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Specific Objectives
By the end of the topic the learner should be able to:
- Define statistics
- Collect and organize data
- Draw a frequency distribution table
- Group data into reasonable classes
- Calculate measures of central tendency
- Represent data in form of line graphs, bar graphs, pie-charts, pictogram,histogram and frequency polygons
- Interpret data from real life situations.
Content
- Definition of statistics
- Collection and organization of data
- Frequency distribution tables (for grouped and ungrouped data)
- Grouping data
- Mean, mode and median for ungrouped and grouped data
- 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
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
Canada angle
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 ≤13.5 13.5 ≤ x ≤15.5 15.5 ≤ x ≤ 17.5 17.5 ≤ 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 | |||||||||
10-29 30-39 40-69 70-74 75-89 90-99 |
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 |
- On the graph paper provided, draw a histogram to represent this information.
- On the same diagram, construct a frequency polygon.
- 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