...What is “Measure Of Central Tendency”? A particular value that attempt to illustrate a set of data by classifying a central position within the set of data is known as the measure of central tendency. The central tendency is distinguish with its dispersion or in other words the variability. It is important to summarize a set of data with a single value of data when interpreting and analyzing data, as it serves the purpose and give a representative value for the overall data. The most common measures of central tendency are the arithmetic mean, the median and the mode. A central tendency can be calculated for either a finite set of values or for a theoretical distribution, such as the normal distribution. Occasionally authors use central tendency to denote "the tendency of quantitative data to cluster around some central value." [1][2] Mean: It is also known as the arithmetic average, mean is the sum of value of all the observation in a set of data divided by the total number of the observations. Median: when values are arranged in a descending or ascending order, the middle value in the distribution is known as the median. Mode: It is the most repeated or commonly occurring value in the distribution. [1] Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP for International Statistical Institute. ISBN 0-19-920613-9 (entry for "central tendency") [2]Upton, G.; Cook, I. (2008) Oxford Dictionary of Statistics, OUP ISBN 978-0-19-954145-4 (entry for "central tendency") ...
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...CENTRAL TENDENCY: Mean, Median, Mode New Statistical Notation • Σ : sigma – The symbol Σ means to sum (add) the scores Central Tendency What Is Central Tendency? • A score that indicates where the center of the distribution tends to be located. • Tells us about the shape and nature of the distribution. d b Measures of Central Tendency • Mode • Median • Mean The Mode • The most frequently occurring score. • Typically useful in describing central tendency when the scores reflect a nominal scale of measurement. l f The Mode • It does not make sense to take the average in nominal data. – Gender: 67 males --- 1 50 females ---- 2 14 13 14 14 10 15 13 12 17 15 13 14 11 14 14 15 13 15 Score S 17 16 15 14 13 12 11 10 f 1 0 4 6 4 1 1 1 What is the mode? N=18 Unimodal Distributions When Wh a polygon h l has one hump (such as on the normal curve) the distribution is called unimodal. 14 15 15 14 10 15 13 12 17 15 13 12 11 12 15 12 13 12 Score S 17 16 15 14 13 12 11 10 f 1 0 5 2 3 5 1 1 What is the mode? N=18 Bimodal Distributions When distribution Wh a di ib i has two scores that are most frequently occurring, it is called d bimodal. Example Score S 7 6 5 4 3 2 1 f 1 4 5 4 6 7 9 N=36 What is the mode? Uses of The Mode • In nominal data – Since we cannot use mean or median • Also in ordinal, interval or ratio data, along with mean and median ih d di Problems...
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...If Q1 (Quartile 1) = 25 and Q3 (Quartile 3) = 40, what is the interquartile rand for the distribution? The interquartile rand is 15. 11. Is the standard deviation a measure of central tendency or dispersion? Standard deviation is a measure of dispersion. 12. In general terms, what information does the standard deviation tell us? In general terms the standard deviation tell us how close or away the value is. 13. Explain why, for certain GSS variables, a large number of the responses may be labeled “missing,’ coded as IAP. A large number of the responses may be labeled “missing,” coded as IAP because the respondent was not asked the particular question. 14. In order to save or print output, which SPSS Statistics window should be the “active window”? In order to save or print output, the SPSS Viewer/Output window should be the “active window.” 15. In order to save your data file, which SPSS Statistics window should be the “active window”? In...
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...Opening Gross: Several central tendency measures (i.e., mean, median, and mode) are calculated for opening gross in the Excel file. As can be seen in the below histogram, opening gross has a right tail (i.e., skewed to the right), so median would be a more appropriate central tendency measure than the mean. The median opening gross was 0.39; 50% of the opening gross values were less than 0.39, 50% were above 0.39. The skewness of opening gross was 3.43 indicating a right tail. The kurtosis of opening gross was 13.81 indicating a leptokurtic distribution. The range of opening gross was 108.43, from 0.01 to 108.44. The standard deviation of opening gross was 18.87. However, because the distribution was skewed, interquartile range (IQR), which is the range for the middle 50% of the values, would be a more appropriate measure of variability. The interquartile range for opening gross was 12.37. Opening Gross Outliers: Based on the box-plot, extreme values were 108.44 (Star Wars: Episode II), 102.69 (Harry Potter and the Goblet of Fire), 77.06 (War of the Worlds), 50.34 (Mr. and Mrs. Smith), 48.75 (Batman Begins), and 33.90 (Wedding Crashers). It is also suggested that values that are less than z-score of -3 or larger than z-score of +3 should be considered outliers. Using that criteria 77.06 (War of the Worlds), 102.69 (Harry Potter and the Goblet of Fire), and 108.44 (Star Wars: Episode II) can be considered outliers. Total Gross: Several central tendency measures (i.e., mean, median...
