Question

Please help me compute standard deviation! Here is the problem, as written.

what is the income distribution of super shoppers. In the following table, income units are in thousands of dollars, and each interval goes up to but does not include the given high value. The midpoint are given to the nearest thousand dollars. Income range: 5-15, 15-25, 25-35, 35-45, 45-55, 55 or more. Next line is Midpoint x: 10, 20, 30, 40, 50, 60. Last line is percent of super shoppers: 21%, 14%, 22%, 15%, 20%, 8%. Part (d): Compute the standard deviation for the income of super shopers

Answer 1

The standard deviation for the income of super shoppers is 76.12.

Explanation:

The formula to compute the standard deviation for the grouped data probability distribution is:

`\sigma=\sqrt{\sum [(x-\mu)^(2)\cdot P(x)]}`

Here,

x = midpoints

`\mu=\sum x\cdot P(x)`

Consider the Excel table attached below.

The mean is:

`\mu=\sum x\cdot P(x)=32.3`

Compute the standard deviation as follows:

`\sigma=\sqrt{\sum [(x-\mu)^(2)\cdot P(x)]}`

`=√(259.71)\\\\=76.1155204\\\\\approx 76.12`

Thus, the standard deviation for the income of super shoppers is 76.12.