TEACHERS’
GUIDE
SUBJECT : MATHEMATICS
TOPIC : STATISTICS
SUB-TOPIC : Data
collection / Display
CLASS : Senior
Three
CLASS
SIZE : 60 Students
TIME
REQUIRED : Minimum: 640 minutes (16 Periods or 3 weeks)
Brief
description of topic
There
was a time when we did not care much about what happened around us,
perhaps because we saw no use in keeping track of events. For
instance, epidemics would break out, run amok and disappear into
oblivion without anyone taking note of the damage or daring to
explain why such epidemics butchered at will or why they condemned
some people and left others Scot free. But then came to realise that
certain events actually seemed to be linked with other past events
that hitherto had been ignored or forgotten. For instance, some
epidemics had a knack of coming back to torment mankind. A closer
look at these past events helped scientists to make sense of what was
happening at that particular moment in time and to predict what was
likely to happen in the near future. And thus a branch of
mathematics, called Statistics, was born.
We
deal with a lot of information on daily basis and some of it goes
unnoticed and/or never interpreted to our benefit. However, the
little that we are able to capture and record can be interpreted for
human use and benefit using statistical methods.
Statistics
equips the learners with the skill of collecting information, which
in its raw form is referred to as data, and representing it in an
organised form so that it makes sense. This data is analysed so that
it can be reliably used to make decisions with a lot of confidence in
business, politics, weather forecast, etc.
The
terms you will meet like, mean, mode, range, bar graph, pie chart,
histograms, and ogive, among others, are very useful in data
analysis. The Ministry of Health, for example, can tell which age
bracket of people is most vulnerable to malaria or asthma by
collecting data and analysing it to find the model age bracket, which
helps it to take appropriate measures to combat it, other than
guessing. It would be embarrassing if the ministry imported more
drugs for a less vulnerable age group and fewer drugs for the age
group that is more vulnerable.
Statistics
helps us to collect, analyse and interpret data so as to make logical
conclusions, thus leading us to the best decision.
Basic
knowledge required
The
learners should have covered Statistics in the first and second years
of secondary school. Devote time to remind learners of the content
that was covered. A quick exercise on such work will do them a lot of
good. Re-emphasize the terms: frequency distribution, bar chart, bar
graph, line graph, pie chart, range, mean, median, mode, pictograms,
frequency polygon, ogive and cumulative frequency distribution.
Content
and Concepts ?????????????????????????
Objectives
By
the end of this topic, learners should be able to;
- Organise raw data into a frequency distribution table.
- Represent the data on a histogram, for:
- Ungrouped data and,
- Grouped data.
- Estimate the mode from a histogram for grouped data.
- Draw a frequency polygon for data in a frequency distribution table.
- Calculate the mean for the grouped data.
- Calculate the mean using an assumed mean.
- Calculate the median value from a group of values.
- Calculate the mode from grouped data.
- Calculate the mean using an Ogive.
- Calculate the mode using a histogram.
- Make sensible decisions based on calculated values of the mean and mode.
- Develop personal and social skills such as collecting data/gathering information, listening skill, hard work, communication skills, budgeting, recordkeeping, decision making, prudence, courtesy, analytical skills and numerical skills.
LEARNERS’ ACTIVITIES
Activity One
Data Collection and Display
Materials required: small
pieces of paper (1 per learner).
Steps:
- Write your age on a piece of paper given to you.
- Send that piece of paper to the teacher through a column representative/leader chosen.
- The task is to find how many people are of a particular age.
The
teacher helps the learners to choose one to read out the age from the
papers and another to record.
He/she
should remind them how tallies are bundled, if needed.
A
frequency distribution table for the age of our class
|
Age
|
Tally
|
Frequency
|
|
14
|
|
|
|
15
|
|
|
|
16
|
|
|
|
17
|
|
|
|
18
|
|
|
|
?
|
|
|
- Class members should observe and confirm whether each tally is placed in the right row.
