DATA HANDLING

• Recap: Displaying Ungrouped Data

• Recap: Displaying Grouped Data

• Measures of Central Tendency in Ungrouped Data

• Measures of Central Tendency in Grouped Data

• Measures of Dispersion

• Five Number Summary

1

MEASURES OF CENTRAL TENDENCY

FOR UNGROUPED DATA

Mean

Is most commonly

Also called the average

Formula:

n

xx

setdatainvaluesofNo

valuesdataofSumMean

_____

___

2

Example

1. Class A consists of 9 learners and Class B consists

of 16 kids. Compare the mean of each class.

Class A 1 1 1 2 4 5 7 9 10

Class B 1 1 1 2 4 5 5 5 5 7 7 8 8 8 9 10

• Mean for class A =

= 4,4

• Mean for class B =

= 5,4

• The average for Class B is better; however the lowest marks in Class A distort the mean.

9

1097542111

16

10988877555542111

Calculating the Mean 3

Marks(10) Tally Frequency (/) Mark x/

1 11 2 2

2 III 3 4

3 iiil 4 12

4 iiii iiii iiii iiii 10 40

5 mi 6 30

6 nil 4 24

7 -B 5 35

8 in 3 24

9 i 1 9

10 n 2 20

Total:40 Total:202

Example

2. Calculate the mean from the frequency table:

Mean = 1,5

40

202

4

Mode

Is the data value that occurs most often

Example

1. Determine the mode:

There are two modes in this set of data: 2 and 4

The data is said to be bimodal.

Class

C

1 1 1 2 2 2 3 4 4 4 5 5 6 7 9 10

5

2. Determine the mode:

Mode = 4

6

Median

Is the data value that lies in the middle of the data set

Need to arrange data in ascending order

If even number of data values, add the 2 data values and divide by 2

Not affected by outliers

Example

1. Determine the median:

The median is 5

Class

A

1 1 2 2 3 4 4 5

M

5 6 7 8 8 9 10

7

2. Determine the median:

Median =

For odd numbers – always add innermost 2 and

divide by 2.

Determining the Median

Class

B

1 2 4 4 4 4 5 6

?

7

?

7 8 8 9 9 9 1

0

5,62

76

Mean, Median & Mode Example

8

EXERCISE

Class results for a test out of 30 are recorded in

the table below:

10A 16 12 16 11 14 15 22 16 17 15 26

10B 20 19 14 10 14 9 8 13 14 30 -

(a) Calculate the mean for each class.

(b) Calculate the mode for each class.

(c) Calculate the median for each class.

9

Estimated Mean

Is the data value that lies in the middle of the data set

Need to arrange data in ascending order

If even number of data values, add the 2 data values and divide by 2

Not affected by outliers

Example

1. Determine the median:

The median is 5

Class

A

1 1 2 2 3 4 4 5

M

5 6 7 8 8 9 10

10

MEASURES OF CENTRAL TENDENCY

FOR GROUPED DATA

Estimated Mean

Can’t find the actual mean as we don’t have the actual data values – only the frequency of data values that lie in the class interval

To calculate estimated mean:

- determine midpoint of

class interval

- multiply each midpoint by

the frequency

- sum the answers and divide

by the number of values in

data set

Class Interval Frequency

0 – 9 years 0

10 – 19 years 11

20 – 29 years 14

30 – 39 years 17

40 – 49 years 13

50 – 59 years 7

60 – 69 years 6

70 – 79 years 5

80 – 89 years 4

90 – 99 years 0

Example

11

Class Interval Frequency Midpoint class

interval

Frequency x

Midpoint

0 – 9 years 0 0 -

10 – 19 years 11 14,5 159,5

20 – 29 years 14 24,5 343

30 – 39 years 17 34,5 586,5

40 – 49 years 13 44,5 586,5

50 – 59 years 7 54,5 387

60 – 69 years 6 64,5 381,5

70 – 79 years 5 74,5 372,5

80 – 89 years 4 84,5 372,5

90 – 99 year 0 -

Totals 77 - 3146,5

Estimated mean = 08,4077

5,3146

12

Modal class

The class interval that has the most data values

Modal class = 30 - 39 years

Class Interval Frequency

0 – 9 years 0

10 – 19 years 11

20 – 29 years 14

30 – 39 years 17

40 – 49 years 13

50 – 59 years 7

60 – 69 years 6

70 – 79 years 5

80 – 89 years 4

90 – 99 years 0

Example

13

Estimated median

The value which lies in the middle of the class interval

Median = 38

Example

Stem and Leaf Diagrams 14