How To Find The Mode Of A Set Of Data

Learning Outcomes

Detect the fashion of a set of numbers

The average is ane number in a set of numbers that is somehow typical of the whole set of numbers. The mean and median are both often called the boilerplate. Yes, it can be confusing when the word average refers to two different numbers, the hateful and the median! In fact, there is a 3rd number that is also an average. This average is the fashion. The mode of a set of numbers is the number that occurs the most. The frequency, is the number of times a number occurs. So the manner of a gear up of numbers is the number with the highest frequency.

Manner

The way of a set of numbers is the number with the highest frequency.

Suppose Jolene kept rail of the number of miles she ran since the offset of the month, as shown in the calendar below.

An image of a calendar is shown. On Thursday the first, labeled New Year's Day, is written 2 mi. On Saturday the third is written 15 mi. On the 4th, 8 mi. On the 6th, 3 mi. On the 7th, 8 mi. On the 9th, 5 mi. On the 10th, 8 mi.
If we list the numbers in order it is easier to identify the i with the highest frequency.

[latex]two,3,5,8,8,8,fifteen[/latex]
Jolene ran [latex]8[/latex] miles three times, and every other distance is listed simply once. And so the style of the data is [latex]viii[/latex] miles.

Identify the fashion of a set of numbers.

Listing the data values in numerical order.
Count the number of times each value appears.
The way is the value with the highest frequency.

example

The ages of students in a college math form are listed beneath. Place the way.
[latex]eighteen,eighteen,18,eighteen,19,19,19,20,20,20,20,20,xx,20,21,21,22,22,22,22,22,23,24,24,25,29,30,40,44[/latex]

Solution
The ages are already listed in order. We will make a table of frequencies to help place the age with the highest frequency.

A table is shown with 2 rows. The first row is labeled 'Age' and lists the values: 18, 19, 20, 21, 22, 23, 24, 25, 29, 30, 40, and 44. The second row is labeled 'Frequency' and lists the values: 4, 3, 7, 2, 5, 1, 2, 1, 1, 1, 1, and 1.
Now look for the highest frequency. The highest frequency is [latex]7[/latex], which corresponds to the age [latex]xx[/latex]. So the manner of the ages in this class is [latex]twenty[/latex] years.

TRY Information technology

The number of sick days employees used last twelvemonth: [latex]3,vi,2,3,seven,5,6,ii,iv,two[/latex]. Identify the mode.

[latex]two[/latex]

#146433

The number of handbags owned by women in a book club: [latex]five,vi,3,1,5,8,1,v,8,5[/latex]. Identify the mode.

[latex]5[/latex]

example

The data lists the heights (in inches) of students in a statistics grade. Identify the mode.

[latex]56[/latex]	[latex]61[/latex]	[latex]63[/latex]	[latex]64[/latex]	[latex]65[/latex]	[latex]66[/latex]	[latex]67[/latex]	[latex]67[/latex]
[latex]60[/latex]	[latex]62[/latex]	[latex]63[/latex]	[latex]64[/latex]	[latex]65[/latex]	[latex]66[/latex]	[latex]67[/latex]	[latex]70[/latex]
[latex]sixty[/latex]	[latex]63[/latex]	[latex]63[/latex]	[latex]64[/latex]	[latex]66[/latex]	[latex]66[/latex]	[latex]67[/latex]	[latex]74[/latex]
[latex]61[/latex]	[latex]63[/latex]	[latex]64[/latex]	[latex]65[/latex]	[latex]66[/latex]	[latex]67[/latex]	[latex]67[/latex]

TRY Information technology

The ages of the students in a statistics class are listed here: [latex]19[/latex] , [latex]20[/latex] , [latex]23[/latex] , [latex]23[/latex] , [latex]38[/latex] , [latex]21[/latex] , [latex]xix[/latex] , [latex]21[/latex] , [latex]nineteen[/latex] , [latex]21[/latex] , [latex]20[/latex] , [latex]43[/latex] , [latex]20[/latex] , [latex]23[/latex] , [latex]17[/latex] , [latex]21[/latex] , [latex]21[/latex] , [latex]20[/latex] , [latex]29[/latex] , [latex]18[/latex] , [latex]28[/latex] . What is the mode?

[latex]21[/latex]

#146434

Students listed the number of members in their household as follows: [latex]6[/latex] , [latex]2[/latex] , [latex]5[/latex] , [latex]6[/latex] , [latex]3[/latex] , [latex]7[/latex] , [latex]v[/latex] , [latex]6[/latex] , [latex]5[/latex] , [latex]3[/latex] , [latex]iv[/latex] , [latex]four[/latex] , [latex]v[/latex] , [latex]vii[/latex] , [latex]6[/latex] , [latex]4[/latex] , [latex]five[/latex] , [latex]2[/latex] , [latex]1[/latex] , [latex]5[/latex] . What is the mode?

[latex]5[/latex]

Some data sets do not have a mode considering no value appears more than any other. And some data sets take more than one manner. In a given set, if two or more than data values take the same highest frequency, we say they are all modes.

Watch teh following video for some other example of how to notice the style of a information set up.