Activity
Two
Data
Collection, Display and Interpretation
- Ask your class to mention 3 or 4 outstanding personalities in music or football or any area of exercise.
- Reach a consensus with your learners and record the names on the chalkboard.
- Each learner is entitled to one vote to choose his/her best of the names on the chalkboard.
- Collect the voting papers and put them in one container.
- Choose with your class, learners to perform the following responsibilities:
- (i) One picking and reading the names.
(ii) 3 observers to ensure
that the one reading does the correct thing.
(iii) One to record the
tallies on the board.
(iv) The rest of the class
will observe to ensure proper recording.
A
frequency distribution table for the best footballer
|
Name
|
Tally
|
Frequency
|
|
Cristiano
Ronaldo
|
|
|
|
Lionel
Messi
|
|
|
|
Kaka
|
|
|
|
Didia
Drogba
|
|
|
|
Fernando
Torres
|
|
|
Questions
- Which person has got the highest number of votes?
- What was the role of the observer?
- Would you be happy if you learnt that the person who was reading, (unfaithfully) rigged for another person?
Activity Three
Data Interpretation
The
maximum temperature of each day in April at Jolly Nursing school was
recorded as below.
29 31 28 31 32 28
27 28 28 31 29 27
28 31 31 32 28 29
29 32 27 33 29 30
31 30 30 27 30 31
(a) What is; - i) The least
value of temperature recorded?
ii) The
maximum temperature?
(b) Prepare a frequency
distribution table for the data above.
(c) From your table, which
temperature has the highest frequency?
Answer: 31 (This is known as
the mode)
Reminder to students:
Mode is the most commonly occurring score/item.
Activity
Four
Representing
Data on a Histogram
Materials required:
Squared paper, squared board and pencils.
Represent the results in the
frequency distribution table in Activity 3 on a histogram.
Note:
The area of each rectangle is proportional to the frequency. The
width of the bars must be the same and their heights should match
with the frequency in the table.
- Find how many different values of temperature are in your table.
- Choose a suitable scale on the horizontal axis that will accommodate all these temperature values.
- Identify the modal frequency from the frequency distribution table and choose a suitable scale on the vertical axis.
Hint: About ¾ of
your squared paper should be used.
- Draw bars for each temperature using the frequency distribution table in Activity 3.
(you
can demonstrate to the learners for the first two temperatures)
Activity
Five
Trial
Question to Test Learners’ Ability to Draw Histograms
- The table below shows the number of students and their favourite colours.
|
Colour
|
Pink
|
Red
|
Yellow
|
Orange
|
Green
|
|
No. of
Students
|
6
|
8
|
12
|
5
|
9
|
Draw
a histogram to represent the above information.
- Forty members in a class were asked the number of times each one had gone for swimming the month before last and the data below was obtained.
5 7 8 4 6 9 10 6
9 10 7 8 8 6 5 6
2 9 3 7 6 7 10 4
7 7 8 7 5 9 5 8
9 6 7 5 8 7 6 6
3. (a) Draw a frequency
distribution table for the class.
(b)
Draw a histogram for the above data.
Activity
6
Representing
Data on a Frequency Polygon
The
information in activity 4 can be represented on a frequency polygon.
- Refer to your histogram for the daily maximum temperature; identify the frequency corresponding to 27o C.
- Repeat the procedure above for all temperatures.
- Join the plotted points with a straight edge.
- What you have joined is called a frequency polygon.
Note:
- A frequency polygon should touch the horizontal axis at both ends, crossing at the mid-points of the first and last bars. When this condition is not met, the resulting graph is called a line graph.
- The frequency polygon can also be drawn without first drawing a histogram by plotting frequencies against the mid-marks or class marks.
Trial Exercise
In a test marked out of 10, the
following results were recorded.
|
Score
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
Frequency
|
2
|
3
|
4
|
7
|
8
|
6
|
3
|
1
|
Draw
a frequency polygon to represent the above data.
