statistics

http://love4mathed.com/wp-admin/post-new.php




Allan M. Canonigo Statistics

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

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.


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?


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.


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.


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.


Grade

7,

45% Grade

8, 20%

Grade

9, 10%

Grade

10,

25%

Population of Students in

2011

0

10

20

30

40

50

60

70

80

90

First

Quarter

Second

Quarter

Third

Quarter

Fourth

Quarter

English

Mathematics

Scores of Students in the Period Examinations for Mathematics and

0

100

200

300

400

500

600

700

800

Grade

7

Grade

8

Grade

9

Grade

10

2010

2011

2012

Enrolment of Students per grade level for three

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?


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?


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]


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.


02468

101214161820

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.


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

5

198

0

198

5

199

0

199

5

200

0

200

5

201

0

Population

in thousand

65

78

80

81

82

86

90

120


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?


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?


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.


Find the mean, median , and mode.

Describe the data in terms of the mean, median, and mode

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


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?


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?

0

5

10

15

20

25

30

Monday Tuesday Wednesday Thursday Friday

No. of Magazines Borrowed


0.75

0.8

0.85

0.9

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?


0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

0-11 12 13-15 16+

0.75

0.8

0.85

0.9

0-11 12 13-15 16+


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.


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.


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?


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.


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)?

statistics

Education

canonigo statistics

study of statistics

analysis of data

statistics inpsychology

organized data

number of data

sample data

complex data