Name of Lecturer: Mr. J.Agius
Course: Level 3 Year 2
Lesson 14
Chapter 4: Statistics
Frequency Distribution
Frequency
Frequency is how often something occurs.
Example: Sam played football on



Saturday Morning,
Saturday Afternoon
Thursday Afternoon
The frequency was
2 on Saturday, 1 on Thursday and 3 for the whole week.
Frequency Distribution
By counting frequencies we can make a Frequency Distribution table.
Example: Goals
Sam's team has scored the following numbers of goals in recent
games:
2, 3, 1, 2, 1, 3, 2, 3, 4, 5, 4, 2, 2, 3
Sam put the numbers in order,
then added up:



how often 1 occurs (2 times),
how often 2 occurs (5 times),
etc,
and wrote them down as a
Frequency Distribution table:
4 Statistics
Page 1
Name of Lecturer: Mr. J.Agius
Course: Level 3 Year 2
From the table we can see interesting things such as


getting 2 goals happens most frequently
only once did they get 5 goals
This is the definition:
Frequency Distribution: values and their frequency (how often each value occurs).
Here is another example:
Example: Newspapers
These are the numbers of newspapers sold at a local shop over the last 10 days:
22, 20, 18, 23, 20, 25, 22, 20, 18, 20
Let us count how many of each number there is:
Papers Sold
Frequency
18
2
19
0
20
4
21
0
22
2
23
1
24
0
25
1
It is also possible to group the values. Here they are grouped in 5s:
Papers Sold
Frequency
15-19
2
20-24
7
25-29
1
(Learn more about Grouped Frequency Distributions)
Graphs
After creating a Frequency Distribution table you might like to make a Bar Graph or
a Pie Chart using the Excel Software Program.
4 Statistics
Page 2
Name of Lecturer: Mr. J.Agius
Course: Level 3 Year 2
Question 1
The Lakers scored the following numbers of goals in their last twenty matches:
3, 0, 1, 5, 4, 3, 2, 6, 4, 2, 3, 3, 0, 7, 1, 1, 2, 3, 4, 3
Which number had the highest frequency?
A
C
3
6
B
D
4
7
Question 2
Which letter occurs the most frequently in the following sentence?
THE SUN ALWAYS SETS IN THE WEST.
A
C
E
T
B
D
S
W
Question 3
Pi is a special number that is used to find the area of a circle. The following
number gives the first 100 digits of the number pi:
3.141 592 653 589 793 238 462 643 383 279 502 884 197 169 399 375 105 820
974 944 592 307 816 406 286 208 998 628 034 825 342 117 067
Which of the digits 0 to 9 occurs most frequently in this number?
A
C
2
8
B
D
3
9
Question 4
A fair die was thrown 100 times. The frequency distribution is shown in the
following table:
How many throws scored less than 3?
A
C
11
45
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B
D
34
56
Page 3
Name of Lecturer: Mr. J.Agius
Course: Level 3 Year 2
Question 5
60 students sat a test. The frequency distribution is shown in the following table:
How many students scored 5 or more?
A
C
11
33
B
D
22
38
Question 6
A fair die was thrown 100 times. The frequency distribution is shown in the
following table:
How many throws scored greater than 2, but less than or equal to 5?
A
C
26
45
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B
D
44
63
Page 4
Name of Lecturer: Mr. J.Agius
Course: Level 3 Year 2
Question 7
60 students sat a test. The frequency distribution is shown in the following table:
How many students scored greater than or equal to 4, but less than or equal to 7?
A
C
19
27
B
D
26
34
Stem and Leaf Plots
A special table where each data value is split into a "leaf" (usually the last digit) and a
"stem" (the other digits). Like in this example:
Example:
"32" is split into "3" (stem) and "2" (leaf).
The "stem" values are listed down, and the "leaf" values go right (or left) from the stem
values.
The "stem" is used to group the scores and each "leaf" indicates the individual scores
within each group.
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Name of Lecturer: Mr. J.Agius
Course: Level 3 Year 2
Question 1
What is the range for the above stem and leaf plot?
A
C
39
45
B
D
40
56
For the above stem and leaf plot, what is the median value?
A
C
28
35.5
B
D
32
39
Question 2
What is the range for the above stem and leaf plot?
A
C
98
86
B
D
97
85
What is the mode for the above stem and leaf plot?
A
C
25
60
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B
D
54
66
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Name of Lecturer: Mr. J.Agius
Course: Level 3 Year 2
Cumulative Tables and Graphs
Cumulative
Cumulative means "how much so far".
Think of the word "accumulate" which means to gather together.
To have cumulative totals, just add up the values as you go.
Example: Jamie has earned this much in the last 6 months:
Month
Earned
March
$120
April
$50
May
$110
June
$100
July
$50
August
$20
To work out the cumulative totals, just add up as you go.
The first line is easy, the total earned so far is the same as Jamie earned that month:
Month
March
Earned Cumulative
$120
$120
But for April, the total earned so far is $120 + $50 = $170 :
Month
Earned Cumulative
March
$120
$120
April
$50
$170
And for May we continue to add up: $170 + $110 = $280
Month
Earned Cumulative
March
$120
$120
April
$50
$170
May
$110
$280
Do you see how we add the previous month's cumulative total to this month's earnings?
Here is the calculation for the rest:



June is $280 + $100 = $380
July is $380 + $50 = $430
August is $430 + $20 = $450
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Name of Lecturer: Mr. J.Agius
Course: Level 3 Year 2
And this is the result
Month
Earned Cumulative
March
$120
$120
April
$50
$170
May
$110
$280
June
$100
$380
July
$50
$430
August
$20
$450
The last cumulative total should match the total of all earnings:
$450 is the last cumulative total ...
... it is also the total of all earnings:
$120+$50+$110+$100+$50+$20 = $450
So we got it right.
So that's how to do it, add up as you go down the list and you will have cumulative
totals.
You could also call it a "Running Total"
Graphs
You can make cumulative graphs if you want. Just plot each Month's cumulative total:
Cumulative Bar Graph
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Cumulative Line Graph
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Name of Lecturer: Mr. J.Agius
Course: Level 3 Year 2
Question 1
The table shows the daily sales made by a mobile ice cream salesman over one
week.
What was the value of the cumulative sales for Friday?
A
C
$57.20
$132
B
D
$81
$286
Question 2
The table shows the cumulative rainfall by month for one year for Delhi, India.
Which month had the greatest rainfall?
A
C
July
September
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B
D
August
December
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Name of Lecturer: Mr. J.Agius
Course: Level 3 Year 2
Question 3
The following table shows the sales of TVs made by a retail store each month last
year:
What is the cumulative total for July?
A
C
14
125
B
D
111
16
Question 4
The conservation department kept a record of the number of rabbits on an island
every ten years from 1950 to 2010. The following graph shows the cumulative
frequency of the rabbit population:
During which decade did the population increase the least?
A
C
1950-1960
1900-2000
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B
D
1960-1970
2000-2010
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