Activity
7
Making
Sense of Grouped Data
If
we are to deal with very many values, our frequency distribution
table would be very long and tedious. Such values are put into groups
and a frequency distribution table is made.
For example, the mass of
parcels for 24 passengers on a plane were found to be:
20 27 26 26 33 27
25 32 32 38 21 29
31 37 36 20 24 34
21 22 23 28 22 35
(a) Working in pairs,
distribute the values in the table below.
|
Class
|
Tally
|
Frequency
|
|
20-24
|
|
|
|
25-29
|
|
|
|
30-34
|
|
|
|
35-39
|
|
|
|
…….
|
|
|
|
……..
|
|
|
Answer:
Frequencies are 8, 7, 5 and 4 respectively.
(b) What would have been the
next two classes?
Answer:
40-44 and 45-49
(c) List down all the masses
that are possible in the class of 20-24.
Answer:
20, 21, 22, 23, 24
- How many values are there in each class?
Answer:
5 values.
This is called the class
interval, and it is
uniform for all classes.
Terms to define
- Class interval or class width: is the length of each class.
It is obtained by getting the
difference between two successive upper class limits or lower class
limits. e.g. 25 – 20 = 5 or 29 – 24 = 5
It
is a common mistake to subtract horizontally i.e. 24 - 20=4, which is
wrong; you realised the class 20-24 has 20, 21, 22, 23 and 24 which
are 5 values.
- Class limits: the value on the left of the class is called the lower class limit, whereas the one on the right is called the upper class limit.
e.g. for class interval 30 –
34:
is
the lower class limit
is the upper
class limit
- Mid-point/class mark
A closer look at parcels in
the class 35-39 shows the raw values present as 35, 36, 37 and 38.
The value 39 is not among the values.
For all classes, we take a
value in the middle of the class, obtained by taking the average of
the upper and lower class limits. The class mark is useful in
calculating the average. The class mark of 35-39 is (35 + 39)/2 = 37
- Class boundaries
(a) Lower class boundary
Parcels weighing 19.9kg,
19.8kg, 19.7kg, 19.6kg and 19.5kg are all taken to be 20 kg. The
value 19.4kg cannot be taken to be 20kg; here the lowest value to be
taken is 19.5kg. This is what we call the lower
class boundary of
the class 20-24.
(b) Upper class boundary
Parcels weighing 24.1kg,
24.2kg, 24.3kg and 24.4kg are all recorded as 24kg. The boundary
above is taken to be 24.5kg, which will be considered as 25kg.
If
the class limits are whole numbers, then the lower class boundary is
got by subtracting 0.5 from the lower class limit, whereas the upper
class boundary is obtained by adding 0.5 to the upper class limit.
i
25-29
.e Class
limits
25 – 0.5-29 + 0.5
25.5-29.5
Class
boundaries
Activity
8
Mean
from Grouped Data
Refer
to the frequency distribution table you made in Activity 7
- Calculate the class mark for all classes and fill in the values in the table below
|
Class
|
Class
boundaries
|
Class
Mark (x)
|
f
|
fx
|
|
20 – 24
|
19.5 –
24.5
|
|
8
|
|
|
25 – 29
|
24.5 –
29.5
|
|
7
|
|
|
30 – 34
|
|
|
5
|
|
|
35 – 39
|
|
|
4
|
|
f
= fx
=
(b) Fill in the remaining class
boundaries.
(c) Calculate the product fx
and fill in the values.
(d) What does the
symbol mean?
Answer:
It means summation/adding.
f means
the sum of all values of f.
(e) In your table, fill in the
values of f
and fx
- The mean value or average value of the mass of the parcels can be got from
Mean
= fx/f
=
…..
Therefore,
the mean mass of the parcels is …kg.
Answer
f
= 24, fx
= 673, mean = 28.04
28kg.
