Answer to Question #228247 in Statistics and Probability for Himanshu

Question

“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 distributio

Answer 1

Part a

In layman's terms, an average is a single number chosen to represent a set of data. Different definitions of average are employed in various situations. The term "average" is frequently used to refer to the mathematical mean, which is the total of the numbers divided by the number of numbers averaged. In statistics, the mean, median, and mode are all regarded as measures of central tendency, and in common parlance, any of these might be referred to as an average number.

Part b

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

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

Part c

Given :

• Mean of a moderately skewed distribution = 42.2
• Median of a moderately skewed distribution = 41.9
  

Formula Used :

• Mode = 3 × median - 2 × mean

Step-by-step explanation :

It is Given that,

Mean = 42.2

Median = 41.9

Mode =?

As We know that,

Mode = 3 × median - 2 × mean

Substituting the values in the above formula, we get,

$= 3 × 41.9 - 2 × 42.2\\ = 125.7 - 84.4\\ = 41.3$

Therefore, Distribution of the mode = 41.3