How To Find The Median Of A Set Of Even Numbers

Supplement for the Lesson on Mean, Median, and Mode

In this lesson supplement nosotros will explore the the three almost common summaries of a collection of numbers or data.  These are called the hateful, the median and the manner.  The mean is a fancy word for the boilerplate, the median is the centre number, and the mode is the number that occurs almost frequently.

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Finding the Mean

It is a mutual occurrence to have several numbers, called data, that we want to make sense of.  Most people are familiar with the discussion "average" and many know that to find the average, we add up all the numbers and divide by the full.  Another word for the average is the mean.

To find the mean, only all up all the numbers and divide past the full number of numbers.  We tin recollect of this as a three stride process:

Stride-by-Footstep Procedure to Discover the Mean

Step i:  Add upwards all the numbers.  The outcome is called the sum.

Step ii:   Count how many numbers there are.  This number is called the sample size.  Nosotros use the letter n for the sample size.

Step 3:   The mean is the sum divided by the sample size n .

Now lets become to an example.

Example one

Over the past five weekends, Steve kept rail of the total amount of coin he spent.

      $xx, $50, $70, $80, $xxx

Discover the mean amount of money Steve spent over the past five weekends.

Solution

Step 1: Add the numbers to observe their sum.

      20 + l + lxx + 80 + xxx = 250

Footstep 2: How many numbers where there.

n = 5

Stride iii: Divide the sum of the numbers by the sample size 'north'

      250
   =  50
5

Therefore the mean of these numbers is 50. We conclude that the mean corporeality of money that Steve spent over the past 5 weekends was $l.

At present try one by yourself.  If you lot want to encounter the answer, put the mouse on the yellow rectangle and the answer will appear.

Exercise 1

The chart below shows the times in minutes that iii runners had in their three trials for the one mile track race.

	Trial 1	Trial 2	Trial 3	Trial iv
Enrique	8	vii	7	9
Monique	9	half-dozen	half dozen	7
Sam	x	12	ix	11

What was Monique'due south mean fourth dimension?

Answer:

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Finding the Median

Another way of describing the information is past looking at the middle number.  When there are an odd number of values, we tin but discover the value so that at that place are the same number of values above equally there are below this middle value.  When in that location is an even number of values, there is an issue in there there is not ane number that acts every bit a middle value.  Instead, the two centre numbers such that there are the same number of values to a higher place as below these two centre numbers.  Equally a compromise, we take the average of these 2 centre numbers.  We call this result the median of the information.  It might help to summarize this in a 3-footstep process.

Footstep by Footstep Process for Finding the Median

Stride 1:  Put the numbers in numerical guild from smallest to largest.

Step 2:  If at that place is an odd number of numbers, locate the middle number and then that there is an equal number of values to the left and to the correct.  If there is an even number of numbers locate the two middle numbers and so that there is an equal number of values to the left and to the right of these ii numbers.

Step 3:  If in that location is an odd number of numbers, this eye number is the median.  If there is an even number of numbers add together the two middles and divide past 2 .  The consequence will exist the median.

Example ii

Rosa measured the weight in pounds of seven packages bags of oranges that were purchased at her fruit stand.  The weights are shown below.

xviii, x, xiii, 10, 17, 11, 9

        Detect the median weight

Solution

Pace 1: First, put the numbers in numerical order from smallest to largest.

            9, 10, 10, 11, 13, 17, 18

Footstep 2: Detect that there are 7 numbers.  This is an odd number of values, so nosotros locate the middle number.  The middle number is 11.  Notice that there are an equal number (3) of numbers to the left of 11 and to the right of 11.

            9, 10, 10, 11 , thirteen, 17, xviii

Step three: We are in the case that there are an odd number of values, then the median is this centre number.  That is, the median is xi.

Now attempt one past yourself.  If you want to meet the answer, put the mouse on the yellow rectangle and the respond will appear.

