Question

Which of the following lists of data has the largest standard deviation? Hint: you should not need to compute the standard deviation for each list.Select the correct answer below:22, 25, 25, 22, 25, 23, 24, 23, 26, 2413, 11, 11, 11, 10, 14, 14, 10, 11, 1116, 14, 15, 15, 16, 16, 15, 16, 18, 1425, 23, 25, 22, 21, 25, 22, 21, 25, 237, 14, 19, 18, 4, 16, 5, 11, 11, 12

Answer 1

7, 14, 19, 18, 4, 16, 5, 11, 11, 12

Explanation:

The standard deviation is a statistic that measures the spread of a dataset relative to its mean.

From the given options, find the range in each of them:

`Range=Highest\;Value-Lowest\;Value`

• Option 1: Range = 26-22=4

,

• Option 2: Range=14-10=4

,

• Option 3: Range=18-14=4

,

• Option 4: Range = 25-21=4

,

• Option 5: Range = 19-4=15

We see that the dataset in Option 5 has a far greater range and thus the dataset will have the biggest spread relative to its mean.

Option 5 has the largest standard deviation.