Question

An intelligence test that has a maximum time for completion of 45 minutes was recently administered to a group of 22 people. Their respective times for completion (in minutes) were as follows.

Answer 1

Given the data set:

23, 29, 32, 32, 33, 34, 37, 39, 39, 39, 39, 39, 39, 41, 42, 43, 43, 43, 43, 43, 44, 44

Let's solve for the following:

(a). Which measures of central tendency take more than one value.

• Let's find the mean.

To find the mean, we have:

The mean of the data set is 38.18. The mean has just one value.

• Let's find the mode.

The mode is the element which occurs more in the data set.

From the data set, the element that occured most is 39. This is because it occured 6 times.

Mode = 39

The mode has just one value.

• Median:

The median is the middle value.

Here the meddle elements are: 39 and 39

Since we have the middle numbers, the median will be the average of both numbers.

Therefore, there is no measure of central tendency with more than one value.

• (b). Let's replace 23 with 11 and solve for the measures of central tendency.

Mean:

The new mean is 37.63

Therefore, the mean will be affected.

Mode:

The mode will still be 39.

Median:

The median will still be 39.

Therefore, if 23 is replaced with 11, the measure that would be affected is the mean.

• (c). Let's remove the smallest measurement which is 23 and solve.

Mean:

The mean is now 38.9

Removing the smallest measurement will change the mean.

Median:

The median will still be 39.

Mode:

The mode will still be 39.

In some cases when a data is removed from a data set, it will affect the median, mode and mean. But in this case the median and mode remains the same while only the mean is affected.

Therefore, removing the smallest measurement in this given data set will change the mean.

ANSWERS:

• (a). None of these measures

,

• (b). Mean

,

• (c). Mean