Transcript Finding the mode

Objective:
Understand and use the MEAN
value of a data set
Remember the three averages and range
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The mean
To calculate the mean of a set of values we add together the
values and divide by the total number of values.
Sum of values
Mean =
Number of values
For example, the mean of 3, 6, 7, 9 and 9 is
3+6+7+9+9
5
=
34
5
= 6.8
Problems involving the mean
A pupil scores 78%, 75% and 82% in three tests. What was
the mean of the three test scores?
78%  75%  82% 235%

 78.3%
3
3
Problems involving the mean
The maximum temperature in Haslemere during one week
was as follows:
6, 9, 10, 15, 4, 6, 7
What was the mean of the temperatures?
6  9  10  15  4  6  7 57
o

 8.1 C
7
7
Remember the three averages and range
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Obj: Finding the mean
Impact Maths 1R
Page 327
Exercise 17A
Objective:
Understand and use the Mode or
modal value of a data set
Finding the mode
The mode or modal value in a set of data is the data value
that appears the most often.
For example, the number of goals scored by the local
football team in the last ten games is:
2,
1,
2,
0,
0,
2,
3,
1,
2,
1.
Is it possible to have more than one modal value?
Yes
The modal score is 2.
Is it possible to have no modal value?
Yes
Finding the mode
A dice was thrown ten times. These are the results:
What was the modal score?
3 is the modal score because it appears most often.
Finding the mode
The mode is the only average that can be used for
non-numerical data.
For example, 25 pupils are asked how they usually travel to
school. The results are shown in a frequency table.
Method of travel
Bicycle
On foot
Car
Bus
Train
Frequency
6
8
2
6
3
What is the modal
method of travel?
Most children travel by foot.
Travelling on foot is
therefore the modal method
of travel.
Finding the mode from a bar chart
This bar chart shows the scores in a science test:
Number of pupils
9
8
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
Mark out of ten
What was the modal score?
6 is the modal score because it has the highest bar.
Finding the mode from a frequency table
This frequency table shows the frequency of different length
words in a given paragraph of text.
Word length 1
Frequency
3
2 3 4
16 12 16
5
7
6
3
7
11
8
6
9
2
10
1
What was the modal word length?
We need to look for the word lengths that occur most
frequently.
For this data there are two modal word lengths: 2 and 4.
Finding the modal class for continuous
data
This grouped frequency table shows the times 50 girls and
50 boys took to complete one lap around a race track.
Frequency
Time (minutes:seconds)
Boys
Girls
2:00 ≤ 2:15
3
1
2:15 ≤ 2:30
7
6
2:30 ≤ 2:45
11
10
2:45 ≤ 3:00
13
9
3:15 ≤ 3:30
8
12
3:30 ≤ 3:45
7
10
3:45 ≤ 4:00
1
2
What is the modal
class for the girls?
What is the modal
class for the boys?
What is the modal
class for the pupils
regardless of
whether they are a
boy or a girl?
Remember the three averages and range
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1R chapter 17 B page 329
Q1a
5, 2, 8, 2, 6, 8, 4, 2, 6, 9
Put in ascending order
2, 2, 2, 4, 5, 6, 6, 8, 8, 9
Mode = 2
Remember the three averages and range
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Mean height of 7W2
Height
Mean = Total
No of pupils
0=
1
0
Finding the median
The median is the middle value of a set of numbers
arranged in order.
For example, find the median of
10,
7,
9,
12,
7,
8,
6,
Write the values in order:
6,
7,
7,
8,
The median is the middle value.
9,
10,
12.
Finding the median
When there is an even number of values, there will be two
values in the middle.
For example,
Find the median of 56, 42, 47, 51, 65 and 43.
In this case, we have to find the mean of the two middle
values.
The values in order are:
42,
43,
47,
51,
56,
There are two middle values, 47 and 51.
65.
Finding the median
To find the number that is half-way between 47 and 51 we
can add the two numbers together and divide by 2.
47 + 51
2
=
98
2
= 49
The median of 42, 43, 47, 51, 56 and 65 is 49.
The median
Remember the three averages and range
