Ask Your Teacher 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 86 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.)

Now  in order to calculate the variance we can use the following formula:

and replacing we got:

And the deviation would be the square root of the variance:

Step-by-step explanation:

We assume the following dataset

Age range (years)               1-10        11-20       21-30       >31

Number of individuals        30            18            23          10

Solution to the problem

We can solve the problem creating the following table:

Class      Midpoint(xi)   fi        xi*fi        xi^2 *fi

1-10             5.5            30       165        907.5

11-20           15.5           18       279       4324.5

21-30          25.5          23       586.5   14955.75

>31              35.5          10        355      12602.5

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Total                            81      1385.5    32790.25

The midpoint is calculated as the average between the lower and the upper interval values.

We can calculate the mean with the following formula:

Now  in order to calculate the variance we can use the following formula:

and replacing we got:

And the deviation would be the square root of the variance:

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step-by-step explanation: