Question

The values for three sets of data are shown below. Data Data Set Values 1 42, 48, 50, 88, 49 2 63, 29, 35, 28, 30 3 2, 5, 3, 8 Without calculating any statistics, Anna knows that data set 3 would have the least mean absolute deviation among the three sets. Which statement explains how she knows?

Answer 1

Answer:

data set 3 would have the least mean absolute deviation among the three sets since there is less spread of the data and the data values in set-3 lie close to the mean.

Step-by-step explanation:

The mean absolute deviation is a  measure of spread of the data.

• If the data values in the given data set are widely spread then we obtain a higher mean absolute deviation.

• if the data values of a given data set are close to each other i.e there is a less spread of the data and hence the mean absolute deviation will be low as the data values will lie close to the mean.

We are given three data set as:

set- 1             42, 48, 50, 88, 49

set- 2             63, 29, 35, 28, 30

set- 3                2, 5, 3, 8

Hence, we could observe that the data values in set 1 and set 2 are widely spread.

In set-1 the data value 88 is  much higher value as compared to other data values.

Similarly in set-2 the data value 63 is again a much higher value as compared to other data values.

Whereas in set-3 the data values are all closely related and there is not much spread in the data.

Answer 2

Answer:

data set 3 would have the least mean absolute deviation among the three sets since there is less spread of the data and the data values in set-3 lie close to the mean.