1. STATISTICS “CALCULATING DESCRIPTIVE STATISTICS –Measures of Dispersion” 4.0 Measures of Dispersion

2. Measures of Dispersion – Describe how far individual data values have strayed from the mean (average) – The ways to measure the dispersion of our data are range, variance (sample & population) and standard of deviation. 3.0 Measures of Dispersion

3. RANGE 1.The simplest measure of dispersion and is calculated by the difference between the highest value and the lowest value in the data set. 2.The range of a sample is obtained by subtracting the smallest measurement from the largest measurement 3.0 Measures of Dispersion

4. VARIANCE 1.One of the most common measurement of dispersion in statistics 2.Summarize the squared deviation of each data value from the mean. 3.The variance describes the relative distance between the data points in the sets and the mean of the set. 3.0 Measures of Dispersion

5. Variance σ² = ∑ n i =1 n σ² = the variance of the population X i = the values in the sample; X 1 = first data, X 2 = second data nn i =1 nn (x i - x ) n x = the sample mean N = the size of the population (x i - x ) = the deviation from the mean for each value in the data set 2 3.0 Measures of Dispersion

6. Variance (Group Data) σ² = ∑ n i =1 n σ² = the variance of the Group data X i = the values in the sample; X 1 = first data, X 2 = second data nn i =1 nm (x i - x ) fi x = the sample mean m = the number of classes (x i - x ) = the deviation from the mean for each value in the data set 2 fifi n = the total number of values in the data set 3.0 Measures of Dispersion

7. STANDARD DEVIATION 1.Very straightforward and clear 2.A standard deviation is the square root of variance. 3.Describe the actual and useful measure since the standard deviation is in the units of the original data sets 3.0 Measures of Dispersion

8. Std Deviation (Sample) S = ∑ n i =1 S² = the variance of the sample X i = the values in the sample; X 1 = first data, X 2 = second data i =1 (x i - x ) n x = the sample mean n = the size of the sample (x i - x ) = the deviation from the mean for each value in the data set 2 √ 3.0 Measures of Dispersion

9. Std Deviation (Group Data) s = ∑ n i =1 n σ² = the variance of the Group data X i = the values in the sample; X 1 = first data, X 2 = second data nn i =1 nm (x i - x ) x = the sample mean m = the number of classes (x i - x ) = the deviation from the mean for each value in the data set 2 fifi f = the total number of values in the data set √ fi 3.0 Measures of Dispersion

10. Measures of Relative Position 1.Describe the percentage of the data below a certain point. 2.The technique to measure relative position is Quartiles and Interquartile Range 3.0 Measures of Relative Position

11. QUARTILES 1.Divide the data set into 4 equal segments after it has been arranged in ascending order. 2.25% data points = first quartile Q 1 (Mean data below median) 50% data points = second quartile Q 2 (Median) 75% data points = third quartile Q 3 (Mean data after median) 3.0 Measures of Relative Position

12. INTERQUARTILE RANGE 1.Simple the difference between the third and first quartiles. IQR = Q 3 –Q 1 2.The interquartile range measures the spread of the center half of the data set. 3.0 Measures of Relative Position

13. INTERQUARTILE RANGE 3.Use to identify outliers, which are extreme values that should be discarded before analysis Q 1 - 1.5(IQR) > Outliers (Discarded) > Q 3 + 1.5(IQR) 3.0 Measures of Relative Position

14. Table below indicates a survey that MAS carried out on 50 consumer base on the number of flight hours they are willing to travel. Calculate the mean, median, mode, variance and Standard deviation of the table below. Try This!

15. The following frequency distribution indicates the daily number of foreigner from European region landed on Malaysia using MAS in 50 days. Try This ClassesFreq 10168 172311 24305 31376 38447 45515 52587 59651 50 Calculate the RFD, CFD, mean, median, mode, variance and standard deviation of the data above

16. QUIZ 2 3061992998 4856778535 67884310055 2539436268 3352667380 4589749375 The scores of Statistics Examination (100%) is as follows: a) Construct a frequency distribution with 6/7/8 classes: b) Construct a relative and a cumulative FD from the data a) c) Calculate the mean, median,mode, variance and Std. Deviation of the passengers d) The all the results obtained in a,b and c, describe statistically in your own words your own observation of scores

17. QUIZ 3 3061992998 4856778535 67884310055 2539436268 3352667380 4589749375 The scores of Statistics Examination (100%) is as follows: a) Construct a frequency distribution with 8 class b) Calculate the the Q1, Q2 and Q3 c) Calculate the IQR and Outliers (Discarded) data d) Describe in your own words, the validity of the outliers