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  1. 1.  Measures of central tendency, or “location”, attempt to quantify what we mean when we think of as the “typical” or “average” score in a data set.The concept is extremely important and we encounter it frequently in daily life. For example, we often want to know before purchasing a car its average distance per liter of petrol. Or before accepting a job, you might want to know what a typical salary is for people in that position so you will know whether or not you are going to be paid what you are worth. Or, if you are a smoker, you might often think about how many cigarettes you smoke “on average” per day. Statistics geared toward measuring central tendency all focus on this concept of “typical” or “average”.
  2. 2. A.To get a single value the describes the characteristics of the entire group. It enables one to get a bird’s eye view of the entire data. For example, it is impossible to remember the individual scores of students in a test. But if the average score obtained, we get a single value to represent the entire group. B.To facilitate comparison By reducing the mass of data into one single figure, comparison between 2 groups can easily be made.
  3. 3.  Simple arithmetic mean (or simply mean)  The most common measure of central tendency and is also average.  Its value is obtained by adding together all the values and dividing this total by the number of items  The mean for a finite population with N elements is denoted by µ (Greek letter mu)  The mean for a sample of n elements is denoted by X  Arithmetic mean may be categorized into simple arithmetic mean and weighted arithmetic mean.
  4. 4.  Formula in getting the population mean  µ=Exi/N Where µ is the symbol for population mean Exi is the sum of all the values of variable X N is the number of observations Formula in calculating the sample mean: X=Exi/n Or X= x1+x2+x3+…Xn/n Where X is the symbol for sample mean Exi is the sum of all the values of variable X N is the number of observations
  5. 5. 1. Add together all the values of the variable x and obtain the total, i.e. Exi 2. Divide the total by the number of observations, i.e N or n Example: Calculate the average of the ff population values: 3, 7, 5, 13, 20, 23, 39, 23,40 Solution: µ= Exi/N
  6. 6.  How to calculate the menu of ungrouped data using MS excel 1. Open MS excel 2.Type or encode your data values in one column 3. On a vacant cell, type =average(a1:a10) 4. Press Enter
  7. 7.  1. simple method ▪ Population Sample Formula µ= Exifi/N X= Exifi/N µ is the population mean X is the sample mean fi is the frequency fi is the frequency xi is the midpoint of the class interval N is the total frequency(population) (Sample)
  8. 8.  When a data set is arranged in ascending or descending order, it can be divided not just in 2 parts but into various parts by different values such as quartiles, deciles and percentiles.These values are collectively called quantiles or centiles and are the extension of the median formula.
  9. 9.  Illustration Lower Q Median Upper Q Interpretation: 25% of all the data are less than or equal to Q1 50% of all the data are less than or equal to Q2 or median 75%of all the data are less than or equal to Q3 50% of all the data are lies between Q1 and Q3
  10. 10.  For un grouped data 3, 4, 5, 6, 6, 7, 8, 9, 9, 10 11 Find the lower and upper quartiles. Interpret the answers. Solutions: Since there are 11 values, the 3rd item is Q1=5, the middle item is Q2=7 and the 9th item is Q3=9 Now what does this mean?
  11. 11.  ¼ or 25% of the data has a value that is less than or equal to 5  ½ or 50% of the data has a value that is less than or equal to 7  ¾ or 75% of the data has a value that is less than or equal 9 and  ½ or 50% of the data lies between 5 and 9
  12. 12.  A decile is any of the nine values that divide the sorted data into ten equal parts, so that each part represents 1/10 of the sample or population.  Deca means ten.
  13. 13. D1 D2 D3 D4 D5 D6 D7 D8 D9 100% D1 is denoted as the 1st decile under which 10% of the total population lies. D2 is denoted as the second decile under which 20% of the total population lies. D3 is denoted as the third decile under which 30% of the total population lies.
  14. 14.  D1=P10;D2=P20;D3=P30 and so on. For every one decile you multiply 10 to get the percentile.  The 25th percentile is also known as the 1st quartile(Q1), the 50th percentile as the median or 2nd Quartile (Q2) and the 75th percentile as the 3rd Quartile (Q3)
  15. 15.  A percentile is any of the 99 values which divide an ordered data set into 100 equal parts so that each part represents 1/100 of the data set.The word “percentile” comes from the latin word per centum which means “per hundred”.  Percentiles are generally used for large sets of data.  Sometimes low percentile=good and high percentile = good, depending on the context.
  16. 16.  70th percentile for a test was 16/20. what does this mean?  Answer:  Analysis: 1/20; 2/20; 5/20; 6/20; 11/20; 13/20;16/20;17/20 Smallest to Largest percentile 70% got 16/20 or less in the test 30% got more than 16/20 Here a high percentile would be considered good since answering more questions correctly is desirable
  17. 17.  Runners in a race want to finish in a time that is less than anyone else. low percentile is better- want a fewer people to have that is less than yours suppose the 20th percentile is 5.2 minutes.This means that 20% of the people had a time that was quicker or less than 5.2 minutes. 80% of the people hat a time that was slower or more than 5.2 minutes.Thus, 5.2 minutes is considered as good.
  18. 18.  Mary, a teacher, receives a salary that falls in the 78% percentile. This means that 78% of teachers has a salary that is less than or equal to hers. 25%? Of the teachers has a salary that is more than hers. Mary should be pleased with this fact.

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