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...QUANTITATIVE ANALYSIS: DESCRIPTIVE STATISTICS Introduction Suppose that we have carried out a survey on the effect of carrying out a management audit with three groups of nine participant institutions each i.e. small medium and large. Each group was given the same survey questions in questionnaire format and the answers from the scores were tagged between 0 and 20. What is to be done with the raw scores? There are two key types of measures that can be taken whenever we have a set of scores from participants in a given condition. First, there are measures of central tendency, which provide some indication of the size of average or typical scores. Second, there are measures of dispersion, which indicate the extent to which the scores cluster around the average or are spread out. Various measures of central tendency and of dispersion are considered next. For this assignment, a survey is the type of data collection method in consideration and how the results of that survey would be analysed. SURVEYS Surveys are a very popular form of data collection, especially when gathering information from large groups, where standardization is important. Surveys can be constructed in many ways, but they always consist of two components: questions and responses. While sometimes evaluators choose to keep responses “open ended,” i.e., allow respondents to answer in a free flowing narrative form, most often the “close-ended” approach in which respondents are asked to select from a range of...
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...Introduction In this paper the authors will analyze the Whitner AutoPlex data using descriptive statistics. Team D will use these statistics to calculate the measures of central tendency, dispersion, and skew the data. Team D will also display the descriptive data using graphic and tabular techniques. A frequency distribution tablet and a histogram style graph will illustrate the Whitner AutoPlex data set in measuring terms. Based on skew value and histogram, a discussion of the best measures between central tendency, and dispersion will be included. Central Tendency, Dispersion and Skew The best measures of the central tendency and dispersion data are that by seeing how the order of our information tends to be that the older the consumer the cheaper are the vehicles purchased by them. With this data we can market our sales to the younger consumer because he or she tends to spend more. The tendency in this could be because older people value their money a bit more and are less willing to spend it as much as younger individuals. As a result we can look to market our advertising to a younger audience and design items that a younger audience would be willing to buy and spend money on. By using this data we should be able to maximize profits while attracting a more diverse spectrum of customers at the same time. We can continue to produce items for the population interested in purchasing currently. Information gathered from a whisker box graph shows the same age grouping...
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...The Key Formulas for the central tendency measures are calculated for opening gross in the provided school Excel file. Opening gross has a right tail, so therefore the median would be more central tendency mean than the measure. The median opening gross was 0.39; 50% of the opening gross values were less than 0.39, 50% were above 0.39. The skewness of opening gross was 3.43 indicating a right tail. The range of opening gross ranged from 0.01 to 108.44. The standard deviation of opening gross was 18.87. The interquartile range for opening gross was 12.37. Based on the opening gross the extreme values were 108.44, 102.69, 77.06, 50.34, 48.75 and 33.90. The values that are less than z-score of -3 or larger than z-score of +3 should be considered outliers. Therefore with that criteria 77.06, 102.69 and 108.44 are considered the outliers. The range of total gross was from 0.03 to 380.18. The standard deviation of total gross was 63.16. The interquartile range for total gross was 47.03. Based on the total gross the extreme values were 380.18, 287.18, 234.21, 209.22, 205.28, and 186.22. The values are less than z-score of -3 or larger than z-score of +3 should be considered outliers. Therefore with that criteria 380.18, 287.18, and 234.21 are once again considered outliers. The tendency measures are calculated for the number of theaters has a right tail so median would be a much more appropriate central tendency measure than the mean. The median was 410; 50% of values on the number...
