Measures of Central Tendency. Measures of Central Tendency. Definition Measures of Central Tendency (Mean, Median, Mode). Central Tendency. Refers to a characteristic where the frequency of a variable tends to cluster around the ‘center’. Measures of Central Tendency. Arithmetic Mean
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Median • Ungrouped data (1) • Data (units produced by workers) 20, 10, 30 (odd) Array 10, 20, 30 Median position Median 20
Median • Ungrouped data (1) • Data (units produced by workers) 20, 10, 40, 30 (even) Array 10, 20, 30, 40 Median position Median
Median • Ungrouped data (2) • Data (units produced by workers) 10, 20, 20, 25, 25, 25, 25, 30, 30, 50, 50, 50 c.f. Median position= √ Median= 25 units
Median • Grouped data (2) • Data (units produced by workers) 12, 24, 24, 25, 25, 25, 25, 32, 32, 45, 45, 45 Median position = c.f. √ Median Class = 20-30 Median =
Features of Median • Not affected by extreme values • When data is skewed, the median is often a better indicator of “average” than the mean. • Time consuming • Unfamiliar to most people
Mode • Ungrouped data (1) • Data (units produced by workers) 10, 20, 20, 30 • Mode = 20
Mode • Ungrouped data (2) • Data (units produced by workers) 10, 20, 20, 25, 25, 25, 25, 30, 30, 50, 50, 50 25 √ Mode =
Mode • Grouped data (2) • Data (units produced by workers) 12, 24, 24, 25, 25, 25, 25, 32, 32, 45, 45, 45 The highest frequency: √ Modal group= 20-30 units Mode =
Mode • Ungrouped data • Data with the highest frequency • Grouped data
Features of Mode • Not affected by extreme values • Maybe more than one mode, or no mode • May not give a good indication of central values
Measures of Dispersion • Definition • Measures of Dispersion(Range, Quartile Deviation, Mean Deviation, Standard Deviation, Variance, Coefficient of Variation)
Dispersion • It describes the level of variation and also indicates the level of consistency in the distribution.
Measures of Dispersion • Range • Quartile Deviation • Mean Deviation • Standard Deviation • Variance • Coefficient of Variation
Range • It measures the difference between the highest and the lowest piece of data. Data1: Data2: 10, 20, 30 0, 20, 40 Range1 = xmax – xmin = 30 - 10 = 20 Range2 = xmax – xmin = 40 - 0 = 40
Feature • It is easy to calculate and easy to understand. • It is distorted by extreme values.
Quartile Deviation 1. Array 2.Quartile position 3. Quartile Value 4. IQR,QD
Quartile Deviation • It excludes the first and last quarters of information and in doing so concentrates on the main core of data, ignoring extreme values. • 45 46 50 55 60 65 67 69 69 70 71 72 73 74 76 78 78 79 80 82 83 85 90 95 Q1 Q2 Q3 Interquartile Range = Q3 - Q1 Quartile Deviation =
