph,

The stem and leaf graph are justified because of various reasons as the distribution is normal and so that we can assume a normal distribution and can use the central tendency measure to make conclusions