Diagnostic
Exercise
The
masses of fifty stones were recorded as follows
|
Mass
kg
|
0-4
|
5-9
|
10-14
|
15-19
|
20-24
|
25-29
|
|
Frequency
|
14
|
13
|
9
|
6
|
5
|
3
|
Use
the grouped data above to calculate the mean mass of the stones.
Activity
9
Histogram
of Grouped Data
Consider
the frequency distribution table you obtained in Activity 8. The
histogram is prepared by plotting frequency against class boundaries.
Procedure
- Obtain a graph paper.
- Mark on its horizontal axis the class boundaries and on its vertical axis the frequencies.
- Draw bar graphs following the frequency of each class. Notice that the base of each bar graph is marked on either side by its class boundaries.
For
the above frequency distribution table, the histogram would appear as
shown below.
Diagnostic
Exercise: Drawing a Histogram of Grouped Data
|
Age of
guests at a party
|
30-39
|
40-49
|
50-59
|
60-69
|
70-79
|
|
Frequency
|
5
|
9
|
6
|
4
|
2
|
- Prepare a frequency distribution table.
- Draw a histogram for the grouped data above.
- Calculate the mean age of the guests.
WORKING
MEAN /ASSUMED MEAN
We
can estimate a value of the most likely mean value, called the
assumed mean,
A
or x’,
using the calculation method.
Activity
10
Calculating
Mean for Ungrouped Data Using Working/Assumed Mean
Consider
the points scored by 17 teams in a basketball league.
-
Points scored (x)No of Teams4356647381
- Get a working/assumed mean from the points scored if none is suggested. A quick look at the points column may lead us to take our assumed mean as 6, i.e. A = 6 points.
(ii) Find the difference
between each score and the assumed mean, known as the deviation
or difference,
d, abbreviated as
d
= (x
– A).
(iii) Draw a table akin to the
one given above, adding on columns for deviation, d,
and the product of frequency, f,
with the deviation, d.
(iv)
Complete the table by filling in the missing values in the last two
columns added.
A=6
-
Points, xFrequency, fDeviation, d =(x – 6)fd43-2-656-1-6640073138122
f =
fd =
(v) Find
the values, f
and fd
(vi)
Calculate the mean using the following relation:
Mean = Assumed mean +fd/f
Or Mean = A + fd/f
In
this case, mean = 6 + -7/17
= 6 –
0.412
=
5.588
5.6
5.6
points does not exist in the real sense but this is closer to 6. Such
scores that are only whole numbers are said to be discrete,
e.g. No of vehicles y = 5, but not 5.2 vehicles, whereas those that
can take on any value are said to be continuous,
like the length of a leaf = 3.29cm, weight of a stone = 6.3N
Activity
11
Calculating
Mean for Grouped Data Using Working/Assumed Mean
Consider
the test results of a S.3 class in Biology.
|
Marks
|
40-49
|
50-59
|
60-69
|
70-79
|
80-89
|
|
Frequency
|
1
|
4
|
19
|
15
|
3
|
- Get a working/assumed mean from the test results if none is suggested.
(ii) Taking the assumed mean,
A, as 64.5%, find the difference between each test result and the
assumed mean, known as the deviation
or difference,
d, abbreviated as d
= (x
– A).
(iii) Draw a table having
columns for class/group, class mark and frequency, adding on columns
for deviation, d,
and the product of frequency, f,
with the deviation, d.
(iv)
Complete the table by filling in the missing values in the last two
columns added.
A = 64.5%
-
ClassClass markfD=(x – A)fd40-4944.51-20
50-5954.54…-4060-6964.5190..70-7974.415..15080-8984.5320..
..f=…
..fd=….
(v) Find
the values, f
and fd
(vi)
Calculate the mean using the following relation:
Mean = Assumed mean +fd/f
Or Mean = A + fd/f
In
this case f
= 42, fd
= 150 and
Mean
= A + fd/f
=
64.5 + 150/42
=
64.5 + 3.57
=
68.07
The
mean mark is 68%.
