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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
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
   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
   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
   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
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
   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
   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
   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
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
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
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
   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
   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
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
   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
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
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
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+
Allan M. Canonigo   Statistics
   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
   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
   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
   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
   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

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Making communications land - Are they received and understood as intended? we...
Making communications land - Are they received and understood as intended? we...Making communications land - Are they received and understood as intended? we...
Making communications land - Are they received and understood as intended? we...
 

Statistics

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  • 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+
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  • 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