### Mode, Median and Mean

```MODE
Mode = the item that appears most often
- the most common number
2, 3, 6, 4, 2, 2, 3, 6, 5
this
group
fruit
group
of of
numbers
In In
this
transport
survey
APPLES
areMODE.
the MODE.
2 is
the
MODE.
CARS
are
the
There
more
apples
2 appears
more
than
any
There
areare
cars
than
than
anyvehicle
other fruit.
other
number
any
other
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MODE - continued
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What is the mode in each of the following? :Click the mouse when you want to see each answer
10, 11, 10, 8, 5, 8, 10, 8, 6, 7, 8, 8, 9, 12
8
20,
20, 20,
20, 22,
22, 25,
25, 40,
40, 13,
13, 20,
20, 21,
21, 22,
22, 20,
20, 40,
40,
20
2, 4, 8, 2, 3, 3, 3, 2, 4, 4, 2, 2, 2, 9, 5, 2, 4
2
102, 105, 120, 102, 103, 104, 166, 124, 132
102
65, 61, 67, 66, 67, 66, 61, 66, 64, 66, 67, 65
66
Median
The value of the middle number when they are arranged in order
10, 5, 2, 1, 8, 7, 6
1
2
First, put the numbers into order:5
6
7
8
10
middle
Now find the number that is in the middle
6 is the MEDIAN
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Median
The value of the middle number when they are arranged in order
4, 19, 3, 22, 15, 1, 9 First, put the numbers into order:1
3
4
9
15
19
22
middle
Now find the number that is in the middle
9 is the MEDIAN
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Median - continued
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Find the MEDIAN in the following:Click the mouse to see the answers
4, 9, 5, 2, 3, 10, 1
1
2
3
4
5
9
10
16
22
median
22, 16, 5, 29, 32, 10, 1
2, 6, 15, 24, 32, 10, 9
1
2
5
6
10
median
9
10
median
15
29
32
24
32
Now that you’ve got the idea of MEDIAN
there’s just one more thing to remember!
If there are an EVEN amount of numbers you
can’t find the middle straight away……
4
6
7
9
What’s the
middle
number?
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12
15
To find the median ADD the
two middle numbers together,
then DIVIDE by 2.
7 + 9 = 16 16÷ 2 = 8
So, the MEDIAN is 8
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Let’s find the median of this group of numbers
6, 5, 5, 7, 1, 4, 10, 7, 8
FIRST, put the numbers into ORDER
1
4
5
5
6
7
7
8
10
Make sure you’ve
got the right
amount – there
are 9 numbers in
this group
MEDIAN
NOW, find the middle
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The MEDIAN is 6
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Let’s find the median of this group of numbers
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6, 5, 5, 7, 1, 4, 10, 7,
FIRST, put the numbers into ORDER
1
4
5
5
6
7
7 10
Make sure you’ve
got the right
amount – there
are 8 numbers in
this group
What is the MEDIAN? Add the middle two numbers:
5 + 6 = 11
NOW, find the middle
Divide by 2
The MEDIAN is 5 . 5
11 ÷ 2 = 5 . 5 (or 5 ½)
Try these: click the mouse when you are ready to see the answer
Find the MEDIAN
Find the middle
5, 9, 5, 3, 10, 5, 8, 6, 5, 10, 12 3 5 5 5 5 6 8 9 10 10 12
Make sure you’ve got 11
Put into
order
median
Find the middle
5, 9, 7, 2, 1, 4, 9, 6, 11, 10, 42
Put into
order
1 2 4 5 6 7 9 9 10 11 42
Make sure you’ve got 11
median Click mouse
Mean
Mean is another word for AVERAGE
It’s easy to work out
First, add all the numbers together:Then, divide by the number of items (the number of ‘numbers’!)
6
4
5
6
2
8
4
1
2
3
4
5
6
7
6 + 4 + 5 + 6 + 2 + 8 + 4 = 35
35 ÷ 7 = 5
5 is the MEAN
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Mean
Try this one – find the MEAN
First, add all the numbers together:Then, divide by the number of items (the number of ‘numbers’!)