Diagnostic
Question:
The
test results of 50 children were recorded
|
Marks
|
50-59
|
60-69
|
70-79
|
80-89
|
9-99
|
|
Frequency
|
6
|
11
|
19
|
9
|
5
|
Choose
a suitable working mean and use it to calculate the mean mark.
Hint:
Use one of the class marks that is somewhere in the middle. There can
be several working means but choose one you estimate to be close to
the answer.
THE
MODE
The
mode is defined as the value that occurs most often (or the value
with the highest frequency).
(a) Finding
the mode of raw data
When
finding the mode, we first arrange the data in either ascending or
descending order. We then pick out the item that appears most.
Example
Find
the mode of each of the following sets.
(i) 4,
5, 5, 1, 2, 9, 5, 6, 4, 5, 7, 5, 5 (ii) 1, 8, 19, 12, 3, 4, 6, 9
(iii) 2,
2, 3, 5, 8, 2, 5, 6, 6, 5
Solution
(i) Arranging
data in ascending order
1,
2, 4, 4, 5, 5, 5, 5, 5, 5, 6, 7, 9
Hence
the mode is 5 as it occurs more often.
(ii) Arranging
data in ascending order
1,
3, 4, 6, 8, 9, 12, 19
The
mode does not exist since all items appear once.
(i) Arrange
data in ascending order.
2,
2, 2, 3, 5, 5, 5, 6, 6, 8
The
modes are 2 and 5. In this case the distribution is said to be
bimodal.
(b) The
mode of ungrouped data
here
the item with the highest frequency is the mode.
Example:
Find
the mode for the data below
|
x
|
0
|
1
|
2
|
3
|
4
|
5
|
|
f
|
3
|
5
|
8
|
4
|
2
|
1
|
Solution:
The
mode is 2 since it appears most times (i.e. it has the highest
frequency).
c) The
mode of grouped data
when
data has been grouped into classes, the class which has the largest
frequency is called the
modal
class. An estimate of the mode can be obtained from the modal class.
The mode for grouped data can be estimated using two methods.
Method
1
Using
the formula: Mo = L + C[(d1/
(d1
+ d2)]
Where
L
= Lower class boundary for the modal class
d1 = difference
between the frequency of the modal class and the frequency of the
class just before the modal class.
d2 = difference
between the frequency of the modal class and the frequency of the
class just after the modal class
C = class
width of the modal class.
Method
2
The
mode can also be estimated from the histogram as shown below. Notice
how the elements in the formula above are represented on the graph.
Activity
12
Estimating
the Mode from a Histogram
Refer
to your histogram from the diagnostic exercise in Activity 9.
- Identify the tallest bar. This represents the modal class.
- Join the tips of this bar to those of the neighbouring bars on either side, with the one on the left joined to that on the right and vice-versa. The lines used to join these tips cross each other at some point in this bar.
- Drop a perpendicular line from the tip of the point where these lines meet to the base of the bar (horizontal axis). The point where it meets the base is the mode.
- Read off the value at the base using the estimation method.
The
mode is read off the horizontal axis.
In
this case, the mode is 39.5 + 5.5 = 45.
The
modal age of visitors is approximately 45 years.
Activity
13
Estimating
the Mode By Calculation Method
Use
the formula above to calculate the mode of the visitors’ age in
Activity 9.
From
the graph we see that L = 39.5, C = 10, d1
= 4 and d2
= 3
Using
Mo = L + C [(d1/
d1
+ d2)]
we obtain
Mo
= 39.5 + 10(4/7)
=
39.5 + 40/7
=
39.5 + 5.7
=
45.2 years old
THE
MEDIAN
This
is defined as the middle value of a set of numbers arranged in order
of magnitude, either in ascending or in descending order.
