SUBJECT: MATHEMATICS

CLASS: SS 1

DATE:

TERM: 3rd TERM

REFERENCE BOOKS

New General Mathematics SSS 1 by M.F. Macrae et al
Essential Mathematics SS 1

WEEK 6

TOPIC: STATISTICS

CONTENT: COLLECTION, TABULATION AND PRESENTATION OF DATA

What is statistics? This is defined as the collection of data and the presentation of the collected data in a clearer form, for better interpretation. There are two possible ways of presenting the collected data, for better interpretation and these are:

Tabular Presentation (Tables)
Graphical Presentation (Graphs)

Data:There are two possible ways in which data can be classify and these are Grouped and Ungrouped data.Data is/are sometimes referred to as information. Althoughthey differs in so many ways,i.e,information is wider than data,hence data is found under the information of a certain event.Example,I can gather the information of a class,such as SSS 1,each student in such class has their individual particular,these particulars of each of the student is then known as DATA. Simply put INFORMATION is the collection of data.

When data are collected at first,they are said to be RAW,because they are yet to be arranged in an order of magnitude.Therefore,it is important tore-arrange such data in an order of magnitude,(ascending or Descending, Order)

TYPES OF DATA

Quantitative Data:Since,the word quantitative, refers to as quantity,therefore,quantitative data, takes numeric values(Numbers).Quantitative data is sub-divided into two and these are:

Discrete Data: This data can simply be obtain by mere counting. Such as the number of student in a class, population of a country, number of cars in a garage, number of houses on a street etc.It must be noted that, Discrete data, always take a whole number value, as no counting can be in decimal.eg,43 students and not 42.5 students.
Continuous Data: These data are obtain by measurement, eg, weight, height,age,sizes,scores/marks etc,they can take whole number and decimal.

Qualitative Data: This type of data is concern about the quality of a data. it can be describe in word,eg,taste,colour,make of shoes etc.

It is a common practice to present data in frequency tables. Frequency tables are used for summarising data before analysis.

Example

1)A teacher gives a spelling test to 40 students. The number of errors made by the students is shown in table below. Represent the data in a frequency table.

1	2	3	0	4	5	3	5	3	0
0	1	2	3	4	2	2	1	0	4
0	2	1	0	2	3	2	2	1	0
0	2	1	0	2	3	2	2	1	0
4	5	3	1	2	0	1	2	3	4

The data first summarised by first using tally marks as shown below

Number of errors

Tally

Frequency

IIII III

IIII II

IIIIIIII

IIII II

IIII

III

The data are then presented in a frequency table

Number of errors	0 1 2 3 4 5
Frequency	8 7 10 7 5 3

Evaluation

Prepare a frequency table for the data below:

The number of beans in a sample of 30 cocoa pods are as follows

26 32 25 29 30 30

29 28 30 30 26 28

28 27 29 32 25 26

25 26 27 28 32 31

30 31 29 28 28 27

UNGROUPED DATA

Data are said to be ungroup if and only, each of the quantity/variable. Can stand as a unit without any combination.The variables are not large,therefore,to prepare the frequency table will be very easy.

Tabular Presentation of ungrouped data:

The table used in the presentation of statistical data is known as Frequency distribution table and consist of atleast three Column and in some cases, extra column may be required. The basic column required are listed and defined bellow:

Variable Column (First column):It is mostly denoted with x.This column contains the item collected or required.such as Height,Ages,Weights,Test and Examination Scores of students. The variable column can also contain the population of a country.
Tally Column(Second Column) : The tally is the use of strokes to represent an item collected,it makes the counting and the recording of the Frequency very easy.Tally is always in a bundle of five strokes.
Frequency Column (Third Column):This is denoted with f,It is defined as the number of times an item occur.The use of tally can facilitate the accurate record of the frequency.

Example 1: The weight of some students in SSS1 class in Good Shepherd Schools are as listed below: 55,57,57,59,50,55,61,61,55,57, 57,57,59,55,55,50,55,55,50,57

57,57,59,50,50,55,57,57,55,5050,50,55,57,61,57,59,61,59,55

, 61,55,57,55,50,61,59,55,57,61

Prepare the frequency distribution table for the information.

Solution:

Weight (x)	Tally	Frequency(f)
50	I IIIIII	8
55	I II II I III	11
57	I II II I III	11
59	I IIIII	7
61	I III	5

The above frequency table is prepared for the ungrouped data,as each weight recorded stands as a unit.

Example 2:Prepare a frequency table,showing the percentage scrores of each of the scores obtained in a mathematics test of students in SSS 1 Shephered.The scores are:

9, 7 ,8, 5, 4, 6, 5, 8, 6, 6, 10, 5, 6, 7, 6, 6, 5, 5, 7, 8, 10, 2, 8, 6, 6

2, 6, 4, 5, 5, 8, 8, 6, 6, 5, 9, 9, 2, 7, 4, 6, 3, 5, 6, 2, 7, 2, 9, 8, 10

Solution:

MARKS	TALLY	FREQUENCY	PERCENTAGE%
2	I III	5	10
3	I	1	02
4	I II	3	06
5	I IIIIIII	9	18
6	I II II I IIIII	13	26
7	I III	5	10
8	I IIIII	7	14
9	I III	4	08
10	I II	3	06

Calculation of Range, Median and Mode of Ungrouped Data

RANGE

The range of a set of numbers is the difference between the largest and the smallest numbers.

