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# Bba 2001

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### Bba 2001

1. 1. Page 1 of 37 1.0 CONTENT NO. TOPIC PAGES 1.0 CONTENT 1 2.0 TASK 1 2-3 3.0 TASK 2 4-10 4.0 TASK 3 11-16 5.0 TASK 4 17-19 6.0 TASK 5 20-23 5.0 REFERENCE 24 6.0 COURSEWORK 25-37
2. 2. Page 2 of 37 1.0 INTRODUCTION Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In applying statistics to, e.g., a scientific, industrial, or social problem, it is conservative to create with a statistical population or a statistical model process to be studied. Populations can be different topics such as "all people living in a country" or "every atom composing a crystal". Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments. Some popular definitions are: Merriam-Webster dictionary defines statistics as "classified facts representing the conditions of a people in a state – especially the facts that can be stated in numbers or any other tabular or classified arrangement[2]". Statistician Sir Arthur Lyon Bowley defines statistics as "Numerical statements of facts in any department of inquiry placed in relation to each other".
3. 3. Page 3 of 37 When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can safely extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation.
4. 4. Page 4 of 37 2.0 TASK 1 Today’s Special Frequency Fried chicken 12 Meat loaf 14 Turkey pot pie 8 Fish and chips 10 Lasagna 6
5. 5. Page 5 of 37 The choice of method is influenced by the data collection strategy, the type of variable, the accuracy required, the collection point and the skill of the enumerator. Links between a variable, its source and practical methods for its collection can help in choosing appropriate methods. The main data collection methods are: 0 2 4 6 8 10 12 14 16 Fried chicken Meat loaf Turkey pot pie Fish and chips Lasagna CustomerChoice Customer Choice
6. 6. Page 6 of 37 · Registration: registers and licenses are principally valuable for complete enumeration, but are limited to variables that change slowly, such as numbers of fishing vessels and their characteristics. · Questionnaires: forms which are completed and returned by respondents. An inexpensive method that is useful where literacy rates are high and respondents are co- operative. · Interviews: forms which are completed through an interview with the respondent. More expensive than questionnaires, but they are better for more complex questions, low literacy or less co-operation. · Direct observations: making direct measurements is the most accurate method for many variables, such as catch, but is often expensive. Many methods, such as observer programmes, are limited to industrial fisheries. · Reporting: the main alternative to making direct measurements is to require fishers and others to report their activities. Reporting requires literacy and co-operation, but can be backed up by a legal requirement and direct measurements.
7. 7. Page 7 of 37 When we are graphing and organizing the collected data, students' experiences in displaying data should progress from the concrete, to the pictorial, to the abstract. When creating bar graphs, for example, they may progress from using objects, such as blocks or pieces of candy, to using sticky notes, to creating single-bar graphs, to using a color key to identify different bars of a double-bar graph. From the beginning, students should learn to label graphs with a title, the labels for each axis (x and y), the units of analysis (e.g., feet, meters, dollars) and how to create a key. Over time, students should learn the names of the different parts of different graphs. Questions that can be addressed with numerical data include, "How many pets do you have?" or "When were you born?" Line plots, bar graphs, scatterplots, and stem-and- leaf plots are often used to represent numerical data. The most effective way to analyze numerical data is to look at the mean, median, counts, and the shape (for example, the arc of a bell curve or the clustering of scatter plots) of the data. Questions about categorical data are not answered with numbers, but with words. Generally line plots, bar graphs, and circle graphs are used to represent categorical data. An effective way to analyze categorical data is by counts or percentages.
8. 8. Page 8 of 37 Questions that can be addressed by collecting data over time (longitudinal data) include "What is the average temperature in the month of June?" or "What was the daily weather conditions in month of June?" Descriptions of the various graphs students will learn to make as they progress from the primary to the middle grades are listed below, with examples:  Bar Graph: Used when comparing various items or ideas.  Histogram: Used to show frequency and compare items or ideas; each bar represents an interval of values.  Line Graph: Used to show change over time.  Pictograph: Used to show frequency and compare items or ideas.  Circle Graph (or Pie Graph): Used to show parts or percentages of a whole.
