# The Mode of a Set of Data

Problem: The number of points scored in a series of football games is listed below. Which score occurred most often?

7,  13,  18,  24,  9,  3,  18

Solution: Ordering the scores from least to greatest, we get:

3,  7,  9,  13,  18,  18,  24

Answer: The score which occurs most often is 18.

This problem really asked us to find the mode of a set of 7 numbers.

Definition: The mode of a set of data is the value in the set that occurs most often.

In the problem above, 18 is the mode. It is easy to remember the definition of a mode since it has the word most in it. The words mode and most both start with the letters mo. Let's look at some more examples.

Example 1: The following is the number of problems that Ms. Matty assigned for homework on 10 different days. What is the mode?

8,  11,  9,  14,  9,  15,  18,  6,  9,  10

Solution: Ordering the data from least to greatest, we get:

6,  8,  9,  9,  9,  10,  11  14,  15,  18

Example 2: In a crash test, 11 cars were tested to determine what impact speed was required to obtain minimal bumper damage. Find the mode of the speeds given in miles per hour below.

24,  15,  18,  20,  18,  22,  24,  26,  18,  26,  24

Solution: Ordering the data from least to greatest, we get:

15,  18,  18,  18,  20,  22,  24,  24,  24,  26,  26

Answer: Since both 18 and 24 occur three times, the modes are 18 and 24 miles per hour. This data set is bimodal.

Example 3: A marathon race was completed by 5 participants. What is the mode of these times given in hours?

2.7 hr,  8.3 hr,  3.5 hr,  5.1 hr,  4.9 hr

Solution: Ordering the data from least to greatest, we get:

2.7,  3.5,  4.9,  5.1,  8.3

Answer: Since each value occurs only once in the data set, there is no mode for this set of data.

Example 4: On a cold winter day in January, the temperature for 9 North American cities is recorded in Fahrenheit. What is the mode of these temperatures?

-8,  0,  -3,  4,  12,  0,  5,  -1,  0

Ordering the data from least to greatest, we get:

-8,  -3,  -1,  0,  0,  0,  4,  5,  12

Answer: The mode of these temperatures is 0.

Let's compare the results of the last two examples. In Example 3, each value occurs only once, so there is no mode. In Example 4, the mode is 0, since 0 occurs most often in the set. Do not confuse a mode of 0 with no mode.

Summary: The mode of a set of data is the value in the set that occurs most often. A set of data can be bimodal. It is also possible to have a set of data with no mode.

### Exercises

Directions: Find the mode of each set of data. Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

 1 The test scores of 9 seventh grade students are listed below. Find the mode. 82,  92,  75 ,  91,  92,  89,  95,  100,  86 ANSWER BOX:   RESULTS BOX:
 2 The typing speeds of 12 secretaries are recorded below (in words per minute). Find the mode. 35,  43,  39,  46,  43,  47,  38,  51,  43,  38,  40,  45 ANSWER BOX:   RESULTS BOX:
 3. The manager of a video shop recorded the number of blank tapes sold per day in 2 weeks (below). Which of the following statements is true? 132,  121,  119,  116,  130,  121,  131,  117,  119,  135,  121,  129,  119,  134 There is no mode.The mode is 119.The mode is 131.The modes are 119 and 121. RESULTS BOX:
 4. Ten earthquakes were measured using the Richter scale and their magnitudes are listed below. Which of the following statements is true? 7.0,  6.2,  7.7,  8.0,  6.4,  7.2,  5.4,  6.6,  7.5,  5.9 There is no mode.The mode is 6.4.The mode is 5.4.The data set is bimodal. RESULTS BOX:
 5. Eleven daily temperatures for Juneau, Alaska are listed below, in degrees Fahrenheit. Which of the following statements is true?-21,  0,  +2,  -15,  0,  +5,  -18,  +7,  0,  -32,  +21 There is no mode.The mode is 0.The mode is -21.The data set is bimodal. RESULTS BOX:
 Introduction to Statistics Range Arithmetic Mean Non-Routine Mean Median Mode Practice Exercises Challenge Exercises Solutions