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 92 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.) 1-10 11-20 21-30 31 and over Age range (years) Number of individuals 37 24 18 13 x-15.9 Need Help?Read It

Answer 1

Solution:

Given that,

Class	Frequency	Mid - point	D=X - A / H	fd	fd2
1 -10	37	5.5	-2	-74	148
11-20	24	15.5	-1	-24	24
21-30	18	25.5 = A	0	0	0
31-40	13	35.5	1	13	13
	n = 92		$\sum$fd = -85		$\sum$fd2 = 185

a ) The sample mean is $\bar x$

Mean $\bar x$   = (A + ($\sum$fd / n) * h)

= (25.5 +( - 85 / 92 ) * 10

= 25.5 + - 0.9239 * 10

= 25.5 + - 9.2391

= 16.2609

Mean = 16.3

b ) The  sample variance S²

  S² = ( $\sum$ fd² ) - (( $\sum$ fd )² / n ) / 1 -n ) * h²

= (185 ( (- 85 )² / 92 ) / 91 * 10²

   = ( 185 - 78.5326 / 61 ) * 100

= (106.4674 / 91 )* 100

= 1.17 *100

= 116.9971

The  sample variance S² is 117.0

The sample standard deviation is S

S =  $\sqrt{}$ variance

=  $\sqrt{}$ 117.0

= 10.8

The sample standard deviation is S = 10.8