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博文教育

Pt3MATHEMATICS

STATISTICS

Data (F2)

Frequency (F2)

Represent and Interpret Data (F2)

Pie Charts (F3)

Mode, Median and Mean (F3)

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Pusat Tuisyen MINDA CERDAS JAYA 中小学补习中心(UPSR PT3 SPM)

DATA

- Data is a collection of information, especially facts or numbers.

- Numerical data can be classified as：

(a) Data obtained from countingFor example, the data below shows the number of students counted in fivedifferent classes.39, 41, 42, 38, 39

(b) Data obtained from measuringFor example, the data below shows the heights of ten students measured in cm.150, 152, 149, 151, 151, 148, 156, 155, 153, 148

- The data collected should be recorded systematically in tables for easy reference.

For example:

Form One : 15 classesForm Two : 10 classesForm Three : 8 classes

(a) By arranging the data horizontally

Form One Two ThreeNumber of classes 15 10 8

(b) By arranging the data vertically

Form Number of classesOne 15Two 10

Three 8



FREQUENCY

- Frequency is the number of times a certain number, measurement, score or itemoccurs.

For example, the following set of data shows the ages of 10 students:

10, 8, 9, 8, 8, 10, 8, 9, 10, 8

Based on the data, the following frequencies are determined:

(a) The frequency of 8 is 5.(b) The frequency of 9 is 2.(c) The frequency of 10 is 3.

Tally ChartFor example:

4, 2, 4, 6, 4, 4, 5, 6, 3, 46, 4, 5, 3, 1, 4, 2, 6, 3, 5

The data above shows the scores obtained by throwing a dice 20 times. Find thefrequency of each score.Solution:

Frequencies can be easily obtained by using a tally chart shown below:

HELPFUL TIPS In the tally chart, the data is grouped in fives to ease counting. Example: means 5



REPRESENT AND INTERPRET DATA

Pictogram

- A pictogram represents data in the form of a picture diagram.

- When constructing a pictogram, use a symbol that is easily understood.

Example:

Year Frequency2002 302003 502004 202005 40

The table shows the number of cars sold by a company from year 2002 to 2005.Construct a pictogram to represent the data given.

Solution:

Number of cars sold from year 2002 to 2005

- We can obtain a lot of information by studying a pictogram.




Bar Chart

- A bar chart is a representation of data using vertical or horizontal bars.

- It is a frequency diagram using rectangles of equal width. The height or length ofeach rectangle is proportional to the frequency it represents.

For example:

Vertical bar Horizontal bar

- A dual bar chart can be constructed to represent two sets of data in the same chart.

For example:

(a) Using separate bars for boys and girls (b) Using a single bar for both boys andgirls

- We can obtain a lot of information by studying a bar chart.




Line Graphs

- Line graphs are usually used to represent changes in data over a period of time, suchas

(a) change in a patient’s temperature in 24 hours.(b) Change in production in a factory in the first six months.

- By looking at the lines in a line graph, we can tell whether something is increasing,decreasing or static over a period of time.

For example:

Month Jan Feb Mar Apr MayMarks 50 60 10 70 40

The table shows the monthly test marks of Swee Lee for Mathematics. Draw a linegraph to represent the given data.

- We can obtain a lot of information by studying a line graph.




Pie Charts

- A pie chart is a circle, divided into sectors of various sizes, with each sectorrepresenting the corresponding data.

- Information can be obtained from a pie chart by studying the angle or area of eachsector.

For example:

From the pie chart given, we can obtain information as follows:

(a) The number of Malay students is the highest because the sector representing

Malay students is the biggest. That is 53

360216

0

0

.

- To construct a pie chart, find the angle of each sector.

Angle of sector0360x

data overall ofquantity data ofcategory each ofquantity



MODE, MEDIAN AND MEAN

Mode

- The mode of a set of data is the value or item which occurs most frequently.

- We can determine the mode from

(a) a given set of data(b) a frequency table(c) a pictogram, bar chart, line graph or pie chart

Example 1:

Determine the mode of the following sets of data.

2, 3, 4, 5, 3, 2, 2, 7

Solution:The mode is 2.

Example 2:

Marks 0 1 2 3 4Frequency 3 4 3 1 5

The table shows the distribution of test marks obtained. Determine the mode.

Solution:The mode is 4 marks.



Determine the mode and its corresponding frequency in each of the following.

(a) Number of books sold in a bookshop

Solution:The mode is Mathematics books.Frequency of mode = 5 x 50

= 250

(b) Number of kuih sold in a food stall

Solution:The mode is kuih keriaFrequency of mode = 60



(c) Number of eggs sold in a week

Solution:The mode is 250 eggs.Frequency of mode = 2

(d) Grouping of 240 workers in a factory

Solution:The mode is the Malay group.Frequency of mode = 45% x 240

= 108



Median

- The median is the middle value when all the data are arranged in an increasing ordecreasing order.

- When finding the median of data in a frequency table, use the following methods.

(a) By listing all the numbers.(b) By finding the cumulative frequency.

Example 1:

Determine the median of each of the following sets of data.

(a) 5, 2, 4, 8, 2, 3, 1(b) 13, 18, 10, 22, 15, 24, 16, 11

Solution:



Example 2:Score 1 2 3 4 5 6Frequency 1 2 4 5 3 2

Find the median of the data given in the frequency table.

Example 2:Score 1 2 3 4Frequency 8 14 16 12

Find the median of the data given above.



Mean

- Mean is the arithmetic average of a set of data.

- Mean can be calculated using the formula:

data ofnumber totaldata of values theall of sumMean

Example 1:

Find the mean of 3, 8, 5, 9, 11 and 6.

Solution:Mean =

66119583

=642

= 7

Example 2:Score 1 2 3 4 5Frequency 4 6 7 0 3

Find the mean of the data given above.

Solution:

data ofnumber totaldata of values theall of sumMean

=30764

(5x3)(4x0)(3x7)(2x6)x4)1(

=20

15021124

=2052

= 2.6

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