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...Measures of central tendency are also called measures of central location because they are single values that tends to describe a given set of data by identifying their central locations.In his book introduction to statistical methods and data analysis, R. Ott Longnecker argues that measures of central tendency seek to describe the centre of distribution of measurements and also how the measurement vary about the centre of distribution.Central tendency measures include mean, mode nd median.On the other hand measures of variability describes a given set of of data by analyzing how data varies from its centre of distribution.examples of variability measures include range, standard deviation and variance. There are two main branches of statistics that include descriptive statistics and inferential statistics.Descriptive statistics gives numerical measures that describes the features of a given set of data. Inferential statistics on the other hand takes a sample of a given population, analyses the sample, and from it draw conclusions about the population .Malcolm.O.Asadoorian and Demetrius Kantarelis in their book: Essentials of inferential statistics argue that descriptive statistics organize , summarize and display data whereas inferential statistics utilize probabilistic techniques to analyze sample information from a certain population to improve our knowledge about the population. Measures of central tendancy and variability fall under descriptive statistics. Inferential statistics...
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...Financial Modelling and Forecasting Lecture 1 Introduction and Descriptive Statistics The need for forecasts A forecast helps deal with an uncertain future by making decisions today No single forecasting method will lead to an accurate forecast. Forecasts can be wrong! “What’s the point of forecasting?” A business requires predictions as inputs E.g., Inventory, Personnel, Ordering, Production planning. Governments require forecasts to guide monetary and fiscal policy Lecture 1 2 Lecture 1 1 Forecasting Considerations Application to Finance A sensible forecast allows proactive decisions to be made today Without it, management decisions are reactive. Need to ensure sales forecasts can actually be satisfied Eliminate bias Sometimes forecasting can be too difficult Correct model selection is an important factor Financial management decisions are often classified into Investment and Financing The investment decision relates to the analysis and selection of ‘good’ assets One critical input the CFO must consider are the future sales of a new project Financial analysts value a business by forecasting the future cash flows of the entire firm Lecture 1 4 The entire firm is a just collection of assets Not all relationships are linear Lecture 1 3 Quantitative Forecasting Example Forecasts can be classified as quantitative or qualitative. Quantitative forecasting...
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...QNT-351 Discussion Question Responses * DQ#1: What is the importance of statistics in business decision making? Describe a business situation where statistics was used in making a decision. 1. Using statistics to evaluate the performance of your business. Taking all factors into account, determine whether you are making or losing money. In addition, determine the trend of your business. For example, determine whether, over time, you are making more or less profit (or loss). Track the share of the market that your business holds, and how this changes over time. Evaluate all these factors for each product type, even each model, in your company's line. The statistics to use here are simple line and bar graphs of data. These data can alert you to where you need to change aspects of your business, and how quickly you have to make that change. Furthermore, statistics are an excellent way to determine how you should allocate your resources to increase sales. Sales in a given market are a result of a number of factors, such as pricing, the size of the sales force, and the type and number of advertisements placed. However, these factors will not be equally important for every product. You would use multiple regressions to determine which of these factors are most important, and how much changing your asset allocation (for example, the size of the sales force) will change sales. 2. Statistics: The science of collecting, organizing, and analyzing data. Descriptive Statistics...
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...frequencies together to get a 100% Data Presentation Summary Table Pareto Diagram is almost the same as a bar chat. *Summation Notation n=sample size Central Tendency is the set of mesurements- ie the tendency of the data to cluster, or center, about ceratin data. Variability is the set of measurements. Focus on sample and population. N-pOPULATION SIZE n- sample size Mean Common measure of central tendency and acts as balance point, affected by extreme values. Median Measure of central tendency, middle value in ordered sequence(if n is odd, middle value of sequence) Mode Value that occurs most often, not affected by extreme values. Shape It will be skewed if they are etxtreme values. Symmetric is when the mean or median are close. Left-skewed: Mean would be smaller than median Right-Skewed: Median would be larger Range:It ignores how datas are distributed Maximum value-Minimum Value Standard Deviation Measures of dispersion Most common measures considers how data are distributed. Shows variation about mean Skip Cheymuk and 2.7 Interpreting Standard Deviation Empirical Rule Applies to data sets that are mound shaped and symmetric. Is the theory of quality control. Numerical Z-Score EG Chapter 3 Probability Numerical measure of the likelihood that event will occur p(event) Union and Intersections Outcomes in either events A&B... Conditional Probability...
