In statistics, the mode is the value that occurs the most frequently in a data set or a . In some fields, notably education, sample data are often called scores, and the sample mode is known as the modal score .
Like the statistical mean and the median, the mode is a way of capturing important information about a random variable or a population in a single quantity.
The mode is at best a rough measure and is generally less useful than the mean or median.
Example 1:
|
Marks
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1
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2
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3
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4
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5
|
6
|
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Number of students (Frequency)
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7
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9
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10
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x
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9
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11
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Solution:
x is as least 12
(if x is less than 12 then 4 will not be the mode)
Example 2:
The number of points scored
in a series of football games for Manchester united club is listed below. Which score occurred most often?
8, 14, 19, 23, 9, 3, 19, 5
Solution: Ordering the scores from least to greatest, we get:
3, 5, 8, 9, 14, 19, 19, 23
Answer: The score which occurs most often is 19.
Example
3:
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
4: 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.
