- Understand the concept of mode.
- Identify the mode or modes of a data set for both quantitative and qualitative data.
- Describe a distribution of data as being unimodal, bimodal, or multimodal.
- Identify the mode of
- Understand the concept of mode.
- Identify the mode or modes of a data set for both quantitative and qualitative data.
- Describe a distribution of data as being unimodal, bimodal, or multimodal.
- Identify the mode of a set of data given in different representations.
Before class begins, bring out the blocks that you and your classmates chose from the pail for the lesson on mean. In addition, have the grid paper on display where each student in your class posted his or her number of blocks.
To begin the class, refer to the comments on the measures of central tendency that were recorded from the lesson 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.
The mode of 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 word modal is 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 called unimodal. Likewise, a data set that has 2 values that occur with the greatest frequency is referred to as bimodal. Finally, when a set of data has more than 2 values that occur with the same greatest frequency, the set is called multimodal. 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.
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:
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
The weekly wages of 7 randomly selected employees of Wendy’s were $98.00, $125.00, $75.00, $120.00, $86.00, $92.00, and $110.00, respectively. What is the mode of these wages?
Each value in the above data set occurs only once. Therefore, this data has no mode.
The ages of 12 randomly selected customers at a local coffee shop are listed below:
What is the mode of the above ages?
The above data set has 3 values that each occur with a frequency of 2. These values are 21, 23, and 24. All other values occur only once. Therefore, this set of data has 3 modes.
Modes = 21, 23, and 24
Remember that the mode can be determined for qualitative data as well as quantitative data, but th