Question

The mean deviation of first 8 composite numbers is

• A. $3.0$
• B. $4.83$
• C. $5.315$
• D. $3.5625$

Answer 1

The correct option is A $3.0$

Mean deviation is the mean of the absolute differences between each value in the data set and the mean of the data set.

Mean is the sum of the values in the data set divided by the total number of values.

A composite number is an integer which is not a prime.

The first $8$ composite numbers are $4,6,8,9,10,12,14,15$

Mean of the composite numbers is $\frac{4+6+8+9+10+12+14+15}{8}$

$⟹mean=\frac{78}{8}=9.75$

The absolute difference between the data values and mean is $|9.75-4|,|9.75-6|,|9.75-8|,|9.75-9|,|9.75-10|,|9.75-12|,|9.75-14|,|9.75-15|$

Therefore, the data values after finding the absolute differences are $5.75,3.75,1.75,0.75,0.25,2.25,4.25,5.25$

Therefore, the mean deviation is $\frac{5.75+3.75+1.75+0.75+0.25+2.25+4.25+5.25}{8}=\frac{24}{8}=3$

Therefore, the mean deviation of first eight composite numbers is $3$