Textbook Problem

Terminology Consider the following measures of central tendency: mean, median, mode. Match each type to the appropriate description:

(i) the central value of a data set after it has been ordered from smallest to largest

(ii) the data value occurring most frequently in a data set

(iii) the sum of all the data values in a data set divided by the number of data values in the set

To determine

The mean or median or mode type to the appropriate description.

Answer to Problem 1CR

Solution: Median for (i), mode for (ii), and mean for (ii).

Explanation of Solution

The median of a set of data values is the middle (center) value of the data set when it has been arranged in ascending order. To find the median, organize each number in order by size; the number in the middle is the median.

Hence, the (i) description that the central value of a data set after it has been ordered from smallest to largest is called the median of the data.

The mode is the most common number in the set of data or this is the number that occurs most often. The average that represents the most frequent value of the distribution is called mode. So, the mode is appropriate to (ii) description.

The mean is often called the average. To find the mean, take a set of data and calculate the sum of the data, after that divide the sum by the number of pieces in the set. Hence, mean takes all specific values into account. The mean is appropriate to (iii) description.