If
there are n
items, the median is the 1/2(n
+
1)th
value.
If
n
is odd then there is a middle value which is the median.
If
n
is even and the two middle values are x
and y,
then median is 1/2(x
+
y).
Note:
sometimes
the 1/2(n
+
1) is replaced by n/2
if
n
is fairly large, since in that case (n
+ 1)/2
n/2
(a) The
median of raw data
Example
Find
the median for the data below
- 25, 32, 16, 18, 40
- 29, 21, 62, 47, 41, 36
Solution
We
arrange data in order of magnitude
16,
18, 25, 32, 40 n
= 5
The
median is given by ½(n + 1)
th
value
=
½(5 + 1) = 3rd
value
Therefore
median is 25
(ii) Arranging
the data in increasing order,
21,
29, 36, 40, 47, 62
Here
n=
6, hence the median is given by the
½(n
+ 1)
th
= 3.5th
value.
This
value lies between 36 and 40.
Therefore
the median = ½(36 + 40) = 38
(b) The
median of ungrouped data
The
median is found directly from the cumulative frequency distribution.
Example
The
table below shows the number of children in a family for 41 families
in the Eastern region. Find the median number of children per family.
|
Number
of children
|
0
|
1
|
2
|
3
|
4
|
5
|
|
Frequency
|
4
|
7
|
11
|
9
|
6
|
4
|
Solution:
The
median is given by the ½(n
+ 1)th
value.
This is the ½(41 + 1)th
= 21st
value, which is read from the cumulative frequency table as shown
below.
Looking
at the column for cumulative frequency, you may realise that when the
frequencies for the first two scores (number of children per family)
are added, we still fall shot of the 21st
mark. This means that the median lies in the next cumulative
frequency, which is 22.
|
Number
of children
|
Frequency
|
Cumulative
frequency
|
|
0
|
4
|
4
|
|
1
|
7
|
11
|
|
2
|
11
|
22
|
|
3
|
9
|
31
|
|
4
|
6
|
37
|
|
5
|
4
|
41
|
Here
lies the 21st
position
Thus
the median is 2. So we can say that the average number of children
per family is 2.
(c) The
median of grouped data
Once
the information has been grouped we can only estimate a value for the
median. This can be done by one of the following methods:
(i) from
a cumulative frequency curve (ii) by calculation
(i) From
the cumulative frequency curve (Ogive)
the
median is got by locating the value that lies midway between the
given values, the n/2th
value,
on the Ogive as shown in the graph below.
The
(n/2)th
value is used to draw a horizontal line to the Ogive, from which
point we drop a perpendicular line to the horizontal axis. Where this
line touches the horizontal axis is the median.
(ii) By
calculation
the
median is given by M = L + C[(n/2
– F)/f]
where: L = lower
class boundary for the median class interval
n = total
frequency
f = frequency
for the median class
C = class
width for the median class
F = cumulative
frequency up to L
Note: The
median class is the class that contains the median i.e the class
which has the
n/2th
value.
UNEB
QUESTIONS
UNEB
2007 PAPER 1: Question 7
The
data given below represents the ages in years of 30 senior four
students of a certain school.
|
Age class
|
15-17
|
18-20
|
21-23
|
24-26
|
|
No of
students
|
7
|
11
|
9
|
3
|
Use
the table above to draw a histogram and state the modal class.
UNEB
2005 PAPE 1.Question 15.
The
table below shows the marks obtained in a chemistry test by s4
students in a certain school.
|
54
|
49
|
60
|
58
|
54
|
|
60
|
51
|
57
|
56
|
54
|
|
53
|
59
|
56
|
52
|
55
|
|
57
|
62
|
54
|
54
|
56
|
|
48
|
51
|
52
|
55
|
58
|
|
65
|
55
|
54
|
57
|
61
|
- Using class width of 3 marks and starting with the 48-50 class, mark a frequency distribution table.
- Use your table to:
- draw a histogram.