9. 9. Page 9 of 37  Box-and-Whisker Plot: Used to show the range of values as well as the median, quartiles, and outliers; five-number summary is another name for this representation.  Line Plot: Used to easily organize one group of data.  Scatterplot (or Scattergram): Used to determine if a correlation exists between two data sets, and how strong it is, also used to calculate line or curve of best fit.  Stem-and-Leaf Plot: Used to show frequency; data is grouped according to place value, using the digit in the greatest place. It is valuable for students to explore various ways to represent the same data. Students can determine which graph makes the most sense to use and which graph can help them answer their questions most easily. For example, a favorite book survey can be shown as a table, a bar graph, a circle graph and a picture graph. Students can discuss which
10. 10. Page 10 of 37 representation most clearly shows which book got the most votes or the difference in votes. Students can remove the least favorite book and vote again to explore the change in data. It is also valuable for students to understand that the same data is not always best represented in different ways. For example, line plots, bar graphs, scatterplots, and stem- and-leaf plots are best used to represent numerical data. However, longitudinal data are best represented by line graphs. Categorical data are not displayed in a specific order and most often are represented by line plots, bar graphs, and circle graphs.
11. 11. Page 11 of 37 3.0 TASK 2 a) Produce a suitable histogram. b) Describe the shape of the histogram. The histogram that I draw is a random distribution, as shown above, has no apparent pattern. Like the uniform distribution, it may describe a distribution that has several peaks. Due to the histogram has this shape, I have already check to see the several sources of variation have been combined. I analyze them separately. The multiple sources of variation do not seem to be the cause of this 0 5 10 15 20 25 0 to 1 1 to 2 2 to3 3 to 4 4 to 5 5 to 6 6 to 7 Number of employee spent on the internet against working hours
12. 12. Page 12 of 37 pattern, different groupings can be tried to see if a more useful pattern results. This could be as simple as changing the starting and ending points of the cells, or changing the number of cells. A random distribution often means there are too many classes. c) The graph tells me that most of the employees seldom spent on the internet during the working hours. The mode of the graph is (1-2) hours. The median class of the graph is (1-2) hours. The median of the graph is 3 hours. The mean of the is calculated, which is 2.25.
13. 13. Page 13 of 37 4.0 TASK 3 The number of the sick days due to cold and flu last year was recovered by a sample of 15 adults. The data are 5,7,0,3,15,6,5,5,9,3,8,10,5,2,0,12: a) Compute the mean, median, and mode. Mean = (5+7+0+3+15+6+5+9+3+8+10+5+2+0+12) 15 = 90 15 =6 Median = 5 Mode = 5 • The mean, median and mode are all valid measures of central tendency • But, under different conditions, some measures of central tendency become more appropriate to use the others. • Mean ( Arithmetic)
14. 14. Page 14 of 37 The mean (or average) is the most popular and well known measure of central tendency.It can be used with both discrete and continuous data, although its use is most often with continuous data.The mean is equal to the sum of all the values in the data set divided by the number of values in the data set. • Median The median is the middle score for a set of data that has been arranged in order of magnitude.The median is less affected by outliers and skewed data. • Mode The mode is the most frequent score in our data set.On a histogram it represents the higher bar in a bar chart or histogram. Sometimes consider the mode as being the most popular option b) Mean, median and mode are used to calculating central tendencies of any data/distribution. These numbers quickly summarize the data. So they are also called the estimates.
15. 15. Page 15 of 37 Mean helps us to quantify average value in the data. (This is highly susceptible to outliers i.e. extreme values). Median helps us to identify the range of the data. i.e. 50% of the data lies below or above median value. (Median is also called as 50th percentile). Mode is used to identify most frequent values. Let’s take an example. Consider number of children per household in USA.It would make sense to consider median and mode values but it also depends on the question we need to answer. Median will tell us how many children does 50% of the population has.Mode will tell us how many children most of the households have. Mean, for example, average number of children per household is 2.5… Does this number make sense? Can anyone have two and half children? Then why do we consider computing averages in such cases? The averages are computed for conducting some statistical tests. Consider scenarios in which we have to compare the number of children an American household and British household has. We behavior some statistical tests (t-tests etc.) to conclude are these number statistically significantly different or they are similar.
16. 16. Page 16 of 37 So Median, Mode and mean has its own advantages and limitations. We must choose proper estimates to answer real world questions.
