Answer to Question #147475 in Statistics and Probability for Bilal Asif

Question

According to the All Pakistan Software Developer Association (APSDA), developers generally spend more than 40 hours each week working on software and web development. The Table 4.1 shows the number of hours worked per week for a sample of 15 Software developers and a sample of 10 Web developers.

Table 4.1
Software Developers 56 54 54 49 61 48 58 60 59 53 50 58 55 57 52
Web
Developers 47 50 46 47 48 49 46 55 44 42 ----


a) What is the third quartile of spending working hours for Software developers?
b) Create a box plot for the number of hours worked for Software developers.
c) Create a box plot for the number of hours worked for Web developers.
d) Comment on the differences between the box plots for Software & Web developers.

Answer 1

a) Arranging the data (Software Developers) in ascending order:

48, 49, 50, 52, 53, 54, 54, 55, 56, 57, 58, 58, 59, 60, 61

n = 15

The median of the data set is 8^th value = 55. The 3rd Quartile (Q3) is the median of the second half of the data set, that is, last 7 observations. Therefore, Q3 = 4^th Observation. Taking 56 as the first observation and counting from thereon, Q3 = 58.

b)

Minimum Value = 48

First Quartile = 53

Median = 55

Third Quartile = 58

Maximum Value = 61

c)

Minimum Value = 42

First Quartile = 46

Median = 47

Third Quartile = 49

Maximum Value = 50 and 55 is the Outlier

d) The first box plot (Software Developers) shows that the data is more or less symmetric. A measure of dispersion, the inter quartile range = Q3 – Q1 = 58 – 48 = 10 which means that the data is dispersed uniformly. Also, the data contains no outliers.

The second box plot (Web Developers) shows that the data is skewed to the left. A measure of dispersion, the inter quartile range = Q3 – Q1 = 49 - 46 = 3 which means that the data is less dispersed. The data also contains an outlier (55).