This was presented during the national training of trainers for Grade 7 teachers

2. The learner demonstrates understanding of the
key concepts, uses and importance of statistics
and probability, data collection/gathering and
the different forms of data representation.
engage in statistical investigations
 Explain the basic concepts, uses and importance of Statistics
 Pose questions and problems that may be answered using Statistics
 Collect or gather statistical data and organize the data in a frequency
table according to some systematic considerations
 Use appropriate graphs to represent organized data: pie chart, bar
graph, line graph, and histogram
 Find the mean, median and mode of statistical data
 Describe the data using information from the mean, median and
mode
 Analyze, interpret accurately and draw conclusions from graphic and
tabular presentations of statistical data
Allan M. Canonigo Statistics

3. 120, 118, 123, 124, 138, 137, 130, 119, 120,
125, 118, 118, 123, 124, 132
125, 135, 119, 115, 120, 140, 123, 125
119, 132, 130, 130, 130, 131, 132
132, 130, 118, 131, 130, 125, 125, 126
128, 121, 140, 132, 119, 129, 108
 What do these numbers represent?
 Can we get clear and precise information
immediately as we look at these numbers?
Why?
 How can we make these numbers meaningful
for anyone who does not know about the
description of these numbers?
Allan M. Canonigo Statistics

4.  In our daily activities, we encounter a lot of
sorting and organizing objects, data, or things
like what you just did. These are just few of the
activities involved in the study of Statistics.
◦ What are some of the few activities that you just did?
◦ What is Statistics?
 Give some examples of activities which you think
Statistics is involved.
 List down some problems or questions that can
be answered using Statistics.
Allan M. Canonigo Statistics

5.  Statistics is the science of collection, analysis,
and presentation of data.
 Statisticians contribute to scientific inquiry by
applying their knowledge to the design of
surveys and experiments; the collection,
processing, and analysis of data; and the
interpretation of the results.
 Statistics is the study of the collection,
organization, analysis, and interpretation
of data. It deals with all aspects of this, including
the planning of data collection in terms of the
design of surveys and experiments.
Allan M. Canonigo Statistics

6.  Statistics helps in providing a better understanding and
exact description of a phenomenon of nature.
 Statistics helps in proper and efficient planning of a
statistical inquiry in any field of study.
 Statistics helps in collecting an appropriate quantitative
data.
 Statistics helps in presenting complex data in a suitable
tabular, diagrammatic and graphic form for an easy and
clear comprehension of the data.
 Statistics helps in understanding the nature and pattern of
variability of a phenomenon through quantitative
observations.
 Statistics helps in drawing valid inference, along with a
measure of their reliability about the population
parameters from the sample data.
Allan M. Canonigo Statistics

7. Population of Students in Enrolment of Students per
2011 Scores of Students in the Period grade level for three
Examinations for Mathematics and 800
Grade 700
90
10, 80 600 2010
70
25% 60
500
50
English 400 2011
Grade 40 300
30 Mathematics 2012
Grade 7, 20 200
9, 10% 10 100
45% 0
Grade 0
First Second Third Fourth
Grade Grade Grade Grade
8, 20% Quarter Quarter Quarter Quarter
7 8 9 10
1. What information can we get from each of the above charts
or graphs? Do they present the same information?
2. Describe each of the charts/graphs. What do you think are
some uses of each of the charts or graphs?
Allan M. Canonigo Statistics

8.  What are the different kinds of graphs?
 How are they used?
 What are some important things that you
should consider in creating graphs?
 Why do we use lists, tables, diagrams, or
charts to display data?
Allan M. Canonigo Statistics

9.  In statistics, a histogram is a graphical representation
showing a visual impression of the distribution of
data. It is an estimate of the probability
distribution of a continuous variable and was first
introduced by Karl Pearson. A histogram consists of
tabular frequencies, shown as adjacent rectangles,
erected over discrete intervals (bins), with an area
equal to the frequency of the observations in the
interval. The height of a rectangle is also equal to the
frequency density of the interval, i.e., the frequency
divided by the width of the interval. The total area of
the histogram is equal to the number of data.
[Source: Howitt, D. and Cramer, D. (2008) Statistics in
Psychology. Prentice Hall]
Allan M. Canonigo Statistics

10.  A pie chart is a disk divided into pie shaped pieces
proportional to the frequencies. It shows how a part of
something relates to the whole. It is important to define
what the whole is.
 A bar, either horizontal or vertical, to represent counts for
several categories. One bar is used for each category with
the length of the bar representing the count for that one
category. Bar graphs are used to present and compare
data.
 There are two main types of bar graphs: horizontal and
vertical. They are easy to understand, because they consist
of rectangular bars that differ in height or length
according to their value or frequency.
 A line graph shows trends in data clearly. This displays
data which are collected over a period of time to show how
the data change at regular intervals.
Allan M. Canonigo Statistics

