Answer to Question #252577 in Statistics and Probability for rasha

Question

HR manager in L&B real-state company is working with finance department in improving the salaries and the following descriptive statistics were obtained. Table (2) Department Mean SD CoefVar Min Q1 Median Q3 Max IQR Skewness Finance 6.052 3.874 64.01 1.630 3.393 (a) 7.500 22.860 4.107 2.00 HR 5.441 3.235 (b) 2.000 3.200 4.100 6.430 21.860 3.230 (C) IT 5.880 3.887 66.10 0.530 3.250 4.630 (d) 24.980 3.550 2.18 Marketing 6.010 3.737 62.18 1.670 3.475 5.000 6.645 22.200 3.170 2.14 Training 6.095 3.719 61.02 1.500 3.330 5.000 7.640 20.000 4.310 2.00 CoefVar stands for coefficient of variation graph (1) The company has hired you to answer the following questions: 1) Find the missing values of (a), (b), (c) and (d). Finance HR IT Marketing Training 25 20 15 10 5 0 Department salary Boxplot of salary |2) Do you think that the salaries in the departments are skewed, justify your answer with proper measure from table (2). 3) Based on the boxplot for the salaries by department in graph (1),

Answer 1

1)

a)

median = $3\overline{x}-s\cdot Sk$

where Sk is skewness,

$\overline{x}$ is mean,

s is standard deviation

median = $3\cdot 6.052-3.874\cdot 2=10.408$

b)

Coefficient of variation = $s/\overline{x}=3.235/5.441=0.595$

c)

skewness = $\frac{3\overline{x}-Md}{s}=\frac{3\cdot 5.441-4.1}{3.235}=3.778$

where Md is median

d)

from boxplot:

$Q_3=5.3$

2)

salaries in the departments are skewed:

from table:

Skewness for departments:

Finance: 2.00

HR: 3.78

IT: 2.18

Marketing: 2.14

Training: 2.00