How To Find The Median If There Are Two Numbers

Supplement for the Lesson on Mean, Median, and Mode

In this lesson supplement nosotros will explore the the 3 almost mutual summaries of a drove of numbers or data. These are called the hateful, the median and the mode. The mean is a fancy word for the average, the median is the middle number, and the fashion is the number that occurs near frequently.

Finding the Mean

Information technology is a mutual occurrence to have several numbers, called data, that we want to brand sense of. Virtually people are familiar with the discussion "boilerplate" and many know that to find the average, we add upward all the numbers and divide by the full. Another word for the average is the mean.

To notice the mean, just all up all the numbers and split up past the total number of numbers. Nosotros can think of this as a three pace process:

Footstep-past-Stride Procedure to Find the Mean

Footstep ane: Add up all the numbers. The result is chosen the sum.

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

Footstep 3: The hateful is the sum divided by the sample size n .

Now lets get to an example.

Example 1

Over the past five weekends, Steve kept runway of the total amount of money he spent.

$twenty, $50, $seventy, $lxxx, $30

Find the mean amount of money Steve spent over the by v weekends.

Solution

Step 1: Add the numbers to observe their sum.

20 + l + 70 + lxxx + 30 = 250

Step 2: How many numbers where at that place.

northward = five

Step iii: Divide the sum of the numbers by the sample size 'northward'

250
= 50
5

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

Now try ane by yourself. If y'all desire to see the answer, put the mouse on the yellow rectangle and the answer will appear.

Exercise i

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

	Trial 1	Trial ii	Trial 3	Trial four
Enrique	8	7	7	9
Monique	ix	6	6	vii
Sam	10	12	9	11

What was Monique's mean time?

Answer:

Finding the Median

Another way of describing the data is past looking at the middle number. When in that location are an odd number of values, we tin can but find the value so that there are the same number of values higher up every bit there are below this centre value. When in that location is an even number of values, there is an issue in there there is non 1 number that acts as a middle value. Instead, the ii middle numbers such that in that location are the same number of values above as below these ii middle numbers. As a compromise, we take the average of these ii eye numbers. We call this result the median of the information. It might help to summarize this in a iii-step process.

Footstep by Stride Process for Finding the Median

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

Footstep 2: If there is an odd number of numbers, locate the middle number and so that in that location is an equal number of values to the left and to the right. If there is an even number of numbers locate the two middle numbers so that at that place is an equal number of values to the left and to the right of these ii 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 ii middles and separate by ii . The outcome volition exist the median.

Example 2

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, xiii, ten, 17, 11, nine

Notice the median weight

Solution

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

9, ten, 10, xi, thirteen, 17, 18

Step 2: Notice that there are 7 numbers. This is an odd number of values, and so we locate the middle number. The middle number is 11. Discover that there are an equal number (3) of numbers to the left of 11 and to the correct of 11.

9, ten, 10, 11 , 13, 17, eighteen

Stride 3: We are in the instance that there are an odd number of values, so the median is this eye number. That is, the median is 11.

Now try one past yourself. If y'all want to see the answer, put the mouse on the yellowish rectangle and the reply will announced.

Exercise 2

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

Find her median homework score.

Answer:

Here is another example of finding the median.

Example three

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

Notice the median historic period of the brothers and sisters in Lupe'south family.

Solution

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

11, 11, 14, eighteen, twenty, 22

Footstep 2: Detect that there are six numbers. This is an even number of values, so we locate the two middle numbers. The two middle numbers are 14 and eighteen. Notice that there are an equal number (ii) of values to the left and to the right of these two middles.

11, xi, 14 , 18 , xx, 22

Footstep 3: We are in the case that there are an even number of values, and then the median is this average of the ii middle numbers. Add these ii middle numbers and divide by 2.

14 + 18
= 16
ii

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

Now attempt one by yourself. If you want to see the answer, put the mouse on the xanthous rectangle and the answer volition appear.

Exercise iii

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

$24.00, $48.00, $25.00, $30.00, $36.00, $52.00, $25.00, $90.00

What is the median cost?

Answer:

Finding the Fashion

A tertiary number that nosotros use to describe data is called the mode of the data. The mode is the number or numbers that occur the most frequently. Here is a 2-step process for finding the mode.

Two- Step Process for Finding the Median

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

Step 2: Get down the listing 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 most often occurring number, so just state that both numbers are the mode.

Example iv

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

nine 0, 50, 70, lxxx, 30, 60, 50, thirty, 50

What is the mode of these data?

Solution

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

30, 30, 50, 50, l, 60, 70, fourscore, xc

Footstep two: Now go downwards the list and determine if at that place is a number that appears in the list more than any other number.

30, 30, 50 , 50 , fifty , 60, seventy, 80, 90

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

At present try ane by yourself. If you want to see the respond, put the mouse on the yellow rectangle and the respond will announced.

Exercise 4

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

four, 6, 2, 4, vi, 5, 2, vii, 6, iii

What is the mode of these data?

Reply:

Now for another example.

Example 5
The box below shows the number of copse growing in the backyard of each house on plumb street.

seven, 9, 9, 4, xi, 7, 9, 12, 3, 7

What is the mode of these information?

Solution

Step ane: Kickoff, put the numbers in size place, smallest to largest.

iii, 4, 7, 7, 7, ix, 9, 9, eleven, 12

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

3, iv, 7 , 7 , seven , 9 , ix , nine , xi, 12

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

Note: There may exist No style, ONE fashion, or multiple modes for a given sample of numbers.

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

Practice 4

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

5, iv, 5, viii, 2, 2, i, 6, five, 1, 2

What is the mode of these information?

Answer: