ch5_processing_of_large_data_sets.studentview

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Unformatted text preview: is If skewed to the right skewed (i.e. positively skewed), as the left positively ), part is more dense and the right tail is longer (Figure 2). • • When Mean< Median, the When distribution is skewed to the left skewed (i.e. negatively skewed), as the negatively ), right part is more dense and the left tail is longer (Figure 3). left The formula for Skewness is : The 3( µ − Med ) Sk = σ Example 5: Find the skewness for the data of Table 1. Solution: 3(45.75 − 47.45) Sk = = −0.3687 = −36.87% 13.8333 (See Ex 2 & Ex 3 for the calculation of the mean, s.d. and median) median) Some interesting examples Some For the table, state the For boundaries of the class interval if the data referred to are: (i) lengths (i) (ii) ages Class Interval frequency 15-19 11 20-24 27 25-29 38 30-34 41 ….. …… ….. ….. Solution Solution (i) For lengths the boundaries are lengths shown in the table: shown For cases such as measuring we For employ the usual rounding up and down practice. and For example, For measurement data values such as For 19.5, 19.6, 19.7, 19.8, 19.9 we round up to 20. For data such as 24.0, 24.1, 24.2, 24.3, 24.4 we round down to 24. 24. So data in the range of 19.5 to 24.5 So belong in the class 20-24. belong Class Interval Class Class boundary boundary 15-19 14.5-19.5 20-24 19.5-24.5 25-29 24.5-29.5 30-34 29.5-34.5 ….. …… ….. ….. Although our true age may be 24years Although 1day, 24yrs 2months, 24years 11mths, 24years 11mnths 29days, we still give our age as 24. we A person is 24 until the day of their person birthday and then their 25. birthday This idea involves TRUNCATION as This the method of rounding. the Eg. Consider the numbers 20.0, 20.1, Eg. 20.2, 20.3, 20.4, 20.5, 20.6, 20.7, 20.8, 20.9, 20.99, 20.99999 when truncated they all become 20. 20. Now, consider the numbers 24.0, 24.1, Now, 24.2, 24.3, 24.4, 24.5, 24.6, 24.7, 24.8, 24.9, 24.99, 24.99999 when truncated they all become 24. 24. So data in the range of 20.0 to 24.9999 So belong in the class 20-24. belong Solution Solution Class Interval Class Class boundary boundary 15-19 15-20 20-24 20-25 25-29 25-30 30-34 30-5 ….. …… ….. ….. Compare these five examples: Compare Question 1. (See Simple Exercises Ch4 , Q5) Find the mode, median, range, mean, s.d. and variance of the following data: Find of 4, 32, 2 , 4, 7, 8 4, Solution: Order the data: Order This is UNGROUPED data This UNGROUPED Mode = 4 Median = 5.5 Range = 30 Mean = 9.5 Mean s.d. = 10.259 Variance = 105.25 2, 4, 4, 7, 8, 32 2, N = 6 (even number of data). Note: “32” is an “extreme” value. Note Here, the median is a better indicator of the centre than the mean. Q2: Q2: Find the mean, s.d., variance, mode, median, range. x 6.2 7.5 8.3 9.1 total f 10 15 20 25 N=70 N=70 This is UNGROUPED data. This UNGROUPED Mean = 8.114 s.d. = 0.9804 Variance = 0.9612 Mode = 9.1 Median = 8.3 Range = 2.9 It’s MULTIPLE data. MULTIPLE Q3: Q3: Find the mean, s.d., variance, mode, MEDIAN, range. x...
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