11.1 Measures of Center and Variation

What We Will Learn Compare mean, median, and mode Find range and standard deviation Identify effects of transformations on data

Needed Vocab Measure of center: mean, median, and mode Mean: sum of the data divided by total number of data values, aka average Median: middle number when values written in order Mode: value or values that occur the most Outlier: data value much larger or smaller than the other values Measure of variation: describes the spread or distribution Range: difference of greatest value and least value Standard deviation: how much a value in the data set differs from the mean Data transformation: use a mathematical operation to change a data set into different data set

Ex. 1 Comparing Measures of Center Aka Measures of Central Tendency A. Find mean, median, and mode B. Which measure best represents the data? Mean = 9.65 Median = 8.7 Remember to write in numerical value to find median, if even number the add middle two and divide by 2 Mode = 8.25 Median - as mean bigger than most data values, and modes less than most data values Hourly Wages 16.50 8.25 8.75 8.45 8.65 9.10 9.25

Ex. 2 Removing an Outlier Hourly Wages 16.50 8.25 8.75 8.45 8.65 9.10 9.25 How does outlier affect the mean, median, and mode? Run mean, median, and mode with outlier and then run without and see difference With outlier mean = 9.65, median = 8.7 and mode = 8.25 Without mean = 8.67, median = 8.65, and mode is 8.25 Mean decreased by .98, median decreased by .05, and mode stayed the same

Ex. 3 Finding Range Simply subtract highest and lowest data value What is the range of contestants on show A? 31 – 19 12 years

Ex. 4 Finding Standard Deviation Find standard deviation of the ages in show B. Use 𝑠𝑢𝑚 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛𝑠 𝑡𝑜𝑡𝑎𝑙 𝑖𝑡𝑒𝑚𝑠 Can make a table if you want, easier to see for some people Steps 1. find the mean of the data 2. find deviation by taking data value and subtracting the mean found in step 1 3. square each deviation found in step 2 4. add all the squared deviations and then divide by total items 5. take square root of answer from step 4

Ex. 4 Continued mean 26 x 25 20 22 27 48 32 19 21 24 x-mean -1 -6 -4 1 -7 -5 -2 squared 1 36 16 484 49 25 4 1+36+16+1+484+36+49+1+1+16+25+4 12 55.8 7.5 years

Your Practice Find standard deviation Page 591 number 22 7.29+21.16+8.41+.49+9.61+.01+2.25+4.84 8 6.7575 2.6

Ex. 5 Effects of Data Transformations

Ex. 5 Continued Find the values of the measures shown when each value is increased by 14. Find the values of the measures when values multiplied by 1.2. Mean = 62, median = 56, mode = 49, range = 46, standard deviation = 15.5 Increased by 14: Mean = 76, median = 70, mode = 63, range = 46, standard deviation = 15.5 Multiplied by 1.2: Mean = 74.4, median = 84, mode = 75.6, range = 55.2, standard deviation = 18.6