Specific Objectives

By the end of the topic the learner should be able to:

1. Define statistics
2. Collect and organize data
3. Draw a frequency distribution table
4. Group data into reasonable classes
5. Calculate measures of central tendency
6. Represent data in form of line graphs, bar graphs, pie-charts, pictogram,histogram and frequency polygons
7. Interpret data from real life situations.

Content

1. Definition of statistics
2. Collection and organization of data
3. Frequency distribution tables (for grouped and ungrouped data)
4. Grouping data
5. Mean, mode and median for ungrouped and grouped data
6. Representation of data: line graph, Bar graph, Pie chart, Pictogram, Histogram, Frequency polygon interpretation of data.

Introduction

This is the branch of mathematics that deals with the collection, organization, representation and interpretation of data. Data is the basic information.

Frequency Distribution table

A data table that lists a set of scores and their frequency

Tally

In tallying each stroke represent a quantity.

Frequency

This is the number of times an item or value occurs.

Mean

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This is usually referred to as arithmetic mean, and is the average value for the data

The mean

Mode

This is the most frequent item or value in a distribution or data. In the above table its 7 which is the most frequent.

Median

To get the median arrange the items in order of size. If there are N items and N is an odd number, the item occupying.

If N is even, the average of the items occupying

Grouped data

Then difference between the smallest and the biggest values in a set of data is called the range. The data can be grouped into a convenient number of groups called classes. 30 – 40 are called class boundaries.

The class with the highest frequency is called the modal class. In this case its 50, the class width or interval is obtained by getting the difference between the class limits. In this case, 30 – 40 = 10, to get the mid-point you divide it by 2 and add it to the lower class limit.

The mean mass in the table above is

Mean

Representation of statistical data

The main purpose of representation of statistical data is to make collected data more easily understood. Methods of representation of data include.

Bar graph

Consist of a number of spaced rectangles which generally have major axes vertical. Bars are uniform width. The axes must be labelled and scales indicated.

The students’ favorite juices are as follows

Red 2

Orange 8

Yellow 10

Purple 6

Pictograms

In a pictogram, data is represented using pictures.

Consider the following data.

The data shows the number of people who love the following animals

Dogs 250, Cats 350, Horses 150 , fish 150

Pie chart

A pie chart is divided into various sectors .Each sector represent a certain quantity of the item being considered .the size of the sector is proportional to the quantity being measured .consider the export of US to the following countries. Canada \$ 13390, Mexico \$ 8136, Japan \$5824, France \$ 2110 .This information can be represented in a pie chart as follows

Mexico

Japan France

Line graph

Data represented using lines

Histograms

Frequency in each class is represented by a rectangular bar whose area is proportional to the frequency .when the bars are of the same width the height of the rectangle is proportional to the frequency .

Note;

The bars are joined together.

The class boundaries mark the boundaries of the rectangular bars in the histogram

Histograms can also be drawn when the class interval is not the same

The below information can be represented in a histogram as below

 Marks 10- 14 15- 24 25 – 29 30 – 44 No.of students 5 16 4 15

Note

When the class is doubled the frequency is halved

Frequency polygon

It is obtained by plotting the frequency against mid points.

End of topic

 Did you understand everything?If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

Past KCSE Questions on the topic.

1.  The height of 36 students in a class was recorded to the nearest centimeters as follows.

148  159  163  158  166  155  155  179  158  155  171  172  156  161  160  165  157  165  175  173  172  178  159  168  160  167  147  168  172  157  165  154  170  157  162  173

(a) Make a grouped table with 145.5 as lower class limit and class width of 5. (4mks)

2.  Below is a histogram, draw.

Use the histogram above to complete the frequency table below:

 Length Frequency 11.5 ≤ x ≤13.513.5 ≤ x ≤15.515.5 ≤ x ≤ 17.517.5 ≤ x ≤23.5

3.  Kambui spent her salary as follows:

 Food 40% Transport 10% Education 20% Clothing 20% Rent 10%

Draw a pie chart to represent the above information

4.  The examination marks in a mathematics test for 60 students were as follows;-

 60 54 34 83 52 74 61 27 65 22 70 71 47 60 63 59 58 46 39 35 69 42 53 74 92 27 39 41 49 54 25 51 71 59 68 73 90 88 93 85 46 82 58 85 61 69 24 40 88 34 30 26 17 15 80 90 65 55 69 89 Class Tally Frequency Upper class limit 10-2930-3940-6970-7475-8990-99

From the table;

(a) State the modal class

(b) On the grid provided , draw a histogram to represent the above information

5.  The marks scored by 200 from 4 students of a school were recorded as in the table below.

 Marks 41 – 50 51 – 55 56 – 65 66 – 70 71 – 85 Frequency 21 62 55 50 12

1. On the graph paper provided, draw a histogram to represent this information.
2. On the same diagram, construct a frequency polygon.
3. Use your histogram to estimate the modal mark.

6.  The diagram below shows a histogram representing the marks obtained in a certain test:-

(a) If the frequency of the first class is 20, prepare a frequency distribution table for the data

(b) State the modal class

(c) Estimate:   (i) The mean mark   (ii) The median mark

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