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# Basic statistics

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Basic Stats - Courtesy FICCI

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### Basic statistics

1. 1. INTRODUCTION TO BASIC FICCI QUALITY FORUM STATISTICS 1 Training on assuring quality of test results
2. 2. "There are three kinds of lies : lies, damned lies, and statistics". American humorist Mark Twain Or British Prime Minister Disraeli FICCI QUALITY FORUM 2 Training on assuring quality of test results
3. 3. STATISTICS DEALS WITH 1. 2. 3. 4. FICCI QUALITY FORUM Collection of data Summarization of data Analysis of data Drawing valid inference from data 3 Training on assuring quality of test results
4. 4. SAMPLE A product or quantity of a product chosen at random to represent all products in a batch Sample measurements would mean a finite number of measurements out of a possibility of large number of measurements FICCI QUALITY FORUM 4 Training on assuring quality of test results
5. 5. POPULATION When an infinite number of observations are made in a measurement process, it would result in infinite possible outcomes. With each possible outcome, associate a sample point. we may Totality of these sample points is called statistical universe or population FICCI QUALITY FORUM 5 Training on assuring quality of test results
6. 6. DATA SUMMARIZATION METHODS ARE 1. GRAPHICAL Bar Chart, Pie Chart etc. 2. TUBULAR Histogram 3. NUMERICA L a) Measures of central tendency b) Measures of dispersion FICCI QUALITY FORUM 6 Training on assuring quality of test results
7. 7. Important measures of central tendency are : 1. 2. 3. Mean Median Mode Important measures of dispersion or variability of a set of numbers or data are : 1. 2. 3. 4. FICCI QUALITY FORUM Range Deviation Variance Standard deviation 7 Training on assuring quality of test results
8. 8. ARITHMATIC MEAN OR AVERAGE The sum of the results divided by the number of measurements. If x1, x2, x3, .... xn, are the results of measurements, then the average is given by = 1/n (x1+ x2 + x3 + .... + xn) Example - 1 Data = 45, 48, 35, 39, 51, 42, 45, 39, 45, 44, 45 Average = 43.45 FICCI QUALITY FORUM 8 Training on assuring quality of test results
9. 9. MODE : It is the value which occurs the maximum in the set of data Example of computing Mode Example - 2 Data 25, 23, 22, 31, 35, 32, 30, 33, 22 Arranged data 22, 22, 23, 25, 30, 31, 32, 33, 35 Mode = 22 FICCI QUALITY FORUM 9 Training on assuring quality of test results
10. 10. Example - 3 Data 45, 48, 35, 39, 51, 42, 39, 45, 44 Arranged data 35, 39, 39, 42, 44, 45, 45, 48, 51 Mode = 39 & 45 FICCI QUALITY FORUM 10 Training on assuring quality of test results
11. 11. MODE : The mode can be very useful for dealing with categorical data. For example, if a PIZZA shop sells 10 different types of PIZZA, the mode would represent the most popular PIZZA. FICCI QUALITY FORUM 11 Training on assuring quality of test results
12. 12. MEDIAN : It is the middle value of a set of numbers arranged according to magnitude. If two middle values exist in an even number of determinations, the median is the mean of the two middle values. Advantage of Median over Mean is that it is not affected by extreme values FICCI QUALITY FORUM 12 Training on assuring quality of test results
