Question

What was the age distribution of prehistoric Native Americans? Extensive anthropological studies in the southwestern United States gave the following information about a prehistoric extended family group of 98 members on what is now a Native American reservation. For this community, estimate the mean age expressed in years, the sample variance, and the sample standard deviation. For the class 31 and over, use 35.5 as the class midpoint. (Round your answers to one decimal place.)

Age range (years)	1-10	11-20	21-30	31 and over
Number of individuals	39	25	21	13

x	=
s2	=
s	=

Answer 1

To calculate mean, sample variance and sample sd, we need to calculate the following table.

where x_i is the midpoint of class and given by,

Class	xi	fi	xifi	xi2 fi
1-10	5.5	39	214.5	1179.75
11-20	15.5	25	387.5	6006.25
21-30	25.5	21	535.5	13655.25
31 and above	35.5	13	461.5	16383.25
Total		98	1599	37224.5

Now, the mean is given by,

sample mean = = = 1599/98 = 16.316 16.3 year.

Sample variance = s²= = 114.791114.8

and sample standard deviation = = 10.71410.7