- Determine the median and mean marks.
UNEB
2002 PAPER 1: Question 15
The
marks obtained by a class of 40 pupils in an English test are given
below.
50 71 40 48 61 70 30 62
44 63 60 51 55 25 32 65
54 62 65 50 45 40 25 45
48 45 30 38 30 28 24 48
30 48 28 35 50 48 50 60
- Using class intervals of 5 marks, construct a frequency table, starting with the 20-24 class group.
- Represent this information on a histogram. Use the histogram to estimate the modal mark.
- Estimate the mean using a working mean of 47.
UNEB
1998 PAPER 1 Question 12.
Sixty
13-year old senior one students from a certain school were tested to
find their resting pulse-rated and the following figures were
obtained for a number of beats per minute.
72 70 66 74 81 70 74 53 57 62
58 92 74 67 62 91 73 68 65 80
78 67 75 80 84 61 72 72 69 70
76 74 65 84 79 80 76 72 68 63
82 79 71 86 77 69 72 56 70 67
76 56 86 63 73 70 75 73 89 64
(a)
By arranging the data in a class of 50-54, 55-54, 55-59,….etc make
a frequency table.
(b)
Draw a bar chart displaying the given data.
(c)
Using your grouped data, calculate the mean and median pulse rates.
UNEB
1996 PAPER 1. Question 16.
|
Scores
|
Class
mark
x
|
Frequency
(f)
|
Frequency x
class mark f X x
|
|
41-49
50-58
59-67
68-76
77-85
86-94
|
63
--
90
|
16
--
--
13
4
|
450
1575
864
--
360
|
|
|
|
f
=…
|
fx =…
|
The
table above shows the number of students who passed an end of year
English promotional examination in terms of mark scores
(a)Study
the table and use the information available to complete the missing
details.
(b)
(i) State the class interval of the scores.
(ii)Calculate
the average score of the marks.
(c)
If, all the above students were promoted and represented 4/5 of the
class. Find the
number
of students in the class who sat the examination.
UNEB
1993 PAPER 2. Question 13
The
information results were obtained in an experiment to measure the
length of leaves from the stalk to the apex (to the nearest tenth of
a cm).
6.6 8.5 7.4 10.8 11.2 9.1 8.7 9.9
12.4 10.0 6.5 7.3 12.8 8.2 6.4 8.9
8.9 8.1 8.3 9.0 7.6 7.1 8.8 10.4
11.7 9.2 10.2 9.8 9.5 12.3 6.2 8.8
7.0 7.9 9.3 6.9 7.7 6.2 8.6 7.4
(i)
Starting with 6.0-6.9 as the first class and using classes of equal
length, draw up the
frequency
table for the data.
(ii)
Give the modal class for the grouped data in (i) above.
(iii)
Calculate the mean of the leaves.
UNEB
2008 PAPER 2, Question 15
The
table below shows the weights in kilograms of thirty pupils.
48 44 33 52 54 44
53 38 37 35 53 46
59 51 32 37 49 42
48 59 52 40 54 46
45 62 35 54 48 35
(a)
Construct a frequency table with a class width of 5 starting from the
class of 30-34.
(b)
Use your table in (a) to:
(i)
Estimate the mean weight of the pupils.
(ii)
Draw a histogram and use it to estimate the modal weight of the
pupils.
MATHEMATICS
SAMPLE
LESSON PLAN
|
DATE
|
CLASS
|
SUBJECT
|
NO.OF
LEARNERS
|
DURATION
|
TIME
|
|
…./…./…
|
SENIOR
THREE
|
PHYSICS
|
60
|
80 MINS
|
8.00 –
9.20am
|
TOPIC :
STATISTICS
SUB
– TOPIC : Data Collection / Display
SKILLS :
???????????????
Objectives
:
By the end of
the lesson, learners should be able to:
- Organize raw data into a frequency distribution table.
