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Name: what was the age distribution of prehistoric Native America? Extensive
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Description: what was the age distribution of prehistoric Native America? Extensive , anthropological studies in the southwestern United states gave the following information about a prehistoric extended family group of 82 members on what is now a native america

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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what was the age distribution of prehistoric Native America? Extensive , anthropological studies in the southwestern United states gave the following information about a prehistoric extended family group of 82 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 deviation. For the class 31 and over, use 35.5 as the class midpoint. 39,16, 20,7

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1

From the information given, the frequency table is,

Class	1 - 10	11 - 20	21 - 30	31 and over
Frequency	39	16	20	7

The mean formula is,

$\bar{x} = \frac{\sum_{i} f_{i} x_{i}}{\sum_{i} f_{i}}$

The sums are,

Class	Frequency(f)	Midpoints(x)	fx
1 - 10	39	$\frac{1 + 10}{2} = 5.5$	214.5
11 - 20	16	$\frac{11 + 20}{2} = 15.5$	248
21 - 30	20	$\frac{21 + 30}{2} = 25.5$	510
31 and over	7	35.5	248.5
Total	82		1,221

The mean age expressed in years is,

$\begin{array}{rcl} \bar{x} & = & \frac{1, 221}{82} \\ = & 14.89 \end{array}$

Thus, the mean age expressed in years is 14.89.

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