Measures of Relative Position, Lecture notes of Mathematics

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| Measures of Dispersion Z Measures of dispersion describe the spread of a data set. ae b- 2® -b 1. The range is the difference between the largest and the smallest data values. Find the range of this data set: -9, 4, 6, 15, -10, 13, 8, 20, 11 20 - (-10) =30 2. The tallest man in history was Robert Pershing Wadlow. He was 8 feet 11.1 inches tall. The shortest man in history was Chandra Dangi. His height was 21.5 inches. Find the yo ha \ 4 O7 range in their heights. YO (IZ) = 107.| IN Renee = 107. \- 3. While the range is easy to compute, it can be deceiving because it relies only on the largest and smallest values. A measure of dispersion that is less sensitive to extreme values is the standard deviation. The standard deviation is a measure of how SPREAD CUT the data is in relation to the MEAN . Data sets that are clustered tightly around the mean will have a LONE R standard deviation than SMALLER. data sets that are more spread out. 4. Two students, Ramiro and Tara, took the same six tests. Ramiro’s Scores: 55, 66, 80, 82, 97, 100 Tara’s Scores: 76, 76, 81, 81, 82, 84 a) Find the median and mean for each student. Use only the median and mean to compare the scores of the two students. Perneo: Medan =8! “Roa :Median'= 8 | Fa papan) = SSA azeTWN | Fett D 4B BIT OF. ¥ b =O Usiner THESE, THe s SEO TO TEST =B0 THE SAme b) Examining the individual test scores, would you come to the same conclusion as you did in part a? Which student do you predict will have the lower standard deviation? NO \TACAIS SOUS. Wee MUCH LESS CPREAO GT Ron) RAMOS. SO Tata IC A MOE CONSRrEST TES” R aver|l AWiLe Have A Lovee /SMALLag STAND AD Devito ( Tuan QamiRO will. 107