Measures of Variablity.kjc.ppt
- 1. Measures of Variability 21COM2T412: Business Statistics Dr. Neerupa Chauhan Asst. Professor Kristu Jayanti College, Autonomous (Reaccredited A++ Grade by NAAC with CGPA 3.78/4) Bengaluru – 560077, India
- 2. Main measures of variability Range: the difference between the highest and lowest values. Interquartile range: the range of the middle half of a distribution. Standard deviation: average distance from the mean. Variance: average of squared distances from the mean.
- 3. The range of a set of data is the difference between the largest and smallest values, the result of subtracting the sample maximum and minimum.
- 4. Measures of Variability Range Highest score – lowest score Example: 7, 6, 3, 3, 1 ---- range = 6 3, 4, 4, 5, 4 ---- range = 2 4, 4, 4, 4, 4 ---- range = 0 Variance Standard Deviation
- 5. Interquartile range (IQR) The interquartile range (IQR) is a measure of variability, based on dividing a data set into quartiles. The values that divide each part are called the first, second, and third quartiles; and they are denoted by Q1, Q2, and Q3, respectively. Q1 is the “middle” value in the first half of the rank-ordered data set. Q2 is the median value in the set. Q3 is the “middle” value in the second half of the rank-ordered data set.
- 7. Measures of Variability Standard Deviation Variance
- 8. Standard Deviation Standard Deviation: A measure of the spread of the scores around the mean. Average distance from the mean. Example:Can you calculate the average distance of each score from the mean? (X=4) 7, 6, 3, 3, 1 (distance from the mean: 3,2,-1,-1,-3) 3, 4, 4, 5, 4, (distance from the mean: -1,0,0,1,0) You can’t calculate the mean because the sum of the ditance from the mean is always 0.
- 9. Formula for Standard Deviation s = (X-X)2 n-1 Standard deviation of the sample Sigma: sum of what follows Each individual score Mean of all the scores Sample size
- 10. Why n-1? s (lower case sigma) is an estimate of the population standard deviation ( :sigma) . In order to calculate an unbiased estimate of the population standard deviation, subtract one from the denominator. Sample standard deviation tends to be an underestimation of the population standard deviation.
- 11. Variance Variance: Standard deviation squared. S = (X-X)2 n-1 Not likely to see the variance mentioned by itself in a report. Difficult to interpret. But it is important since it is used in many statistical formulas and techniques.
- 12. Thank you