Video: Determining the Data Set with the Lowest Standard Deviation

Without calculating the exact standard deviations of the following sets, determine which of them has the lowest standard deviation. [A] 41, 41, 41, 41, 41, 42 [B] 35, 38, 42, 48, 48, 48 [C] 75, 75, 75, 75, 75, 1500 [D] 10, 20, 30, 40, 50, 60 [E] 100, 200, 300, 400, 500, 600.

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Video Transcript

Without calculating the exact standard deviations of the following sets, determine which of them has the lowest standard deviation.

Standard deviation is a measure that is used to quantify the amount of variation from the mean of a set of data values. In this case, we will look at the five sets and see which ones are closest to the mean. For set A, our mean is 41.16 recurring. For set B, our mean is 43.16 recurring. Set C has a mean of 312.5. The mean for set D is 35. And the mean for set E is 350.

It’s immediately clear that sets D and E contain values that are a long way away from the mean. Therefore, the data is spread out. This means that these two sets would have a high standard deviation. Whilst five of the values in set C are equal to 75, the final value 1500 is an outlier as it is a long way away from the other data values. This has resulted in the mean being much higher β€” 312.5. Therefore, once again, the standard deviation would be large for this data set.

Whilst all the values in set B are relatively close to the mean, set A’s values are all within one of the mean. Five of the values are 41, one of the values is 42, and the mean is 41.16 recurring. This means that set A would have the lowest standard deviation as the variation from the mean is lowest.

We could calculate the exact standard deviation of each data set using the formula square root of the sum of π‘₯ minus π‘₯ bar all squared divided by 𝑛, where π‘₯ bar is the mean of the data set and 𝑛 is the number of terms in the data set.

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