Question

Which of the following is true about the standard deviations of the two data sets in the table above?

- The standard deviation of data set B is larger than the standard deviation of data set A.
- The standard deviation of data set A is larger than the standard deviation of data set B .
- The standard deviation of data set A is equal to the standard deviation of data set B .
- There is not enough information available to compare the standard deviations of the two data sets.

Hint:

**Hint:**

Standard deviation is measure of how dispersed the data is from the mean. In simpler terms, it measures how much the data is clustered around the mean and how farther it is. We need to observe the given sets of data and see which one of these is more dispersed, that one will have a larger standard deviation.

## The correct answer is: The standard deviation of data set B is larger than the standard deviation of data set A.

### The mean of data set A is given by:

The mean of data set B is given by:

We can clearly observe that the values in Data set B are dispersed from the mean, whereas the values in Data set A are not so dispersed.

Hence, the standard deviation of data set B is larger than the standard deviation of data set A.

Thus, the correct option is A

**Note:**

We could also calculate the standard deviation for both the data sets

The formula for standard deviation is

Where,

= standard deviation

= total number of terms

= terms given in the data

= mean

After finding both the standard deviations, we can compare them. This is a tedious task and needs precision.

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