Question

The average distance covered by the different age groups during a morning walk is given in the table.

Age group	11-20	21-30	31-40	41-50	51-60	61 and above
Average distance covered (in meters)	1200	5000	4500	3600	2200	1500

Which age group of people vary the most from the mean of the given data?

• A. 40–50
• B. 60 and above
• C. 10–20
• D. 20–30

Answer 1

The correct option is D 20–30

Arranging the distances from least to most:
$1200,1500,2200,3600,4500,5000$
Mean of distance covered by all the age groups $=\frac{\text{Total distance covered}}{\text{Number of age groups}}$

$=\frac{1200+5000+4500+3600+2200+1500}{6}=\frac{18000}{6}=3000m$

Either the difference between the least value and the mean vary the most or the difference between the greatest value and the mean.
Variation between the least value and the mean $=3000-1200=1800$
Variation between the greatest value and the mean $=5000-3000=2000$
So the age group $20–30$ varies the most from the mean of the given observations.