CIT 2101 - Variation PDF

MEASURES OF VARIATION MEASURES OF VARIATION  Otherwise known as Measures of Dispersion.  Indicate the degree or extent to which numerical values are dispersed or spread out about the average value in a distribution.  Include the range, the interquartile range, the semi-interquartile range or...

MEASURES OF VARIATION MEASURES OF VARIATION  Otherwise known as Measures of Dispersion.  Indicate the degree or extent to which numerical values are dispersed or spread out about the average value in a distribution.  Include the range, the interquartile range, the semi-interquartile range or the quartile deviation, the mean deviation, the variance and standard deviation. RANGE  The difference between the largest and the lowest values in a data set.  For Ungrouped data, the range is obtained by finding the difference between the largest and the lowest values. Range (R) = Highest Value (HV) – Lowest Value (LV)  For Grouped data, the range is determined by subtracting the lower boundary of the lowest class interval from the upper boundary of the highest class interval of a frequency distribution. Range (R) = Highest Upper Boundary (HUB) – Lowest Lower Boundary (LLB) Example1: Example2: INTERQUARTILE RANGE (IQR) The difference between the values of the upper quartile and the lower quartile. IQR = Q3 – Q1 SEMI-INTERQUARTILE RANGE (SIQR) (QUARTILE DEVIATION (QD)) Example3: A manufacturing company produced the following number of units per day for a given period: 21, 25, 20, 28, 30, 23, 22, 31, 32, 27, 19, 33, 24, 29, 26, and 34. Determine the ff: a.) Range, b.) IQR, and c.) SIQR. Solutions: 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34 a. R = HV – LV b. IQR = Q3 – Q1 = 34 – 19 = 30.5 – 22.5 R = 15 IQR = 8 Example4: Solutions: a. R = HUB - LLB The table below shows the average production of 60 employees of a manufacturing company during a given week. Find R, IQR = 95.5 – 60.5 and SIQR. R = 35 60 − 12 Ave. Production No. of b. Q1 = 70.5 + 5 ( 10 ) = 72 4 (classes) employees (f)