3. BAR GRAPHS
Bar graphs represent data using vertical or
horizontal bars.
The height or length of each bar corresponds to
the quantity it represents.
Consider brian a grade 8 student who scored 90 %
in english, 80% in mathematics and 60 % in
kiswahili in term 1 . we can represent this marks
in a bar graph as show below
4. HORIZONTAL BAR GRAPH
A type of graph that represents data using horizontal
bars of varying lengths to show the relationships or
comparisons between different categories or groups.
In a horizontal bar graph.
example
Consider Brian a grade 8 student who scored 90 % in
English, 80% in Mathematics and 60 % in Kiswahili in
term 1 . We can represent this marks in a bar graph
as show below
5. 0 20 40 60 80 100
Maths
English
Kiswahili
marks
6. Vertical bar graph
A type of graph that represents data using vertical
bars of varying lengths to show the relationships or
comparisons between different categories or
groups. In a vertical bar graph.
Example
Consider Brian a grade 8 student who scored 90 %
in English, 80% in Mathematics and 60 % in Kiswahili
in term 1. We can represent this marks in a bar
graph as show below.
8. assessment
1. The marks scored by Ahmed out of 50 in different subjects in
an exam were recorded in a table as shown.
Represent this information on a horizontal bar graph.
2. The number of girls in a school in Grade Three to Eight
is as shown in.
Represent this information on a vertical bar graph.
Subject English Kiswahil
i
Mathematic
s
Integrated
science
Creative
arts
Marks
obtained
29 23 46 44 12
Grade 3 4 5 6 7 8
No. of girls 20 42 32 28 26 30
9. Line Graphs.
Line graphs connect points with straight lines to
show pattern.
Consider Brian a grade 8 student who scored 90
% in English, 80% in Mathematics and 60 % in
Kiswahili in term 1, scored 60 % in English, 70%
in Mathematics and 40 % in Kiswahili in term 2
and scored 80 % in English, 90% in Mathematics
and 90 % in Kiswahili in term 3. We can
represent this information in line graph.
11. ASSESSMENT
1. The table shows the amount of milk delivered to a dairy by a
farmer a certain week,
Draw a line graph to represent the data.
2. The table below shows distance travelled and time taken by
a car between 2 towns.
Draw a line graph to represent the information.
Day of the
week
Mon Tue Wed Thur Fri Sat Sun
Amount of milk 30 25 35 25 20 15 25
Times (hours) 1 2 3 4
Distance (km) 50 80 120 150
12. Mode
The mode is the value that appears most frequently in
a set.
EXAMPLES
Given the ages of 10 students in grade 8:
12, 13, 12, 14, 15, 12, 14, 15, 16, 12. Determine
the mode.
Solution:
The mode is 12, as it appears most often.
13. assessment
1. In a classroom of 30 students, the teacher asks them about their favorite colors. The results are as
follows: 8 students like blue, 7 like red, 6 like green, 5 like yellow, and the rest like purple. What is
the mode of the favorite colors among the students?
2. A grocery store sells five different brands of cereals. During a survey, customers were asked to name
their favorite brand. The results are: 10 customers prefer Brand A, 15 prefer Brand B, 12 prefer Brand
C, 8 prefer Brand D, and 10 prefer Brand E. What is the mode of the preferred cereal brands among
the customers surveyed?
3. In a town, a survey is conducted to determine the mode of transportation used by residents to
commute to work. The results show that 200 people use cars, 150 use bicycles, 180 use public
transport, 100 walk, and the rest use motorcycles. What is the mode of transportation for commuting
to work in the town?
4. A survey is conducted among students in a school to determine their favorite subjects. The results are
as follows: 50 students prefer Mathematics, 60 prefer Science, 40 prefer English, 30 prefer History,
and the rest prefer Geography. What is the mode of the favorite subjects among the students
surveyed?
5. In a group of 50 employees in a company, their monthly salaries are recorded. The salaries are as
follows: 10 employees earn kshs2000, 15 earn kshs2500, 8 earn kshs3000, 10 earn kshs3500, and the
rest earn kshs4000. What is the mode of the monthly salaries among the employees?
14. MEAN
The mean is the sum of all data values divided by the
number of values.
Example 1: Find the mean of test scores: 86, 92, 78,
88, 94.
Solution:
Mean = 86+92+78+88+94=438
438 ÷ 5 = 87.6
Mean is 87.6.
15. assessment
1. The weights of 10 students in a class are recorded as follows: 50
kg, 55 kg, 60 kg, 65 kg, 70 kg, 75 kg, 80 kg, 85 kg, 90 kg, and 95
kg. What is the mean weight of the students in the class?
2. A farmer recorded the milk production (in liters) of each of his 15
cows over a week: 20, 22, 25, 28, 30, 32, 35, 36, 38, 40, 42, 45,
48, 50, and 52. What is the mean milk production per cow for the
week?
3. The test scores of 25 students in a class are recorded as follows:
85, 78, 90, 92, 84, 88, 95, 72, 80, 85, 90, 88, 82, 75, 85, 78, 88,
90, 92, 84, 78, 85, 80, 88, and 92. What is the mean test score of
the students?
4. The ages of 20 employees in a company are recorded as follows:
16. MEDIAN
The median is the middle value when data is arranged in
order from the smallest to the largest or the largest to the
smallest.
Example 1: Given the data set: 8, 15, 22, 17, 10. Arrange it
in ascending order and find the median.
Solution:
Arranged data: 8, 10, 15, 17, 22.
Median = 15.
Example 2: Arrange the following ages in ascending order:
34, 22, 28, 30, 25. Determine the median.
Solution:
Arranged data: 22, 25, 28, 30, 34.
17. assessment
1. In a class of 20 students, the heights (in centimeters) are recorded as follows: 150, 155, 160, 165,
170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, and 245. What is the
median height of the students?
