Question

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

Answer 1

Answer:

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

Step-by-step 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:

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

   $=\sqrt{259.71}\\\\=76.1155204\\\\\approx 76.12$

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