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6.2 Frequency tables and cumulative frequency
Good morning!
Schedule:
Learning goals
Frequency tables
Modal class and median
Homework
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Wiskunde
Middelbare school
vwo
Leerjaar 6
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Good morning!
Schedule:
Learning goals
Frequency tables
Modal class and median
Homework
Slide 1 - Diapositive
Learning goals
At the end of this lessons I can:
Find the mode and median from a grouped frequency table
Draw up a grouped frequency table from a set of data
Calculate the cumulative frequency in a frequency table
Slide 2 - Diapositive
A
The maximum value is 18
B
If choosing a random value there is a 75% chance it will be larger than 9
C
The mean is 12
D
The data is positively skewed
Slide 3 - Quiz
Frequency Tables
Time spend, x (min)
Frequency
Cumulative frequency
0 ≤ x < 30
30 ≤ x < 60
60 ≤ x < 90
90 ≤ x < 120
120 ≤ x < 150
150 ≤ x < 180
Time spent on Youtube per day by MP4's
Slide 4 - Diapositive
Frequency Tables
Time spend, x (min)
Frequency
Cumulative frequency
0 ≤ x < 30
6
6
30 ≤ x < 60
4
10
60 ≤ x < 90
3
13
90 ≤ x < 120
0
13
120 ≤ x < 150
2
15
150 ≤ x < 180
1
16
Time spent on Youtube per day by MP4's
Slide 5 - Diapositive
Grouped frequency tables
To determine the class width for your table:
Divide the range by the amount of classes you want, then round the answer UP
Start value:
Choose a start value less than or equal to your smallest value
Slide 6 - Diapositive
Grouped frequency tables
To determine the class width for your table:
Divide the range by the amount of classes you want, then round the answer UP
Start value:
Choose a start value less than or equal to your smallest value
Rule of thumb:
20 or less data values 5 classes
21-50 values 10 classes
51-100 values 15 classes
100 or more 20 classes
Slide 7 - Diapositive
Grouped frequency tables
Student grades: 64, 68, 73, 75, 78, 79, 81, 83, 83, 84, 89, 90, 91, 94, 96, 97
1. Range =
2. n = 16
3. How many classes?
4. Class width =
5. Start value
Slide 8 - Diapositive
Grouped frequency tables
Student grades: 64, 68, 73, 75, 78, 79, 81, 83, 83, 84, 89, 90, 91, 94, 96, 97
1. Range = 97-64 = 33
2. n = 16
3. I want 5 classes
4. Class width =
5. Start value can be 64 or 63
5
3
3
≈
7
Grades
Frequency
Cumulative frequency
64 ≤ x < 71
2
2
71 ≤ x < 78
2
Slide 9 - Diapositive
1, 2, 5, 3, 3, 2, 2, 1, 2, 1, 1, 4, 3
What is the correct choice
for class ?
Number of pets:
# of pets, x
frequency
cumulative
frequency
a
8
8
2 < x ≤ 4
b
12
4 < x ≤ 6
1
c
a
A
1 < x ≤ 3
B
0 < x ≤ 2
C
2 < x ≤ 6
D
0 < x ≤ 4
Slide 10 - Quiz
1, 2, 5, 3, 3, 2, 2, 1, 2, 1, 1, 4, 3
What is the correct
frequency for ?
Number of pets:
# of pets, x
frequency
cumulative
frequency
a
8
8
2 < x ≤ 4
b
12
4 < x ≤ 6
1
c
b
A
4
B
5
C
6
D
7
Slide 11 - Quiz
1, 2, 5, 3, 3, 2, 2, 1, 2, 1, 1, 4, 3
What is the correct
cumulative frequency for ?
Number of pets:
# of pets, x
frequency
cumulative
frequency
a
8
8
2 < x ≤ 4
b
12
4 < x ≤ 6
1
c
c
A
1
B
20
C
4
D
12
Slide 12 - Quiz
Modal class
What do you think the modal class is?
# of pets, x
frequency
cumulative
frequency
0 < x ≤ 2
8
8
2 < x ≤ 4
4
12
4 < x ≤ 6
1
13
Slide 13 - Diapositive
Modal class
The
modal class
is the class with the highest
frequency
# of pets, x
frequency
cumulative
frequency
0 < x ≤ 2
8
8
2 < x ≤ 4
4
12
4 < x ≤ 6
1
13
Slide 14 - Diapositive
Modal class
Time spend, x (min)
Frequency
Cumulative frequency
5 < x ≤ 20
7
7
20 < x ≤ 35
4
11
35 < x ≤ 50
2
13
50 < x ≤ 65
5
18
65 < x ≤ 80
0
18
80 < x ≤ 95
1
19
Time spent on math homework
Modal class:
Slide 15 - Diapositive
Median value
# of pets, x
frequency
cumulative
frequency
0 < x ≤ 2
8
8
2 < x ≤ 4
4
12
4 < x ≤ 6
1
13
The median is the
th
value.
=
2
(
n
+
1
)
2
(
n
+
1
)
Slide 16 - Diapositive
Median value
Time spend, x (min)
Frequency
Cumulative frequency
5 < x ≤ 20
7
7
20 < x ≤ 35
4
11
35 < x ≤ 50
2
13
50 < x ≤ 65
5
18
65 < x ≤ 80
0
18
80 < x ≤ 95
1
19
Find the class with the median value.
Slide 17 - Diapositive
Median value
Time spend, x (min)
Frequency
Cumulative frequency
5 < x ≤ 20
7
7
20 < x ≤ 35
4
11
35 < x ≤ 50
2
13
50 < x ≤ 65
5
18
65 < x ≤ 80
0
18
80 < x ≤ 95
1
19
Find the class with the median value.
Slide 18 - Diapositive
Time spend, x, (min)
Frequency
Cumulative frequency
10
10
3
13
2
15
0
15
1
16
Modal class =
Class with median value =
Time spent on Instagram
0 ≤ x < 25
25 ≤ x < 50
50 ≤ x < 75
75 ≤ x <100
100 ≤ x < 125
Slide 19 - Question de remorquage
Modal class
Class with median value
Slide 20 - Question de remorquage
Grouped frequency tables
Cumulative frequency
4
10
18
24
30
2
(
3
0
+
1
)
t
h
Median class
Value
= 15.5 th value
Slide 21 - Diapositive
Grouped frequency tables
How would you estimate the range in a grouped frequency table?
Slide 22 - Diapositive
Grouped frequency tables
Slide 23 - Diapositive
Take out your diaries/notebook
Homework for Tuesday 14-3-2023:
p. 329-330: Practice 1 #1, 2, 3 , 4
Slide 24 - Diapositive
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