# When calculating to find the mean and standard deviation of these two sets of numbers: (a)4 0 1 4 3 6 (b)5 3 1 3 4 2 Which data set is more spread out?

##### 1 Answer

Data-set **(a)** is more spread out.

#### Explanation:

Both the given data sets have exactly

As regards which data is more spread out, there are mainly three measures for the same.

First is **Range**, which is the difference of larges and smallest data point. As the range of data-set **(a)** is **(b)** is **(a)** is more spread out.

Another measure is **mean deviation**, which is the average of difference (i.e. absolute value) between data point and mean.

In data-set **(a)** absolute value of deviations (note it makes deviations positive and hence does not cancel out, which will happen if we keep positive or negative sign of differences) is **(b)** absolute value of deviations is **(a)** is higher, it is more spread out.

The third measure is **standard deviation**, for which we square the deviations (again to make them positive), take their average and then take square root.

We have already worked out deviations above. In data-set **(a)** squares of deviations are**(b)** squares of deviations are **(a)** is higher, it is more spread out.