Transcript IB Core: Statistics Section 14.1 Frequency Diagrams

Unit 16: Statistics
Sections 16CDE Frequency
Tables/Grouped Data/Histograms
It is very common to organize large amounts
of data into a frequency table.
Example 1: The marks of some grade 12
students applying to university are given
below
Marks
( xi)
75
Frequency
(fi)
3
80
5
85
9
90
6
95
2
Determine the mean, median, quartiles
and standard deviation for the data
Using our calculator we get:
Our formula for the mean has been
modified for frequency tables.
fx
x
 fi
i i
2120
x
 84.8
25
Sometimes we are given “Grouped Data”
rather than exact data values
Marks
Frequency (fi)
[70,75[
3
[75, 80[
5
[80, 85[
9
[85,90[
6
[90, 95[
2
We no longer know the exact data values.
We can only find an Estimate for the mean and standard
deviation.
To do this we use “mid class values xi
Marks
xi
[70,75[
[75, 80[
[80, 85[
[85,90[
[90, 95[
72.5
77.5
82.5
87.5
92.5
Frequency
(fi)
3
5
9
6
2
The grouped data can be displayed using a
frequency histogram and frequency polygon
Marks
xi
Frequency
(fi)
[70,75[
72.5
3
[75, 80[
77.5
5
[80, 85[
82.5
9
[85,90[
87.5
6
[90, 95[
92.5
2
The grouped data can be displayed using a
Cumulative frequency histogram and
Cumulative frequency polygon
Marks
Frequency
(fi)
Cumulative
Frequency
[70,75[
3
3
[75, 80[
5
8
[80, 85[
9
17
[85,90[
6
23
[90, 95[
2
25
We use the cumulative frequency polygon to
estimate the median, upper and lower
quartiles
We can also display the data using a
“Box and Whisker Plot”
HOMEWORK:
Read page 481 ex 16.8, page 482 key point
16.3
PAGE 475 # 1a, 3ai, 4 - 6
PAGE 483 # 3 – 6
PAGE 486 # 1a, 2, 3