Answer to Question #227207 in Macroeconomics for Anika

Question

Number of Workers2. A certain number of salesmen were appointed in different territories and the following datawere compiled from their sales reports. Calculate the central tendencies (mean, median, mode)for sales from the following data. Comment on the shape of the dataset. Which central tendencyvalue is best suited for the data?Sales (^ * 000 Rs.) : 4-8 8-12 20 - 24 28-32 32-36 36 - 40 No. of salesmen : 11 13 16 14 - 9 17 6 4

Answer 1

Solution:

The table is as below:

a.). Mean calculation = $\sum \frac{Fm}{F} =\frac{1,920}{66} = 29.1$

 

b.). Median = $LCB_{m} + [\sum \frac{F}{2} - \frac{CF_{bmc}}{Fm}]\times W =16+ [\frac{66}{2} - \frac{24}{16}]\times 12 = 16 + 6.75 = 22.75$

 

c.). Mode = $LCB_{m} + [ \frac{\triangle 1}{\triangle 1 + \triangle 2} ]\times W = 16 + [ \frac{3}{3 + 2} ]\times 12= 16 + 7.2 = 23.2$

 

The shape of the data set is skewed or has an asymmetric distribution since one tail is longer than the other.

 

The central tendency that is best suited for the data is the median since the data set is skewed or has an asymmetric distribution.