Unit 16: StatisticsSections 16CDE Frequency

Tables/Grouped Data/Histograms

It is very common to organize large amounts of data into a frequency table.

Marks ( xi) Frequency (fi)

75 3

80 5

85 9

90 6

95 2

Example 1: The marks of some grade 12 students applying to university are given below

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.

8.8425

2120

x

fi

xf

xii

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

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

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

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