2. A group of 15 friends goes out to dinner, and each person pays for their meal. The amounts paid (in
dollars) are: kshs10, kshs15, kshs20, kshs25, kshs30, kshs35, kshs40, kshs45, kshs50, kshs55, kshs60,
kshs65, kshs70, kshs75, and kshs80. What is the median amount paid for the dinner?
3. A survey is conducted to determine the ages of people attending a music concert. The ages recorded
are: 20, 22, 24, 25, 27, 30, 32, 35, 38, 40, 42, 45, 48, 50, and 55 years. What is the median age of
the concert attendees?
4. The scores of 25 students on a math test are recorded as follows: 65, 70, 75, 80, 82, 85, 88, 90, 92,
94, 95, 96, 98, 100, 102, 104, 105, 106, 108, 110, 112, 115, 118, 120, and 125. What is the median
test score?
5. A company has 10 employees, and their monthly salaries (in dollars) are: kshs2000, kshs2500,
kshs3000, kshs3500, kshs4000, kshs4500, kshs5000, kshs5500, kshs6000, and kshs6500. What is the
median monthly salary of the employees?
19. IDENTIFYING EVENTS INVOLVING CHANCE
Chance events are events whose outcomes are not
certain.
Likely events have a higher chance of occurring, while
unlikely events have a lower chance.
Example: Think about the event of drawing an orange
ball from a bag containing red and orange balls. Is this a
likely or unlikely event?
Think about the event of drawing a twenty-shilling coin
from an empty pocket is this a likely or unlikely event?
20. Work in group
Classify the following events as likely, unlikely, must happen and
cannot happen.
1. The sun rising from the East.
2. The sun rising from the North.
3. A bull giving birth to a calf.
4. A buffalo preying on a lion.
5. A fish living outside water.
6. Iron dissolving in water.
7. An axe head floating on water.
(ii) Discuss and compare with other groups.
21. assessment
Identify and write the events that are likely, unlikely,
must happen and cannot happen from the following;
1. A cock laying an egg.
2. Waking up in the morning.
3. A Grade Eight learner is 15 years old.
4. Having sunlight during the day.
5.Lifting the school van up in your hands.
6.Teacher giving learners homework on a school day.
22. Performing Chance Experiments
Chance experiments involve observing the outcomes of
uncertain events.
Exercise: Flip a coin and record whether it lands heads or
tails. Conduct the experiment 10 times and count the
outcomes.
Expressing Experimental Probability
Probability is how likely something is to occur.
Probability is often expressed as a number between 0 and 1,
where:
0 means the event is impossible.
1 means the event is certain to happen
23. assessment
1. Sarah has five cards of different colours in a bag;
red, blue, yellow, green and white. She removes one
card from the bag without looking. List all the
possible colours of the card that she removed.
2. There were four fruits of different kinds in a bag;
orange, apple, lemon and guava. Edwin picked one
fruit from the bag. List all the possible kind of fruit
he picked.
3. A packet contains five coloured pencils; red, blue, y
yellow, pink and green. A pencil is picked from the
packet at random. List all the possible colours of the
pencil picked.
24. PROBABILITY OUTCOMES IN FRACTIONS
The probability of an event can be expressed as
a fraction
Probability as a fraction is expressed as a
normal fraction where the number of outcome
is always the numerator while the total number
of attempts is the denominator. For example, in
our exercise we got 6 heads then the probability
of getting a head is
6
10
25. EXAMPLE
In a bag with 8 red balls and 4 green balls, calculate the probability of drawing a red ball.
8
12 This is the probability of drawing a red ball.
Probability Outcomes in Decimals or Percentages
Probability can be expressed as a decimal or a percentage for easier comparison.
In the flipping a coin example
Expressing probability of getting a head as a percentage would be
6
10
× 100 = 60%
60% can be expressed as a decimal as 0.6
Expressing probability of getting a tail as a percentage
4
10
× 100 = 40%
40% can be expressed as a decimal as 0.4
26. ASSESSMENT
1. There are three books in a bag one mathematics book, one
English book and one Kiswahili book. What is the probability of
picking
c)Mathematics book from the bag
d)English book from the bag
e) Kiswahili book from the bag
2. If Jane flipped a coin once what is the probability of getting
a) a head
b) a tail
27. Expressing Probability Outcomes in
Decimals or Percentages in Different
Situations
LEARNING POINT
Probability of an event can be expressed as a
fraction, decimal or percentage.
28. EXAMPLE
1. There are six oranges and four lemons ina basket. A
fruit is picked at random;
a)find the probability the fruit picked is an orange.
(b) express the probability of picking an orange as a
decimal and as a percentage.
(A). Probability of picking an orange
= number of possible outcome of an
orange
total number of fruits in the basket
= 6
10
= 3
5
(b). 3/5 as a decimal
0.6
5 30 = 0.6
30
3/5 as a percentage is
3/5 x 100
= 60%
29. ASSESSMENT
convert the following probabilities to
percentage
a)
1
2
b)
5
12
c)
7
7
Convert the following probabilities to decimal
33% b) 60% c)3
20
30. EXTENDED assessment
1. In a deck of 52 playing cards, what is the probability of drawing a
heart?
2. A bag contains 8 red balls, 5 blue balls, and 7 green balls. If one ball
is randomly selected from the bag, what is the probability of
selecting a blue ball?
3. A fair six-sided die is rolled. What is the probability of rolling a
prime number?
4. A jar contains 20 marbles: 6 are red, 8 are blue, and 6 are green. If
one marble is randomly chosen from the jar, what is the probability
of selecting a red or green marble?
5. In a class of 30 students, 15 students play soccer, 10 students play
basketball, and 5 students play both sports. If a student is randomly