13. 13. To compute Median i) ii) Arrange data from smallest to largest For odd No. of data, Median = central value iii) For even No. of data, Median = Av. of 2 central values Example - 4 Data 25, 23, 22, 31, 35, 32, 30, 33 Arranged data 22, 23, 25, 30, 31, 32, 33, 35 Median = (30 + 31) / 2 = 30.5 FICCI QUALITY FORUM 13 Training on assuring quality of test results
14. 14. Example - 5 Data 45, 48, 35, 39, 51, 42, 45, 39, 45, 44, 45 Arranged data 35, 39, 39, 42, 44, 45, 45, 45, 45, 48, 51 Median = 45 FICCI QUALITY FORUM 14 Training on assuring quality of test results
15. 15. RANGE It is the difference between the largest and the smallest value in a set of data Examples-6 DATA RANGE 16.5, 11.2, 10.4, 14.1, 17.2, 15.8 6.8 4.52, 4.81, 3.55, 3.97, 5.11, 4.28, 1.56 22, 23, 25, 31, 35, 32, 30 13 FICCI QUALITY FORUM 15 Training on assuring quality of test results
16. 16. DEVIATION It is the difference between the measured value of a quantity and a reference value If is the reference value, the deviation, is given by = (x1 ) The mean deviation, ) + (x2 m = 1/n[(x1 )+ ...+ (xn )] Where „n‟ = No. of observations FICCI QUALITY FORUM 16 Training on assuring quality of test results
17. 17. VARIANCE It is the average of the squared differences between the individual measurements and the mean If is the variance, then 2 = 1/n[(x )2 + (x2 )2+ ...+ (xn 1 2 )2] It is defined as the square of the standard deviation FICCI QUALITY FORUM 17 Training on assuring quality of test results
18. 18. STANDARD DEVIATION It is defined as the root-mean-square deviation of the observed numbers from their arithmetic mean. It is the positive square root of the variance Population Standard Deviation _____________________________ = 1/n * [(X1- )2+(X2- )2+…..+(Xn- )2] n Where FICCI QUALITY FORUM is the mean value of “n” observations 18 Training on assuring quality of test results
19. 19. SAMPLE STANDARD DEVIATION When No. of observations, „n‟ is less than 25, Standard Deviation is calculated from the formula Sample Standard Deviation ________________________________ = 1/(n-1) * [(X1- )2+(X2- )2+…..+(Xn- )2] n-1 Where FICCI QUALITY FORUM is the mean value of “n” observations 19 Training on assuring quality of test results
20. 20. EVALUATION OF STANDARD DEVIATION EXAMPLE - 7 DATA 100.2, 100.5, 100.6, 100.4, 100.3, 100.2, 100.5, 100.6, 100.5, 100.3 Average = 100.41 Standard Deviation, FICCI QUALITY FORUM n-1 = 0.152 20 Training on assuring quality of test results
21. 21. No DATA (Xn) DEVIATION (Xav – Xn) 1 2 3 4 5 6 7 8 9 10 100.2 100.5 100.6 100.4 100.3 100.2 100.5 100.6 100.5 100.3 100.41-100.2 = 0.21 100.41-100.5 = -0.09 100.41-100.6 = -0.19 100.41-100.4 = 0.01 100.41-100.3 = 0.11 100.41-100.2 = 0.21 100.41-100.5 = -0.09 100.41-100.6 = -0.19 100.41-100.5 = -0.09 100.41-100.3 = 0.11 FICCI QUALITY FORUM 21 VARIANCE (Xav – Xn)2 0.0441 0.0081 0.0361 0.0001 0.0121 0.0441 0.0081 0.0361 0.0081 0.0121 Training on assuring quality of test results
22. 22. Add the Variances, i.e. (Xav – Xn)2 = 0.2090 Divide the above by (n – 1) = 10 – 1 = 9 i.e. 0.2090 / 9 = 0.0232 Square root of this value gives us the Standard Deviation, i.e. n-1 = FICCI QUALITY FORUM 0.0232 = 0.152 22 Training on assuring quality of test results
23. 23. NORMAL DISTRIBUTION EMPERICAL RULE FICCI QUALITY FORUM 1 2 3 68.27 % of all observations 95.46 % of all observations 99.73 % of all observations 23 Training on assuring quality of test results
24. 24. “I hear and I forget. I see and I remember. I do and I understand.” Confucius Famous Chinese Thinker & Philosopher (551 – 479 BC) FICCI QUALITY FORUM 24 Training on assuring quality of test results