Answers:
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Explanation:
To find the mean, we add up all the values
18+69+22+27+32+25+16+25 = 234
Then we divide that result by n = 8 since there are 8 values in this list
234/n = 234/8 = 29.25 which is the mean. This value rounds to 29.3 when rounding to the nearest tenth.
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Now onto the median. We first need to sort the items from smallest to largest
This list
{18, 69, 22, 27, 32, 25, 16, 25}
sorts to
{16, 18, 22, 25, 25, 27, 32, 69}
Since n = 8 is an even number, the median will be between two values
It's between the items at slot 4 and 5. Note that n/2 = 8/2 = 4 to help determine that first slot mentioned.
The items in slots 4 and 5 are 25 and 25. In this case, we get the same value but that won't happen every time. Averaging those two values gets us 25.
The median is 25.
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The mode is the most frequent value. In this case that would be 25 since it shows up the most (twice) compared to the other values (which only show up once).
Notes:
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Before we determine anything about outliers, we need to calculate the standard deviation. You'll need your calculator for this one. You can do so by hand, but it's tedious busywork in my opinion.
Use a calculator to find the standard deviation of the given list is approximately 15.746031246
If we started at the center median value of 25, and added on 1.5 times the standard deviation, then we get to:
median+1.5*stdDev = 25+1.5*15.746031246 = 48.619046869
This value is the upper fence. It's the boundary between non-outliers and large outliers. Anything beyond 48.619046869 will be a large outlier. This applies to the value 69 from the original list. This value is effectively an "island" point far from the "mainland" of the cluster of other points.
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Luckily, we don't need a calculator for this part. Subtract the max and min to get the range
range = max - min = 69 - 16 = 53
