How To Find The Median Of Even Set Of Numbers

Supplement for the Lesson on Mean, Median, and Mode

In this lesson supplement we will explore the the three virtually common summaries of a collection of numbers or data. These are called the mean, the median and the mode. The mean is a fancy give-and-take for the average, the median is the centre number, and the way is the number that occurs most frequently.

Finding the Mean

Information technology is a mutual occurrence to have several numbers, called information, that we want to make sense of. Most people are familiar with the word "average" and many know that to find the boilerplate, we add upwards all the numbers and divide by the total. Another word for the boilerplate is the mean.

To find the mean, simply all up all the numbers and split up past the total number of numbers. We can think of this as a 3 stride process:

Stride-past-Pace Process to Find the Hateful

Footstep 1: Add upward all the numbers. The result is called the sum.

Step 2: Count how many numbers there are. This number is chosen the sample size. We use the letter of the alphabet n for the sample size.

Footstep 3: The mean is the sum divided by the sample size northward .

Now lets go to an instance.

Example 1

Over the by five weekends, Steve kept rails of the full amount of coin he spent.

$20, $l, $70, $80, $30

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

Solution

Step ane: Add the numbers to find their sum.

twenty + 50 + 70 + fourscore + thirty = 250

Step 2: How many numbers where there.

n = 5

Footstep 3: Separate the sum of the numbers past the sample size 'n'

250
= 50
v

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

Now try ane by yourself. If you want to see the answer, put the mouse on the yellow rectangle and the respond will appear.

Exercise 1

The chart beneath shows the times in minutes that three runners had in their three trials for the 1 mile rails race.

	Trial ane	Trial 2	Trial 3	Trial 4
Enrique	viii	seven	7	9
Monique	ix	6	6	7
Sam	10	12	9	eleven

What was Monique's hateful time?

Answer:

Finding the Median

Some other fashion of describing the information is by looking at the middle number. When at that place are an odd number of values, we can just find the value so that there are the same number of values higher up as at that place are below this heart value. When in that location is an even number of values, there is an upshot in there there is not one number that acts every bit a middle value. Instead, the two middle numbers such that at that place are the same number of values above equally below these two middle numbers. Every bit a compromise, we accept the average of these ii center numbers. We call this effect the median of the data. It might assist to summarize this in a 3-pace process.

Step past Step Process for Finding the Median

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

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

Step 3: If there is an odd number of numbers, this heart number is the median. If there is an even number of numbers add the two middles and divide by 2 . The result will be the median.

Case two

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

18, 10, 13, 10, 17, 11, 9

Find the median weight

Solution

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

9, 10, 10, 11, 13, 17, 18

Step ii: Find that there are seven numbers. This is an odd number of values, then we locate the center number. The eye number is 11. Observe that there are an equal number (3) of numbers to the left of 11 and to the right of xi.

9, 10, 10, 11 , 13, 17, 18

Footstep 3: Nosotros are in the case that there are an odd number of values, so the median is this middle number. That is, the median is 11.

Now try one by yourself. If you want to run into the answer, put the mouse on the yellowish rectangle and the answer will appear.

Exercise 2

5 of Chang-hee's homework scores for her math class have been graded. Her scores are shown below.

Find her median homework score.

Answer:

Hither is some other case of finding the median.

Example three

There are six brothers and sisters in Lupe's family. Their ages are shown below

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

Solution

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

xi, xi, 14, 18, xx, 22

Footstep 2: Observe that in that location are vi numbers. This is an even number of values, and so nosotros locate the two eye numbers. The ii centre numbers are 14 and 18. Notice that at that place are an equal number (2) of values to the left and to the right of these ii middles.

11, eleven, xiv , 18 , 20, 22

Stride 3: We are in the case that there are an even number of values, so the median is this average of the ii middle numbers. Add these two center numbers and dissever by two.

14 + 18
= 16
2

So the median age of the brothers and sisters in Lupe's family is 16.

Now try i by yourself. If you lot desire to meet the answer, put the mouse on the xanthous rectangle and the answer volition announced.

Practise 3

Oscar priced eight desk-bound 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?

Answer:

Finding the Mode

A third number that we use to draw data is chosen the way of the data. The style is the number or numbers that occur the most frequently. Here is a two-step procedure for finding the fashion.

Two- Footstep Procedure for Finding the Median

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

Step 2: Go downwards the list and determine if at that place is a number that appears in the list more than than any other numbers. If the is a tie for the most frequently occurring number, so just state that both numbers are the way.

Case 4

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

9 0, 50, lxx, eighty, 30, 60, 50, 30, fifty

What is the mode of these data?

Solution

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

30, thirty, 50, l, 50, threescore, 70, 80, 90

Pace two: Now go down the list and make up one's mind if there is a number that appears in the list more any other number.

30, 30, 50 , 50 , 50 , 60, 70, 80, xc

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

At present attempt one by yourself. If y'all want to see the answer, put the mouse on the yellow rectangle and the answer volition appear.

Do 4

The number of bookcases that each of x workers produced at a custom article of furniture factory is shown in the box below

4, 6, 2, four, 6, 5, 2, 7, half-dozen, iii

What is the mode of these data?

Answer:

At present for another instance.

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

seven, 9, nine, four, 11, 7, 9, 12, iii, 7

What is the way of these data?

Solution

Footstep one: First, put the numbers in size place, smallest to largest.

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

Step 2: Now go down the list and determine if there is a number that appears in the list more than whatsoever other number.

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

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

NOTE: There may be No mode, ONE mode, or multiple modes for a given sample of numbers.

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

Exercise 4

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

v, 4, five, 8, 2, 2, 1, 6, five, ane, 2

What is the way of these information?

Answer:

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