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...descriptions have been presented. More specifically, the article provides the readers with different measures of central tendency, namely the mean, median and mode, thus giving the readers enough information about the topic and the population being described. For each of the three leading contributor to traumatic brain injury, the article describes the different age groups and the frequency of occurrence of the injury to each group. The mode, i.e. the age group with the highest number of occurrences of traumatic brain injury was identified. Since this data is purely categorical, using the mode to describe the data was indeed appropriate (Dodge 2008). The median was also used in order to describe the occurrence of traumatic brain injury. With the age ranging from zero to 91 years old, the median age was 23 years. That is, 50% of the total numbers of incidence occur for those below 23 years old, while the other 50% occur for those people who are above 23 years old. Since the data is ordinal in nature, the median was an appropriate measure of central tendency. The average time that it takes for blood to clot, or the mean International Normalized Ratio (INR), was calculated based on the different Glasgow Coma Scores (GCS) groups. Different groups had different mean INR. For the group with Glasgow Coma Scores of below 8, the average INR was 6.0. For this data, the mean was an appropriate measure to be used, since the INR is neither nominal nor ordinal in nature. Moreover, although...
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...different situations that involved crude oil and the reason why it plays a factor on the price of gasoline. Team C thoroughly conducted research with the help of the UOP library and many online sources to help aid in their investigation. There are numerous factors that play a part in the calculation of this data and this paper will focus on the information gathered with the use of calculation of descriptive statistics, frequency distribution, and histogram. A part of descriptive statistics involves calculating the measures of central tendency and dispersion. Central tendency involves estimates of the mean, mode, and median. The mean can be used in describing central tendency. The mode is the most frequently occurring value in the set of scores (Lind, Marchal, Wathem, 2005). And the median is the score that is found at the exact middle of the set of values. By reviewing and analyzing the central tendencies of the data the below graph will help further explain the central tendency, dispersion, and skew for team C’s data. Looking over the histogram regarding gas prices around America, it shows that not only is Las Vegas feeling the pain at the pump but other states are as well. It has fluctuated over the past few years going from as low as $2.90 while reaching heights of $4.40. With the barrel of crude oil rising, and the summer months not far from being over, we may see a rise again. When collecting data you have to take into account all areas of the...
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...Summarizing and Presenting Data Summarizing and Presenting Data The Ballard Integrated Managed Services (BIMS) management team will review the data collected from the case study and present the information using descriptive statistics. Team C will review the measures that the management team will use when reporting the descriptive statistics. Team C will prepare and describe the methods of measurement for mean, median, mode, standard deviation, and provide graphical display of data. Team C will use each measurement method and draw random selections from the BIMS Coding spreadsheet to report conclusions and make recommendations about the data. The following survey was given to every BIMS employee to get an idea on how Ballard satisfied the employees were with the company. The management team will use this information to report conclusions drawn from the data and make recommendations to Ballard’s management team to improve the employee’s morale, communication, and working conditions. Very Negative Very Positive 1. How well do you enjoy working for BIMS? 2. You enjoy your assigned shift. 3. Your request for your desired shift was fulfilled. 4. How many times have you called in sick in the last month? 5. You are well trained for your work. 6. You are paid fairly for the work you do. 7. Your supervisor treats you fairly. 8. Your supervisor’s boss treats your division fairly. 9. The company is good at communicating...
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...these two groups of individuals in their respective occupational fields. The data collection may display a number of possible outcomes. One of the possible outcomes from the data may show on average men do earn considerably more than women. Another outcome may show on average there are no substantial disparities in earnings and wages between men and women. Earlier research shows that there were factors that contribute to wage disparities such as age, experience, education, and job location. Although those factors are important to research so are the data that analyzes average wages and earnings of men and women. According to Orris, ‘measures of central tendency are the methods we use to summarize data by trying to find one number that best represents all the numbers in a sample or population. There are three primary measures of central tendency: the mode, the median, and the mean,’(page 12). The mode is the most frequently occurring data value. It may be similar to the mean and median, if data values near the center of the sorted array tend to occur often. But it may also be quite different from the mean and median. The median is especially useful when there are extreme values, the median lacks some of the mean’s mathematical properties. And the arithmetic mean is the ‘average’, the mean is affected by every sample item, Doane and Seward, (page 119). The three measurements of dispersion connected with the mean are range, variance and the standard deviation. The range refers...
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