Question

1. Listed below are foot lengths in inches for 11 randomly selected people taken in 1988. Find the​ range, variance, and standard deviation for the given sample data. Include appropriate units in the results.
2. Are the statistics representative of the current population of all​ people?
8.9 8.5 9.7 8.9 9.4 9.7 9 9 9.7 9.1 9.2

Answer 1

Answer:

1. Range = 1.2 , variance = 10.153, standard deviation = 3.18611.
2. No.

Step-by-step explanation:

The foot lengths in inches for 11 randomly selected people taken in 1988. are

                        $8.9, 8.5, 9.7, 8.9, 9.4, 9.7, 9, 9, 9.7, 9.1, 9.2$

First, we need to arrange the given data in ascending order.

                       $8.5, 8.9, 8.9, 9, 9, 9.1, 9.2,9.4, 9.7, 9.7, 9.7$

1.  To find the range, we need to determine the maximum value and the minimum value in the given sample, and to subtract them. The maximum value is  9.7 and the minimum value is 8.5. Therefore,

                           $r = x_{max} - x_{min} = 9.7-8.5 = 1.2$

The variance is given by

                                   $s^2 = \frac{1}{n-1} \sum_{i=1}^n (x_i-\overline{x}^2)$

where

                                        $\overline{x} = \frac{1}{n}\sum_{i=1}^{n} x_i$

In this case, $n = 11$. Therefore,

     $\overline{x} = \frac{1}{11}(8.9+8.5+9.7+8.9+9.4+9.7+9+9+9.7+9.1+9.2) = 9.19$

Hence, the variance is

  $s^2 = \frac{1}{10} \sum_{i=1}^{11} (x_i-\overline{x})^2\\\\\phantom{s^2} = \frac{1}{10} ((8.9-9.19)^2+(8.5-9.19)^2+(9.7-9.19)^2+(8.9-9.19)^2+(9.4-9.19)^2+(9.7-9.19)^2+(9-9.19)^2+(9-19)^2+(9.7-9.19)^2+(9.1-9.19)^2+(9.2-9.19)^2 ) \\\\\phantom{s^2} = \frac{101.513}{10} = 10.1513$

Now, we can calculate the standard deviation.

                        $s = \sqrt{s^2} = \sqrt{10.1513} = 3.18611$

2. No, this statistics are not representative of the current population of all​ people, since they are measured for the 1988. population.