- Represent the data on a histogram for;
- Ungrouped data and,
- Grouped data
- Draw a frequency polygon for data in a frequency distribution table
Methods
:
- Role Play
- Information giving
- Guided discovery
- Question and answer
- Illustrations
- Explanations
Teaching
Methods: Graph
papers, manila papers and marker
References:
MK
Secondary Mathematics, Student’s Book 3, Chapter 4
Secondary
Mathematics for Uganda, Book 4
SMUSS
Book 4
MKS
(N.M Patel) Book 3
|
Time
|
Step
|
Theme
|
Teacher’s
Activities
|
Learners’
activities
|
|||||||||
|
5 minutes
|
1
|
Greeting/Role
Call
|
Greets
students
|
Respond
with courtesy
|
|||||||||
|
15 minutes
|
2
|
Introduction
of the review: Data collection (S.1 & S.2 work) |
Asks
students questions relating to data
collection.
Conducts role play
|
Answer
questions and do as instructed. |
|||||||||
|
15 minutes
|
3
|
Review:
Data display on bar |
Gives
students activities with data display graph, line graph, etc. |
Attempt
the activities given
|
|||||||||
|
20 minutes
|
4
|
Data
display on histogram
|
Introduces
the histogram to the learners
|
Listen
carefully and thereafter attempt the problems given
|
|||||||||
|
20 minutes
|
5
|
Data
display on frequency |
Pairs
students to carry out the activity
on
superimposing a frequency polygon pairs and attempt problems given
on a histogram and thereafter having it drawn on its own. Gives
more examples
|
Students
carry out the activity in polygon
|
|||||||||
|
5 minutes
|
6
|
Conclusion
and Exercise |
Recaps
the subtopic and gives an exercise which he/she is to supervise
|
Listen
to recap, ask questions and respond to teacher’s questions
before attempting exercise. |
|||||||||
|
|||||||||||||
Self-evaluation:
…………………………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………..…………………………………………………………………………………
SAMPLE
SCHEME OF WORK
SUBJECT:
MATHEMATICS
NAME
OF TEACHER……………………………………....SCHOOL……..............………………..
TERM…......… CLASS S.3
NO.
OF PERIODS PER WEEK 16
YEAR……...….. NO. OF STUDENTS…………………
|
WEEK
|
PERIOD
|
TOPIC
|
SUB
- TOPIC
|
OBJECTIVES
|
METHODS
|
TEACHING
AIDS
|
REFERENCES
|
Comments
|
|
(date)
|
4
|
Statistics
|
Data
Collection / Display
|
By
the end of this period, learners should be able to;
-
Organise raw data into a frequency distribution table.
-
Represent the data on a histogram, for:
Ungrouped
data and,
Grouped
data.
-
Draw a frequency polygon for data in a frequency distribution
table.
-
Develop personal and social skills such as
collecting data/gathering information, listening skill, hard work,
communication skills, budgeting, recordkeeping,
|
|
-
Household items
-
Money
-
Chalkboard
-
Graph paper
-
Mathematical / geometry set instruments and -- manila paper.
|
1.
MKSM Bk3, Chapter 4
2.
SMU Bk4, Chapter 6
3.
SSM Bk 4
|
|
|
(date)
|
6
|
Statistics
|
Mean
from Grouped Data
|
-
Calculate the mean for the grouped data.
-
Calculate the mean using an assumed mean.
-
Develop personal and social skills such as: recordkeeping,
decision making, prudence, courtesy, analytical skills and
numerical skills.
|
Role
play, Guided discovery,
Demonstrations,
Question and answer
|
“
|
“
|
|
|
(date) |
6 |
Statistics |
Median |
-
Calculate the median value from a group of values.
-
Calculate the mode from grouped data.
-
Calculate the mean using an Ogive.
-
Calculate the mode using a histogram. |
Guided
discovery,
Demonstrations,
Question and answer |
“
|
“
|
|
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