Answer to Question #228005 in Statistics and Probability for rahul

Question

4(a) “Each average has its own special features and it is difficult to say which one is the best”. explain this statement.

4(b) The mean age of the combined group of men and women is 30.5 years. If the mean age of the sub-group of men is 35 years and that of the sub-group of women is 25 years, find out percentage of men and women in the group.

4(c) The mean and median of a moderately skewed distribution are 42.2 and 41.9 respectively. Find mode of the distribution. 

Answer 1

Part 4a

In colloquial language, an average is a single number taken as representative of a list of numbers. Different concepts of average are used in different contexts. Often "average" refers to the arithmetic mean, the sum divided by how many numbers are averaged. In statistics, mean, median, and mode are all known as measures of central tendency, and in colloquial usage, any of these might be called an average value.

Part 4b

$30.5=\frac{35\mu+25(100-\mu)}{100}\\ 3050=35\mu+2500-25\mu\\ 3050-2500=35\mu-25\mu\\ 550=10\mu= 55\\ No.\space of\space men =55\\ No.\space of\space women=100-\mu=100-55=45\\$

$Percentage\space of\space men= 55\%\\ Percentage\space of\space women= 45\%$

Part 4c

Mode= 41.3

Formula; 3 median - 2 mean

Given;

Median = 41.9

Mean = 42.2

Then, mode = 3×41.9 - 2×42.2

= 125.7 - 84.4

= 41.3

Mode= 41.3 ans

Reference

https://opentextbc.ca/introbusinessstatopenstax/chapter/skewness-and-the-mean-median-and-mode/