11. 20
18
16
14
12
10
8
6
4
2
0
Use your imagination and knowledge of charts to
help make sense of the above chart. Think of a
suitable title that explains what the bar chart is all
about. Provide all the needed information and
labels to complete the graph.
Allan M. Canonigo Statistics

12. Organize the following data and present using appropriate graph or chart.
Explain why you are using such graph/chart in presenting your data.
The data below shows the population [in thousands] of a certain city.
Year 197 198 198 199 199 200 200 201
5 0 5 0 5 0 5 0
Population
in thousand 65 78 80 81 82 86 90 120
Allan M. Canonigo Statistics

13. 34 35 40 40 48
21 20 19 34 45
19 17 18 15 16
21 20 18 17 10
19 17 29 45 50
•What score is typical to the group of the students? Why?
•Which score frequently appears?
•What score appears to be in the middle?
•How many students fall below the middle
score?
Allan M. Canonigo Statistics

14.  The average of all values is referred as the
mean. To compute for the mean, add all the
scores and divide the sum by the number of
cases.
 The most frequent scores in the given set of
data is called the mode.
 The middlemost score is called the median.
How to get the median for an even number of
score in a set of data? What about for the odd
number of set of data?
Allan M. Canonigo Statistics

15.  An average is a number that is typical for a
set of data.
 Measures of central tendency or location
attempt to quantify what we mean when we
think of as a typical or average score in a data
set. Statistics geared toward measuring
central tendency all focus on this concept of
typical or average.
Allan M. Canonigo Statistics

16. 34 35 40 40 48
21 20 19 34 45
19 17 18 15 16
21 20 18 17 10
19 17 29 45 50
 Find the mean, median , and mode.
 Describe the data in terms of the mean,
median, and mode
Allan M. Canonigo Statistics

17.  Daria bought 3 colors of T-shirts from a
department store. She paid an average of PhP
74.00 per shirt. The receipt where part of it was
torn is shown below.
◦ How much did she pay for each white shirt?
◦ How much did she pay in all? Why?
Allan M. Canonigo Statistics

18. 30
No. of Magazines Borrowed
25
20
15
10
5
0
Monday Tuesday Wednesday Thursday Friday
 The bar chart shows the number of magazines borrowed in the
library last week.
◦ How many magazines were borrowed on Friday? How many students went
to the library and borrowed magazines on Friday?
◦ What is the mean of the number of magazines borrowed per day last
week?
◦ On what day had the most number of students borrowed magazine?
◦ Describe the number of students who borrowed magazine on Tuesday?
Why do you think so?
Allan M. Canonigo Statistics

19. 0.9
0.85
0.8
0.75
0-11 12 13-15 16+
1. What information can we get from the graphs?
2. What conclusion can you make?
3. What made you say that your conclusion is correct?
4. Estimate the mean, median, and mode What do these
values indicate?
Allan M. Canonigo Statistics

20. 0.95
0.9
0.9 0.85
0.85 0.8
0.8 0.75
0.7
0.75
0-11 12 13-15 16+ 0.65
0.6
0.55
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
Allan M. Canonigo 0-11 12 13-15 Statistics
16+

21. Allan M. Canonigo Statistics

22.  The different scale used to represent the data
strongly influences the appearance of the
graph in case of vertical axis distortion. In
horizontal axis the same data one shows the
heightened peak of the data and the graph
presenting a comparatively the flatter one,
which misguides the actual view of the data
in the trends chart.
Allan M. Canonigo Statistics

23.  In the bar graph presentation where the width
of the bar should be proportional to height. If
not followed it misleads the information to
the reader.
 A graph missing the scale on either of the
side should always be avoided. It is
inappropriate for the sound representation of
the data.
Allan M. Canonigo Statistics

24.  The following sets of data show the weekly income [in
peso] of ten selected households living in two different
barangays in the town of Kananga.
 Brgy.Kawayan: 150, 1500, 1700, 1800, 3000, 2100,
1700, 1500, 1750, 1200
 Brgy.Montealegre: 1000, 1200, 1200, 1150, 1800, 1800,
1800, 2000, 1470, 8000
◦ Compute for the mean and the
median.
◦ What information can we get from
these values? Why do you think so?
◦ Why do you think the median is more
appropriate than the mean?
Allan M. Canonigo Statistics

25.  Mean and median are the two standard kinds of
average. The Median is used when it's obvious
that the mean would be misleading and this
happens if there are extreme scores. Extreme
scores are those are usually referred to as
outliers. These are very high or very low scores.
The mean is affected by extreme scores. In this
example, Median household income is commonly
considered, even though Gross Domestic Product
per person is an equally accurately known as
mean.
Allan M. Canonigo Statistics

26.  Samuel brought ten sachets of chocolate candies. He checked
the content of each sachet and found to contain 12, 15, 16, 10,
15, 14, 12, 16, 15, 13 candies.
AVERAGE CONTENT: 14
 According to the data, what is the mean number of candies per
sachet?
 The above information is written on each pack of candies. Why
do you think this number is different from the answer to (a)?
Allan M. Canonigo Statistics