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Finding the Median
Impact Maths 1R
Page 331 – Exercise 17C
6, 2, 9, 1, 4, 8, 5, 9, 7
Rogue values
The median is often used when there is a rogue value – that
is, a value that is much smaller or larger than the rest.
What is the rogue value in the following data set:
192, 183, 201, 177, 193, 197, 4, 186, 179?
The mean of this data set is:
192  183  201  177  193  197  4  186  179
 168
9
The median of this data set is:
4, 177, 179, 183, 186, 192, 193, 197, 201.
The median of the data set is not affected by the rogue value, 4.
Mean or median?
Would it be better to use the median or the mean to
represent the following data sets?
34.2, 36.8, 29.7, 356, 42.5, 37.1?
median
0.4, 0.5, 0.3, 0.8, 0.7, 1.0? mean
892, 954, 1026, 908, 871, 930? mean
3.12, 3.15, 3.23, 9.34, 3.16, 3.20? median
97.85, 95.43, 102.45, 98.02, 97.92, 99.38? mean
87634, 9321, 78265, 83493, 91574, 90046? median
Objective:
Understand and use the range of
a data set
Understand the range of a data set
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Finding the range
The range of a set of data is a measure of how the data is
spread across the distribution.
To find the range we subtract the lowest value in the set from
the highest value.
Range = highest value – lowest value
2,
5,
3,
2,
8,
1,
6,
5,
1,
2,
2,
3,
5,
5,
6,
8
Range = 8 – 1 = 7
Key Words
Ascending
Numbers which are increasing in value
Descending
Numbers which are decreasing in value
Examples of Ascending and Descending
3, 4, 12, 25, 36, 42
ascending
42, 36, 25, 12, 4, 3
descending
Objective : To understand the terms used.
Objective : To place data in ascending or descending order.
Questions
Write these numbers in ascending order what is the range:
12
4
15
6
4
5
6
10
5
10
12
15
Range = 15 – 4 = 11
Write these numbers in descending order what is the range:
45
72
67
54
24
56
72
56 54
45
24
Range = 72 – 24 = 48
67
Finding the range
Impact Maths 1R
Page 332 – Exercise 17D
6, 8, 3, 9, 7, 2, 5, 5, 3
2, 3, 3, 5, 5, 6, 7, 8, 9
Range = 9 - 2
= 7
Finding the range
The range of a set of data is a measure of how the data is
spread across the distribution.
To find the range we subtract the lowest value in the set from
the highest value.
Range = highest value – lowest value
When the range is small it tells us that the values are similar
What does it mean if the range is small?
in size.
1, 3, 5, 5, 6, 7
Range = 6
When the range is large it tells us that the values vary widely
What does it mean if the range is large?
in size.
1, 6, 67, 83, 99
Range = 98
Have we achieved the objective:
understanding and finding the
Range
Write three sentences about your
understanding of range
Remember the three averages and range
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The mean
Find the missing value
Finding the range
Impact Maths 1R
Page 332 – Exercise 17D
6, 8, 3, 9, 7, 2, 5, 5, 3
Finding the mode from a frequency table
This frequency table shows the frequency of different length
words in a given paragraph of text.
Word length 1
Frequency
3
2
5
3 4
12 10
5
7
6
3
7
11
What was the modal word length?
1, 1, 1, 2, 2, 2, 2, 2, 3, ….
8
6
9
2
10
1
Finding the modal class for continuous data
This grouped frequency table shows the times 50 girls and
50 boys took to complete one lap around a race track.
Frequency
Time (minutes:seconds)
Boys
Girls
2:00 ≤ 2:15
3
1
2:15 ≤ 2:30
7
6
2:30 ≤ 2:45
11
10
2:45 ≤ 3:00
13
9
3:15 ≤ 3:30
8
12
3:30 ≤ 3:45
7
10
3:45 ≤ 4:00
1
2
What is the modal
class for the girls?
What is the modal
class for the boys?
What is the modal
class for the pupils
regardless of
whether they are a
boy or a girl?
Finding the mode
The mode is the only average that can be used for
non-numerical data.
For example, 30 pupils are asked how they usually travel to
school. The results are shown in a frequency table.
Method of travel
Bicycle
On foot
Car
Bus
Train
Frequency
6
8
8
2
6
3
What is the modal
method of travel?
Most children travel by foot.
Travelling on foot is
therefore the modal method
of travel.
Finding the Modal Group
Impact Maths 2G
Page 236 – Exercise 15B
Impact Maths 2G
Page 243 – Exercise 15F