KS3/IGCSE Averages

KS3/IGCSE Averages

Read from a Frequency Table

Understand the concept of Averages

Find the mean, median and mode of Discrete Data

Average

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A calculated "central" value of a set of numbers.

To find the average we must understand the data we are looking at....

Types of data

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In general we have TWO types of data.

Qualitative & Quantitative

Qualitative - words

Quantitative - numbers

Multiple Choice

He ran 50 miles.

• Qualitative data

• Quantitative data

Multiple Choice

The candy was sour.

• Qualitative data

• Quantitative data

Multiple Choice

The flower is red.

• Qualitative data

• Quantitative data

Multiple Choice

The mass of the beaker was 122 grams.

• Qualitative data

• Quantitative data

Multiple Choice

The speed of the car was 45 mph.

• Qualitative

• Quantitative

• Both

• Neither

Multiple Choice

There are 16 red marbles in the bag.

• Qualitative

• Quantitative

• Both

• Neither

Multiple Choice

Dolphins have smooth skin.

• qualitative

• quantitative

Multiple Choice

There are nine dolphins in this pod.

• qualitative

• quantitative

Types of data

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In Mathematics we will usually look at Quantitative data (numbers)

There are TWO types of Quantitative data:

Discrete - Data that can only take certain values [often whole numbers]

Continuous - Data that can take any value (within a range) - [measurements]

Multiple Choice

Heights of Basketball Players

• Discrete

• Continuous

Multiple Choice

The number of medals that the Philippine team won in each of the past 20 Olympic games

• Discrete

• Continuous

Multiple Choice

The distance travelled by different cars using 1-liter of gasoline

• Discrete

• Continuous

Multiple Choice

The number of times a student leaves class to use the bathroom in a term

• Discrete

• Continuous

Multiple Choice

The number of times each student goes to the bathroom in each school day

• Discrete

• Continuous

Multiple Choice

The length of time it takes before a dolphin surfaces in the ocean to breath

• Discrete

• Continuous

Multiple Choice

The distance travelled by different cars using 1-litre of petrol

• Discrete

• Continuous

Multiple Choice

The number of points scored by a NBA team in each game of the 2018 season

• Discrete

• Continuous

Multiple Choice

The time it takes for a light bulb to burn out.

• Discrete

• Continuous

Multiple Choice

The number of suitcases lost by airlines. 

• Discrete
• Continuous

Recording Data

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Data can be presented in a number of ways. Often when first collecting data a tally chart is used to then create a frequency table.

Frequency

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How often something happens (usually during a period of time).

A Frequency table is a quick alternative to writing out a list of numbers

Multiple Choice

For how many weeks did it rain all 7 days?

• 1

• 5

• 6

• 4

Multiple Choice

How many people were surveyed to collect this data?

• 18

• 20

• 22

• 24

Multiple Choice

How many more people studied for 0-30 minutes than people who studied for 121-150 minutes?

• 3
• 6
• 5
• 4

Multiple Choice

How many minutes did the most number of people study?

• 61-90
• 0-30
• 31-60
• 91-120

Multiple Choice

How many baseball teams scored 0 runs per inning?

• 4

• 3

• 2

• 1

Frequency - Two way tables

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Two-way tables are a type of frequency table that can represent two different pieces of information

E.g. Gender and Favourite Subject

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Averages

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Now we know how our data can be presented, we can find averages.

Open Ended

Can you name the three different types of averages?

Averages

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Mean

• Add up all the numbers,

• Divide by how many numbers there are.

Averages

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Median

• Place the numbers in value order

• Find the middle number.

Averages

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Mode

• Most common number in the list

If you have never heard of these before, have a watch of the next video....be warned the song will stay in your head!

Multiple Choice

What is the median of:

6, 12, 16, 11, 8, 4, 1, 11, 4

• 11

• 6

• 8

• 7

Multiple Choice

Find the Mean of:

8, 14, 32, 6, 15

• 15

• 175

• 75

• 12

Multiple Choice

A data set can have more than one median?

• True

• False

Multiple Choice

A data set can have more than one mode

• True

• False

Multiple Choice

Find the median.

12, 5, 9, 18, 22, 25, 5

• 9

• 8

• 12

• 18

Multiple Choice

To find the ________ you put all numbers in order from least to greatest and find the number that is in the middle.

• Mean

• Median

• Mode

• Range

Multiple Choice

To find the _________ you add up all the numbers and then divide by how many numbers you have.

• Mean

• Median

• Mode

• Range

Multiple Choice

Find the median of these numbers:

4,2,7,4,3

• 2

• 5

• 7

• 4

Multiple Choice

Find the mean of these numbers:

2, 57, 38, 42, 6

• 29

• 38

• 50

• 145

Multiple Choice

At Donald's Donuts the number of donut holes in a bag can vary. Help Donald find the mode.

12,10,10,10,13,12,11,13,10

• 13

• 12

• 11

• 10

Averages

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Advantages and Disadvantages

It is important the understand when and why we use each of the three different averages.....why do we need three?

Copy down the advantages and disadvantages from the next slide...

Mode is the ONLY average that can be used for Qualitative data!