Question

To get the best deal on a CD player, Tom called eight appliance stores and asked the cost of a specific model. The prices he was quoted are listed below: $298 $125 $411 $157 $231 $213 $304 $272

Answer 1

Answer:

$84.86

Explanation:

I'm guessing they want you to find the standard deviation.

It would be easy to do this in a statistical calculator, but I suspect they want you to do it by hand.

Here are the steps for a manual calculation.

1. Count the elements in the data set

N = 8

2 Calculate the sum of the data set

$\displaystyle \sum_{i = 1}^{8}x_{i} = 2011$

3. Calculate the mean

$\mu_{x} = \dfrac{2011}{8} = 251.375$

4. Calculate the standard deviation

(a) Subtract the mean from each data point

(b) Square the differences

(c) Add the squares  of the differences

(d) Divide the sum by the number of terms

(e)Take the square root of the result

We can set up a table to organize the calculations.

$\begin{array}{rrr}\mathbf{x} & \mathbf{x - \mu} & \mathbf{(x - \mu)^{2}}\\298 & 46.63 &2174\\125 & -126.38 & 15971\\411 & 156.93 & 254801\\157 & -94.38 & 8907\\231 & -20.38 & 415\\213 & -38.38 & 1473\\304 & 52.63 & 2769\\272 & 20.63 & 425\\\sum = \mathbf{2011} & & \mathbf{57614}\\\end{array}\\\\\sigma = \sqrt{\dfrac{ 57614}{8}} = \sqrt{7201.7} = \mathbf{\ 84.86}$