# How do you find z-score given the data:-6, -9, -6, -4, 10? 1. 0.2321 2. -1.737 3. 0.8685 4. 0.9355 5. 6.500?

Jul 28, 2015

You don't find a z-score with a data set, only with a data point.

#### Explanation:

When finding a z-score you need three things.
the standard deviation
a data point for which you are calculating the z-score.

Above it seems you have two data sets. Let us take them on one at a time.

{-6, -9, -6, -4, 10}, pretty small set with an obvious outlier.

first we can calculate the mean by adding all the values and then dividing by the number of items in the data set.

$\frac{\left(- 6\right) + \left(- 9\right) + \left(- 6\right) + \left(- 4\right) + \left(10\right)}{5} = - 3$

so the mean is -3.

The calculation of the standard deviation is too long for this answer. However, you can find it with many websites and calculators. You can also find the answer on Socratic.

The standard deviation is 7.48.

So the way we calculate the z-score is with the following formula:
$z = \frac{x - \mu}{s . d .}$ where x is a data point and s.d. is standard deviation

I mentioned earlier that 10 was an outlier. Well let us calculate its z-score:
${z}_{10} = \frac{10 - \left(- 3\right)}{7.48} = 1.74$

since it is not more than 2 standard deviations away, it may not be an outlier. But visually it certainly looks like it.

For completeness I will also do the other set:
{1.0, 0.2321, 2.0, -1.737, 3.0, 0.8685, 4.0, 0.9355, 5.0 ,6.500}
$\mu = 2.18$
$s . d . = 2.46$
So is 6.5 an outlier (more than 2 s.d. away)?
${z}_{6.5} = \frac{6.5 - 2.18}{2.46} = 1.76$
so again the answer is no, but this one visually also doesn't look like an outlier.

So there we have two examples with data, and that makes us happy
:)