Example: Find the range of the following set of scores: 79, 60, 52, 34, 58, 60.

Solution

Arrange the set in rank order: 79, 60, 60, 58, 52, 34

The range is 79 – 34 = 45

THE MEAN

There are many kinds of average. T hemean or arithmetic mean, is the most common kind. If there are n numbers in a set, then

Mean = sum of the numbers in the set/ n

Examples

1)Calculate the mean of the following set of numbers.

176 174 178 181 174

175 179 180 177 182

Solution

Mean = 176 + 174 + 178 + .... + 182/10

= 1776/10

= 177.6

2)Five children have an average age of 7 years 11 months . If the youngest child is not included, the average increares to 8 years 4 months. Find the age of the youngest child.

Solution

Total age of all five children

= 5 x 7 yr 11 mo

= 35 yr 55 mo

= 35 yr + 4 yr 7 mo

= 39 yr 7 mo

Total age of the four older children

= 4 x 8 yr 4 mo

= 32 yr 16 mo

= 32yr + 1 yr 4 mo

= 33 yr 4 mo

Age of youngest child

= 39yr 7 mo – 33 yr 4 mo

= 6 yr 3 mo

Evaluation

Find x if the mean of the numbers 13, 2x, 0, 5x and 11 is 9. Also find the range of the set of numbers.
A mother has seven children. The mean age of the children is 13 years 2 months. If the mother’s age is included, the mean age rises to 17 years 7 months. Calculate the age of mother.

MEDIAN AND MODE

MEDIAN: If a set of numbers is arranged in order of size, the middle term is called the median. If there is an even number of terms, the median is the arithmetic mean of the two middle terms.

Examples

Find the median of a) 15, 11, 8, 21, 17, 3, 8 b) 3.8, 2.1, 4.4, 8.3, 9.2, 5.0.

Solution

a)Arrange the numbers in rank order (i.e from highest to lowest).

21, 17, 15, 11, 8, 8, 3

There are seven numbers. The median is the 4th number, 11 .

b)Arrange the numbers from the lowest to highest.

2.1, 3.8, 4.4, 5.0, 8.3, 9.2

There are six numbers. The median is the mean of the 3rd and 4th terms.

Median = (4.4 + 5.0) /2

= 4.7

MODE: The mode of a set of numbers is the number which appears most often, i.e. the number with the greatest frequency.

Example: Twenty-one students did an experiment to find the melting point of naphthalene. The table below shows their results. What was a) the modal temperature b) the median temperature?

temperature (oC) 78 79 80 81 82 83 90

frequency 1 2 7 5 3 2 1

a)Seven students recorded a temperature of 80oC. This was the most frequent result.

Mode = 80oC

b)There were 21 students. The median is the 11th temperature. If the temperatures were written down in order, there would be one of 78oC, two of 79oC, seven of 80oC, and so on. Since 1 +2 + 7 = 10, the 11th temperature is one of the five 81oCs.

Median = 81o C.

EVALUATION

For the following set of numbers:

13, 14, 14, 15, 18, 18, 19, 19, 19, 21

a)state the median, b) state the mode, c) calcilate the mean.

READING ASSIGNMENT

NGM BK 1 PG 196 – 203 Ex 18d nos 17 - 20

GENERAL EVALUATION

Prepare a frequency table for the following sets of data.

1)The shoe sizes of a group of 24 children are

8 6 7 5 4 6 5 7

6 5 7 6 8 5 4 6

5 5 6 7 8 8 6 7

2)The ages of 32 students in Class 2 of a Junior Secondary School are

11 12 11 12 12 14 14 13

15 13 12 13 13 13 13 12

14 14 13 15 14 11 12 14

12 15 14 16 14 14 14 15

WEEKEND ASSIGNMENT

The number of goals scored by a team in nine handball matches are as follows: 3, 5, 7, 7, 8, 8, 8, 11, 15Which of the following statements are true of these scores?a)The mean is greater than the mode.b)The mode and the median are equal.c)The mean, median, and mode are all equal.

Use the table below to question 2-5

The table below shows the number of pupils (f) scoring a given mark (x) in attest.

X 2 3 4 5 6 7 8 9 10 11 12

f 3 8 7 10 13 16 15 15 6 2 5

Find the mode.a)7 b) 8 c) 9 d) 10
Find the median.a) 6 b) 7 c) 8 d) 9
Calculate the mean.a) 6.7 b) 6.8 c) 6.9 d) 6.95
Find the range.a)10 b) 11 c) 9 d) 12

THEORY

x, x, x, y represent four numbers. The mean of the numbers is 9,their median is 11. Find y
Students at a teacher training college are grouped by age as given in table below.

Age (years) 20 21 22 23 24 25

Frequency 4 5 10 16 12 3

Find the modal age.
Find the median age.
Calculate the mean age of the students.

Lesson Notes By Weeks and Term - Senior Secondary School 1