Exercise ii

5 of Chang-hee'due south homework scores for her math course have been graded.  Her scores are shown beneath.

        Discover her median homework score.

Answer:

Here is some other example of finding the median.

Example 3

There are 6 brothers and sisters in Lupe'due south family.  Their ages are shown below

        Find the median historic period of the brothers and sisters in Lupe'southward family unit.

Solution

Step ane: First, put the numbers in numerical order from smallest to largest.

xi, 11, xiv, xviii, 20, 22

Footstep 2: Notice that there are six numbers.  This is an even number of values, so we locate the ii middle numbers.  The two center numbers are fourteen and 18.  Find that at that place are an equal number (2) of values to the left and to the right of these two middles.

11, 11, fourteen , 18 , twenty, 22

Step 3: We are in the case that there are an even number of values, then the median is this average of the 2 eye numbers.  Add these two centre numbers and divide past ii.

        14 + 18
    =  xvi
2

So the median age of the brothers and sisters in Lupe's family is sixteen.

At present endeavor one by yourself.  If you lot desire to see the answer, put the mouse on the yellowish rectangle and the reply will appear.

Exercise three

Oscar priced eight desk-bound lamps.  The prices are shown beneath.

$24.00, $48.00, $25.00, $30.00, $36.00, $52.00, $25.00, $ninety.00

        What is the median price?

Respond:

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Finding the Style

A third number that we utilise to describe data is chosen the style of the information.  The way is the number or numbers that occur the nigh frequently.  Here is a ii-stride process for finding the mode.

Two- Pace Process for Finding the Median

Pace 1:  Put the numbers in numerical society from smallest to largest.

Footstep 2:  Go down the list and determine if in that location is a number that appears in the list more than any other numbers.  If the is a tie for the virtually frequently occurring number, and then just state that both numbers are the fashion.

Instance 4

The box below shows the number of customers that a eating place has had during the by nine days

9 0, fifty, 70, 80, thirty, lx, 50, 30, 50

What is the style of these data?

Solution

Step 1: Commencement, put the numbers in size identify, smallest to largest.

        thirty, 30, 50, 50, l, lx, seventy, eighty, 90

Step two: Now go down the list and determine if in that location is a number that appears in the list more than any other number.

        30, 30, 50 , l , 50 , threescore, lxx, fourscore, 90

Here that number is 50. Therefore, 50 is the mode.

At present try one by yourself.  If you want to see the answer, put the mouse on the yellow rectangle and the answer will appear.

Practise iv

The number of bookcases that each of 10 workers produced at a custom furniture factory is shown in the box beneath

4, 6, ii, 4, 6, 5, ii, 7, 6, three

        What is the manner of these data?

Answer:

Now for another example.

Example 5
The box below shows the number of trees growing in the backyard of each business firm on plumb street.

vii, ix, 9, iv, 11, 7, nine, 12, 3, vii

        What is the manner of these data?

Solution

Pace 1: Start, put the numbers in size place, smallest to largest.

        3, 4, seven, 7, vii, 9, 9, 9, 11, 12

Step ii: Now go down the list and determine if there is a number that appears in the list more than than any other number.

        three, 4, 7 , 7 , vii , nine , nine , 9 , xi, 12

Here we see that both the numbers 7 and 9 appear three times. Therefore, both 7 and ix are both modes

NOTE: There may exist No mode, One manner, or multiple modes for a given sample of numbers.

Now try one by yourself.  If you desire to see the answer, put the mouse on the yellow rectangle and the answer volition appear.

Exercise 4

Sarah was studying how many pairs of Stellar Jays were living within each of 11 acres of country in the national wood.  Her information are shown in the box below

5, four, 5, 8, 2, 2, 1, 6, v, i, 2

        What is the mode of these data?

Answer:

Source: https://ltcconline.net/greenl/courses/CAHSEE/StatisticsProb/CAHSEEMeanMedianMode.htm

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