Week 8 and 9 – Jss 3 First Term Mathematics Lesson Notes

WEEK 8
EVERYDAY STATISTICS
Data Presentation
Frequency Table
Example: The raw data below show the number of mobile phone calls made by a group of students in a certain day.
5    6    7    8    4    4    5    7    8    10
7    6    5    8    5    7    8    7    10    7
6    5    6    7    7    5    4    5    7    8

1. Use a tally mark to prepare a frequency table for this data
2. What calls occur most often?
3. What percentage of students made 8 calls?

SOLUTION

1. No of calls made            Tally            Frequency

   4                                3    
   5                                7    
   6                                4    
   7                                9
   8                                5
   9                                0
   10                                2

2. 7 calls
3. x 100

   = 16%

 Pictogram
Example: The following table shows the colour of cars in a car park one morning. Draw pictogram to illustrate this data.
Colours of car        frequency        
Black                20
White                17
Red                8    
Yellow                5
Green                10

 SOLUTION
Colour of cars
Black        
White    
Red        
Yellow    
Green
Key:         = 2        = 1

 
 
 Bar Chart
Bar charts consist of series of bars with equal width.
Example: Draw bar chart to illustrate the data of the example above

 
 Frequency         colour of cars of the park

 Compound bar chart
It is used to compare two or more different sets of information.
Example:
The following table shows the number of candidates who gained admission into higher institutions at a certain town over a period of years.
Year        Boys        Girls
1997        65        46
1998        50        55
1999        80        73
2000        70        92
2001        45        64

1. Illustrate this information on dual bar chart
2. Illustrate what year did girls leave the highest admission?
3. Illustrate what year did boys have the least admission?
4. How many more boys had admission than girls in 1999?
5. How many more candidates gained admission in 2000 than 1998?

SOLUTION
No of candidates         

 ASSIGNMENT
EXERCISE 22.1; NO 1, 2, AND 3 PAGE 226.

 Pie charts
A pie chart is a circle divided into sectors whose angle are used to display data
Example:

1. In a certain year, the expenditure of a university is shown in the table below.

    
   Items                Expenditure in Million Naira
   Equipment            20
   Salaries and wages        25
   Building projects        70
   Maintenance        25
   Miscellaneous        10

2. Draw a pie chart to illustrate the information
3. What percentage of total expenditure goes on project

SOLUTION
Items                Expenditure in Million Naira        Angles
Equipment            20                     x = 48^o
Salaries and wages        25                     x = 60^o
Building Project            70                     x = 168^o
Maintenance            25                     x = 60^o    
Miscellaneous            10                     x = 24^o
Total                150                     360^o

b)    x = 46.7^o

 
 Example 2

History 40%    , Geography 30%    , Further Mathematicss10% and Physics 20%
The pie chart shows the percentage of students taking Further Mathematics, Physics, History and Geography

1. What angle represented subject?
2. What fraction of students are taking history
3. If the total number of students is 500, how many students are taking physics?

SOLUTION
Subject            Percentage                    Angles
Further Maths        10%                         x = 36^o
Physics            20%                         x = 72^o
History            40%                         x = 144^o
Geography        30%                         x = 108^o    
Total            100%                         360^o
(b)    Fraction for history = =
(c) No of Physics Students = x 500 = 100 Students
Exercise: Ex. 22.2 No 1 and 5 page 228 and 229

 WEEK 9
MEASURE OF CENTRAL TENDENCY (MEAN, MEDIAN, MODE)
Example

1. In a test 10 pupils obtained the following marks 5, 7, 4, 8, 5, 7, 10, 9, 3. Find (a) The mean mark (b) Median mark (c) Modal mark.

SOLUTION

1. Mean = = =

   Mean = 6.4

2. Arrange the marks in ascending order of magnitude 3, 4, 5, 5, 6, 7, 8, 9, 10

   Median = = = 6.5

3. The mode is the value that occurs most the mode are 5 and 7 this is bimodal.

Calculating average from frequency tables
Examples: In a science test. The following score shown in the table below were obtained out of 10 by some students.
Marks    No of Students (Frequency)
0        2
1        1
2        2
3        4
5        1
6        7
7        3
8        4
9         1

1. Find (i) the mode (ii) the median (iii) the mean of the frequency distribution
2. How many students scored at least 5 marks

 
 
 
 SOLUTION

1. (i) Mode = 8

   (ii) 0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9
   Median = = 5.5
   (iii) Sum of values = 0 + 0 + 1 + 2 + 2 + 3 + 4 + 4 + 5 + 6 + 6 + 7 + 7 + 7 + 8 + 8 + 8 + 8 + 9 = 99

Mean = = = 4.95

 
 ALTERNATIVELY

 
Scores frequency (f) frequency x score
0                2                    2 x 0 = 0
1                1                    1 x 1 = 1
2                2                    2 x 2 = 4
3                1                    1x 3 = 9
4                3                    3 x 4 = 12
5                1                    1 x 5= 5
6                2                    2 x 6 = 12
7                3                    3 x 7 = 21
8                4                    4 x 8 = 32
9                1                    1 x 9 = 99
                 = 20 = 99
Mean = = = 4.95
Exercise: Ex 22.3 No 1 and 2 page 231
Range: It gives a measure of how spread and the values are. Range = Highest value – Lowest value
Examples

1. Find the range of these numbers 9, 4, 7, 6, 12, 8, 15, 10

   Solution: Range = 15 – 4 = 11

1. A student obtained the following marks each out of 100 in different geography test 42, 44, 50 40, 54, 48, 10 88. Find (a) The mean (b) the range (c) make a comment why the range in this case is not good to measure the spread.

SOLUTION

1. Mean = =

   Mean = 48

2. Range = 88 – 10

   = 78

3. The two extreme values i.e. 10 and 88 affects the range, so at it not a good measure of spread in this particular case.

Exercise
Find the range of the following

1. 35cm, 50cm, 45cm, 90cm, 30cm
2. 67km, 50km, 20km, 48km, 55km
3. 5.2, 4.7, 8.2, 9.3, 6.4, 5.5

ASSIGNMENT
EXERCISE 22.4; NO 8, 9 AND 10. PAGE 240.