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# Statistics

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

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### Statistics

1. 1. The learner demonstrates understanding of thekey concepts, uses and importance of statisticsand probability, data collection/gathering andthe 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
2. 2. 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
3. 3.  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
4. 4.  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
5. 5.  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
6. 6. 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 9 101. 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
7. 7.  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
8. 8.  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
9. 9.  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
10. 10. 20 18 16 14 12 10 8 6 4 2 0Use your imagination and knowledge of charts tohelp make sense of the above chart. Think of asuitable title that explains what the bar chart is allabout. Provide all the needed information andlabels to complete the graph.Allan M. Canonigo Statistics
11. 11. 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
12. 12. 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 middlescore? Allan M. Canonigo Statistics
13. 13.  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
14. 14.  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
15. 15. 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
16. 16.  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
17. 17. 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
18. 18. 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 thesevalues indicate? Allan M. Canonigo Statistics
19. 19. 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 0Allan M. Canonigo 0-11 12 13-15 Statistics 16+
20. 20. Allan M. Canonigo Statistics
21. 21.  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
22. 22.  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
23. 23.  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
24. 24.  Mean and median are the two standard kinds of average. The Median is used when its 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
25. 25.  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