# Statistical Data analysis With Excel For HSMG.632 students

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1 1 Statistical Data analysis With Excel For HSMG.632 students Dialog Boxes Descriptive Statistics with Excel To find a single descriptive value of a data set such as mean, median, mode or the standard deviation, use FX, insert function in dialog box. The following is recorded hourly incomes of six randomly selected students in three different departments at UB. Student ARC CSI TCC

2 2 Imagine you want to find mean, median, mode, etc..of hourly incomes of only students who are working for the ARC. Let s find the mean hourly income of the ARC workers. 2

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4 4 The result will be placed on the designated cell where the Fx is activated. To find the mean of CSI and TCC students, you can copy B8 and paste on C8 and D8. Similarly you can find other quantities for each column for a particular range of data but you have to get yourself familiared with abbreviation for these quantities from the insert function. Examples of these abbreviations are: Average mean Var Variance Median Median Mode Mode Max Maximum STDEV Standard deviation We can also use a single operation to find these quantities altogether in one step. To do so before entering any data into Excel spread sheet, make sure to install data Analysis Tool Pack on your Excel. 4

6 6 ARC

7 7 In descriptive statistics dialog we also check on confidence interval for mean in order to be able to find a 95% confidence interval for the mean of the population this sample is taken from. 7

8 8 Based on sample information we can be 95% confident that the true mean of population is between and or from to The confidence level in this output represents margin of error. 8

9 9 Normal distribution A distribution is normal if the three measures of locations mean, median and mode are equal. We also assume a distribution is normal if these three measures are roughly equal. General shape of a normal distribution looks like a bell curved figure. The mean of distribution is located in the middle. Fifty percent of all observations are in the left and the other fifty percent are in the right side of the mean. Before we use a standard table to find certain probabilities an observation in a normal distribution, we should learn a rule of thumb for certain percentage in a normal distribution. These rules are called empirical rules: 1) In a normal distribution approximately 68% of all observations are within one standard deviation from the mean. Graphical elastration of this fact look like: For example we know IQ scores are normal with mean of 100 and standard deviation 10. Based on empirical rule number one we can say approximately middle 68% of all IQ scores are within: and or within 90 and

10 10 2) Similarly we can say, in a normal distribution approximately 95% of all observations are within two standard deviations from the mean. Graphical elastration of this fact look like: For example we know IQ scores are normal with mean of 100 and standard deviation 10. Based on empirical rule number two we can say approximately middle 95% of all IQ scores are within: and or within 80 and

11 11 3) Virtually all or 99.7% of all observations are within three standard deviations from the mean. Graphically looks like: In this case, we know also use IQ scores that are normal with mean of 100 and standard deviation 10. Based on empirical rule number three we can say approximately middle 99.7% of all IQ scores are within and or within 70 and 130. OPTIONAL SAMPLE PROBLEMS Based on answers from the above questions, we can also find probability that a person receives score of 120 or higher indirectly. The picture looks like: So the answer is (100% -95%) / 2 that is equal 2.5 %. 11

12 12 Now let s use Excel to find the probability of getting less than a value from a normal curve. Normal Distribution Functions A distribution is normal if the mean, median and the mode in that distribution are equal or roughly equal. The general shape of a normal distribution is bell shaped with mean in the middle where 50% of all observations are in the left and the other 50% of all observations are in the right side of the mean. We could use direct and indirect functions NORMDIS, NORMINV or NORMSINV to find probability of getting observations below a certain observation or the corresponding Percentile of an observation. To have a better understating of problems dealing with normal curve lets solve the following problem. Problem Assume mathematics part of the GRE examination is normal with mean of µ=500 and the standard deviation of σ =100. Answer the following questions: 1) What is the probability that a randomly selected test taker scores less than 650 points? Or we can say what is the percentile rank of a person with score 650 points. Solution: If you wish to solve this problem by hand it would be appropriate to have a normal distribution table and always to draw a bell shaped graph to have a clear understanding of the question. We locate the given observation in this case x =650 in right hand side of the mean µ=500 and calculate its norm Z-score. The area to the left side of the Z score of 650 (Z= 1.5) is the answer. The answer from a normal curve is or approximately 93.32%. If you want to find the probability by Excel, from Fx functions, use NORMDIS as followed. The percentile rank of this person is 93.32%. 12

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