Question

Come up with a set of 6 values that have a standard deviation of 2.

Answer 1

Explanation:

the stages deviation is the square root of the sum (divided by the number of data points) of the squared differences of each individual data point from the mean value.

so, we need to calculate backwards.

to get the standard deviation to be 2, then the square of 2 (4) is the sum of all squares differences divided by 6 (as we need to find 6 values).

4 = sum(diff²) / 6

so the sum of all squared differences from the mean value is 4×6 = 24.

so, we have 6 squared differences.

that means the simplest approach would be to say that each squared difference is 24/6 = 4

and then each difference from the mean value is

sqrt(4) = 2.

that's means we need to find 6 numbers with a mean value that is 2 off of every data point.

e.g.

2, 2, 2, 6, 6, 6

the mean value is

(2+2+2+6+6+6)/6 = 24/6 = 4

so, every data point has a difference of 2 to the mean value.

and this dataset has a steadfast deviation of 2.

Answer 2

Given the question in the image, the following are the solution steps to answer the question

STEP 1: Write the formula for Standard Deviation

`\begin{gathered} \sigma={\sqrt{\frac{\sum(x_(i)-{\mu})^(2)}{N}}} \\ \text{where }\sigma\text{ is the standard deviation} \end{gathered}`

STEP 2: Find the set of 6 values that have a standard deviation of 2

Using Graphing calculator, this involves testing a set of numbers that has a standard deviation of 2

Using the set of numbers below:

Tweaking the set of values to the one below:

`\begin{gathered} A=1,2,5,5,5,6 \\ \text{Standard deviation using graphing calculatore gives }2 \end{gathered}`

Hence, the set of 6 values that have a standard deviation of 2 are 1,2,5,5,5,6