5.6. Mode http://www.ck12.org
To begin the class, refer to the comments on the measures of central tendency that were recorded from the concept
on mean, when the brainstorming session occurred. Highlight the comments that were made with regard to the mode
of a set of data and discuss this measure of central tendency with your classmates. Once the discussion has been
completed, choose a handful of blocks like you did before, with your classmates doing the same.
The mode of the set of blocks can be given as a quantitative value or as a qualitative value. You and your classmates
can tell from the grid paper which number of blocks was picked most. The chart below shows that 5 students each
picked 5 blocks from the pail. This is a mode for quantitative data, since the answer is in the form of a number.
To extend the mode to include qualitative data, you and your classmates should each now determine the color or
colors of block(s) that appear most often in each of your handfuls. To do this, group your blocks according to color
and count them, and have your classmates do the same. There may be more than 1 color that occurs with the same
highest frequency. The color(s) that appear most often for each handful of blocks is the mode for that particular
handful.
Themodeof a set of data is simply the value that appears most frequently in the set. If 2 or more values appear with
the same frequency, each is a mode. The downside to using the mode as a measure of central tendency is that a set
of data may have no mode or may have more than 1 mode. However, the same set of data will have only 1 mean
and only 1 median. The wordmodalis often used when referring to the mode of a data set. If a data set has only 1
value that occurs most often, the set is calledunimodal. Likewise, a data set that has 2 values that occur with the
greatest frequency is referred to asbimodal. Finally, when a set of data has more than 2 values that occur with the
same greatest frequency, the set is calledmultimodal. When determining the mode of a data set, calculations are
not required, but keen observation is a must. The mode is a measure of central tendency that is simple to locate, but
it is not used much in practical applications.
Example A
The posted speed limit along a busy highway is 65 miles per hour. The following values represent the speeds (in
miles per hour) of 10 cars that were stopped for violating the speed limit:
76 81 79 80 78 83 77 79 82 75
What is the mode?
There is no need to organize the data, unless you think that it would be easier to locate the mode if the numbers were
arranged from least to greatest. In the above data set, the number 79 appears twice, but all the other numbers appear
only once. Since 79 appears with the greatest frequency, it is the mode of the data values.
Mode = 79 miles per hour