17. 17. Page 17 of 37 5.0 TASK 4 a) Stem-and-leaf plots  sample 1 Stem Leaf 1 1 2 6 7 2 9  sample 2 Stem Leaf 1 7 8 2 0 2 3  sample 3 Stem Leaf 0 6 2 4 9 3 7 9  Sample 3 has the largest amount of variation because the stem-and-leaf plots in widely spread  Sample 2 has the smallest amount of variation because the central location for the stem-and leaf plots has little dispersion.
18. 18. Page 18 of 37 (a)  Sample 1: Mean = (11 + 12+ 16 + 17 + 29 ) ÷ 5 = 17 Variance = (11 – 17)2 + (12-17)2 + (16-17)2 + (17-17)2 + (29-17)2 = 25.2 5  Sample 2: Mean = ( 17 + 18 + 20 + 22 + 23 ) ÷ 5 = 20 Variance = (17 – 20 )2 + (18-20)2 + (20-20)2 + (22-20)2 + (23-20)2 = 5.2 5  Sample 3: Mean = ( 6 + 24 + 29 + 37 + 39 ) ÷ 5 = 27 Variance = (6 – 27 )2 + (24-27)2 + (29-27)2 + (37-27)2 + (39-27)2 = 139.6 5 Conclusion: My answer in (a) is correct.
19. 19. Page 19 of 37 6.0 TASK 5 Statistics are sets of mathematical equations that are used to analyze what is happening in the world around us. You've heard that today we live in the Information Age where we understand a great deal about the world around us. Much of this information was determined mathematically by using statistics. When used correctly, statistics tell us any trends in what happened in the past and can be useful in predicting what may happen in the future. Let's look at some examples of how statistics shape your life when you don't even know it. 1. Weather Forecasts Do you watch the weather forecast sometime during the day? How do you use that information? Have you ever heard the forecaster talk about weather models? These computer models are built using statistics that compare prior weather conditions with current weather to predict future weather. 2. Emergency Preparedness
20. 20. Page 20 of 37 What happens if the forecast indicates that a hurricane is imminent or that tornadoes are likely to occur? Emergency management agencies move into high gear to be ready to rescue people. Emergency teams rely on statistics to tell them when danger may occur. 3. Predicting Disease Lots of times on the news reports, statistics about a disease are reported. If the reporter simply reports the number of people who either have the disease or who have died from it, it's an interesting fact but it might not mean much to your life. But when statistics become involved, you have a better idea of how that disease may affect you. For example, studies have shown that 85 to 95 percent of lung cancers are smoking related. The statistic should tell you that almost all lung cancers are related to smoking and that if you want to have a good chance of avoiding lung cancer, you shouldn't smoke. 4. Medical Studies
21. 21. Page 21 of 37 Scientists must show a statistically valid rate of effectiveness before any drug can be prescribed. Statistics are behind every medical study you hear about. 5. Genetics Many people are afflicted with diseases that come from their genetic make-up and these diseases can potentially be passed on to their children. Statistics are critical in determining the chances of a new baby being affected by the disease. 6. Political Campaigns Whenever there's an election, the news organizations consult their models when they try to predict who the winner is. Candidates consult voter polls to determine where and how they campaign. Statistics play a part in who your elected government officials will be 7. Insurance You know that in order to drive your car you are required by law to have car insurance. If you have a mortgage on your house, you must have it insured as well. The rate that an insurance company charges you is based upon statistics from all drivers or homeowners in your area.
22. 22. Page 22 of 37 8. Consumer Goods Wal-Mart, a worldwide leading retailer, keeps track of everything they sell and use statistics to calculate what to ship to each store and when. From analyzing their vast store of information, for example, Wal-Mart decided that people buy strawberry Pop Tarts when a hurricane is predicted in Florida! So they ship this product to Florida stores based upon the weather forecast. 9. Quality Testing Companies make thousands of products every day and each company must make sure that a good quality item is sold. But a company can't test each and every item that they ship to you, the consumer. So the company uses statistics to test just a few, called a sample, of what they make. If the sample passes quality tests, then the company assumes that all the items made in the group, called a batch, are good. 10. Stock Market
23. 23. Page 23 of 37 Another topic that you hear a lot about in the news is the stock market. Stock analysts also use statistical computer models to forecast what is happening in the economy.