8
1
4
20
8
2
8
4
2
2
3
4
5
6
7
8
8 + 4 + 20 + 8 + 2 + 8 + 4 + 2 = 56
56 ÷ 8 = 7
7 is the MEAN
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Find the MEAN of these numbers:10, 12, 3, 21, 4, 8, 12, 5, 9, 6
1 2 3 4 5 6 7 8 9 10
10 + 12 + 3 + 21 + 4 + 8 + 12 + 5 + 9 + 6 = 90
15, 22, 12, 9, 6, 10, 3
1 2 3 4 5 6 7
15 + 22 + 12 + 9 + 6 + 10 + 3 = 77
90 ÷ 10 = 9
The MEAN is 9
77 ÷ 7 = 11
The MEAN is 11
5, 7, 10, 3, 12, 6, 7, 19, 5, 1, 13
1 2 3 4 5 6 7 8 9 10 11
88 ÷ 11 = 8
5 + 7 + 10 + 3 + 12 + 6 + 7 + 19 + 5 + 1 + 13 = 88
The MEAN is 8
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Questions on mode, median and mean
Find the MODE and MEDIAN shoe size of 15
children whose shoe sizes are:-
4
2
3
4
4
5
3
6
3
7
5
4
4
3
1
Don’t forget – put
the numbers in
ascending order
1 2 3 3 3 3 4 4 4 4 4 5 5 6 7
Check you have 15 numbers
The MODE is 4
The MEDIAN is 4
4 is the middle number
4 occurs most often
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for help
Questions on mode, median and mean
Find the Mean shoe size of 15 children whose
shoe sizes are:-
4
2
3
4
4
5
3
7
3
8
all the shoe sizes
together
5
4
4
3
1
Divide by the number of
children
4 + 2 + 3 + 4 + 4 + 5 + 3 + 7 + 3 + 8 + 5 + 4 + 4 + 3 + 1 = 60
60 ÷ 15 = 4
The MEAN shoe
size is 4
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for help
Questions on mode, median and mean
Find the MODE, MEDIAN and MEAN of the following data:
17 0131 11
0
3 69 77 910100 11
0 1133 17
6
MODE is 0
MEDIAN
is 7
Put in order; check
you have 11 numbers
MEAN: add all the numbers together
divide by number of items (11)
0 + 0 + 1 + 3 + 6 + 7 + 9 + 10 + 11 + 13 + 17 = 77
77 ÷ 11 = 7
The MEAN is 7
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Questions on mode, median and mean
Find the MODE, MEDIAN and MEAN of the following data:
10
14 10
15 10
11 11
12
10 12
11 14
10 15
10 15
10
10
10
11 11
11
12
14
15
15
MODE is 10
MEDIAN
is 11
Put in order; check
you have 9 numbers
MEAN: add all the numbers together
divide by number of items (9)
10 + 10 + 10 + 11 + 11 + 12+ 14 + 15 + 15 = 108
108 ÷ 9 = 12
The MEAN is 12
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Questions on mode, median and mean
Find the MODE, MEDIAN and MEAN of the following data:
117
6 671783810
131313
131381717
13 313
10
1011
61111
7
Put in order; check
you have 10 numbers
MODE is 13
MEAN: add all the numbers together
MEDIAN is
(8 + 10)÷ 2 = 9
divide by number of items (10)
1 + 3 + 6 + 7 + 8 + 10 + 11 + 13 + 13 + 17 = 90
90 ÷ 10 = 9
The MEAN is 9
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The number of absences for each pupil in a class of 25 is
shown in the table below.
0
18
0
3
1
Absences
1
0
0
3
2
2
0
1
1
2
5
20
2
24
2
5
3
4
0
3
a. Calculate the MEAN number of absences per pupil
b. Find the MEDIAN number of absences per pupil
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a. Calculate the MEAN number of absences per pupil
Absences
0
1
0
0
5
18
3
2
2
3
0
0
1
1
4
3
2
5
20
0
1
2
24
2
3
First, add together all the absences
Then, divide by the number of
pupils (25)
0 + 1 + 0 + 0 + 5 + 18 + 3 + 2 + 2 + 3 + 0 + 0 + 1 + 1 + 4 + 3 + 2 + 5 + 20 + 0 + 1 + 2 + 24 + 2 + 3= 102
It’s really important to include the 0s because
you must count them in your total number of
pupils
The MEAN number
of absences per
pupil is 4·08
102 ÷ 25 = 4.08
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b. Find the MEDIAN number of absences per pupil
First, put all the absences in order
Absences
0
1
0
0
5
18
3
2
2
3
0
0
1
1
4
3
2
5
20
0
1
2
24
2
3
Then, check that you have 25
numbers!
Now, find the middle number
0 0 0 0 0 0 1 1 1 1 2 2 2 2 2 3 3 3 3 4 5 5 18 20 24
median
The MEDIAN number of
absences is 2
END
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