How To Find The Median In Odd Set Of Numbers

Supplement for the Lesson on Mean, Median, and Manner

In this lesson supplement nosotros will explore the the three most common summaries of a collection of numbers or data.  These are called the mean, the median and the mode.  The mean is a fancy word for the average, the median is the heart number, and the style is the number that occurs most frequently.

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Finding the Hateful

It is a common occurrence to have several numbers, called data, that we want to make sense of.  Nigh people are familiar with the word "average" and many know that to find the average, we add upwardly all the numbers and dissever by the total.  Another give-and-take for the average is the hateful.

To detect the hateful, just all upward all the numbers and divide past the total number of numbers.  Nosotros can recall of this as a iii step process:

Step-past-Footstep Procedure to Find the Mean

Footstep one:  Add up all the numbers.  The effect is called the sum.

Step 2:   Count how many numbers there are.  This number is chosen the sample size.  Nosotros apply the letter north for the sample size.

Step three:   The mean is the sum divided by the sample size northward .

Now lets go to an example.

Example i

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

      $20, $50, $70, $eighty, $30

Find the hateful corporeality of money Steve spent over the past five weekends.

Solution

Step 1: Add the numbers to find their sum.

      twenty + l + 70 + 80 + xxx = 250

Step 2: How many numbers where there.

n = 5

Pace three: Dissever the sum of the numbers by the sample size 'due north'

      250
   =  50
5

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

Now endeavor 1 by yourself.  If yous want to meet the answer, put the mouse on the xanthous rectangle and the answer will announced.

Exercise 1

The chart below shows the times in minutes that three runners had in their 3 trials for the i mile runway race.

	Trial i	Trial 2	Trial iii	Trial four
Enrique	8	seven	7	9
Monique	9	6	6	7
Sam	10	12	9	11

What was Monique'due south hateful fourth dimension?

Respond:

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Finding the Median

Another manner of describing the information is by looking at the middle number.  When there are an odd number of values, we can only observe the value and then that in that location are the aforementioned number of values above as there are below this centre value.  When there is an even number of values, there is an issue in there there is not one number that acts as a middle value.  Instead, the two center numbers such that there are the same number of values to a higher place as below these two middle numbers.  As a compromise, nosotros have the boilerplate of these 2 eye numbers.  We telephone call this result the median of the data.  Information technology might help to summarize this in a 3-pace process.

Step by Footstep Process for Finding the Median

Step 1:  Put the numbers in numerical order from smallest to largest.

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

Step iii:  If at that place is an odd number of numbers, this middle number is the median.  If there is an even number of numbers add the two middles and divide by two .  The effect will be the median.

Case 2

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

xviii, 10, 13, 10, 17, 11, 9

        Detect the median weight

Solution

Footstep 1: Starting time, put the numbers in numerical society from smallest to largest.

            nine, 10, 10, 11, thirteen, 17, 18

Step 2: Notice that at that place are 7 numbers.  This is an odd number of values, so we locate the middle number.  The middle number is 11.  Notice that at that place are an equal number (3) of numbers to the left of eleven and to the right of xi.

            ix, 10, 10, 11 , 13, 17, eighteen

Step 3: We are in the instance that in that location are an odd number of values, so the median is this heart number.  That is, the median is eleven.

Now try one past yourself.  If you want to see the respond, put the mouse on the yellowish rectangle and the reply volition appear.

Do 2

Five of Chang-hee'south homework scores for her math class take been graded.  Her scores are shown below.

        Find her median homework score.

Respond:

Here is another example of finding the median.

Example 3

There are half-dozen brothers and sisters in Lupe's family unit.  Their ages are shown below

        Find the median age of the brothers and sisters in Lupe'south family unit.

Solution

Step 1: First, put the numbers in numerical social club from smallest to largest.

11, 11, 14, 18, twenty, 22

Step two: Observe that there are 6 numbers.  This is an fifty-fifty number of values, and so nosotros locate the ii centre numbers.  The ii center numbers are 14 and xviii.  Detect that in that location are an equal number (2) of values to the left and to the correct of these two middles.

xi, eleven, 14 , eighteen , 20, 22

Pace iii: Nosotros are in the case that there are an fifty-fifty number of values, and so the median is this average of the two heart numbers.  Add these two middle numbers and divide past two.

        14 + 18
    =  xvi

2

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

Now attempt ane by yourself.  If yous want to see the answer, put the mouse on the yellow rectangle and the reply will appear.

Exercise 3

Oscar priced eight desk lamps.  The prices are shown below.

$24.00, $48.00, $25.00, $thirty.00, $36.00, $52.00, $25.00, $90.00

        What is the median price?

Reply:

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Finding the Mode

A third number that nosotros use to draw data is chosen the mode of the information.  The mode is the number or numbers that occur the almost frequently.  Here is a two-footstep process for finding the manner.

Two- Step Procedure for Finding the Median

Step i:  Put the numbers in numerical social club from smallest to largest.

Stride 2:  Become downwards the listing and determine if there is a number that appears in the list more than any other numbers.  If the is a tie for the about ofttimes occurring number, then just state that both numbers are the manner.

Instance four

The box below shows the number of customers that a restaurant has had during the past 9 days

ix 0, fifty, 70, 80, 30, 60, 50, thirty, fifty

What is the fashion of these data?

Solution

Step i: Offset, put the numbers in size place, smallest to largest.

        30, 30, 50, 50, 50, 60, 70, fourscore, 90

Footstep two: At present become downward the list and determine if there is a number that appears in the list more any other number.

        thirty, 30, l , l , 50 , 60, lxx, fourscore, 90

Here that number is l. Therefore, l is the style.

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

Do 4

The number of bookcases that each of 10 workers produced at a custom furniture manufacturing plant is shown in the box below

4, 6, ii, 4, vi, 5, two, seven, half dozen, 3

        What is the mode of these information?

Respond:

At present for another instance.

Case 5
The box below shows the number of trees growing in the lawn of each house on plumb street.

7, 9, 9, 4, xi, seven, 9, 12, iii, seven

        What is the manner of these information?

Solution

Step 1: First, put the numbers in size place, smallest to largest.

        3, 4, 7, 7, 7, nine, nine, 9, 11, 12

Step 2: Now go down the listing and determine if at that place is a number that appears in the list more than any other number.

        3, 4, 7 , 7 , 7 , 9 , 9 , 9 , 11, 12

Here nosotros see that both the numbers seven and nine appear three times. Therefore, both 7 and nine are both modes

Annotation: In that location may be No style, One mode, or multiple modes for a given sample of numbers.

At present endeavour ane by yourself.  If you desire to come across the answer, put the mouse on the yellowish rectangle and the respond will appear.

Exercise 4

Sarah was studying how many pairs of Stellar Jays were living inside each of 11 acres of state in the national forest.  Her data are shown in the box beneath

v, four, 5, 8, 2, two, one, 6, v, 1, 2

        What is the fashion of these data?

Respond:

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

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