Mathematics Grade 11 Unit 5 Measures of Dispersion (Range, Variance & Standard Deviation)‪@mathT_21‬ ​

Mathematics Grade 11 Unit 5 Measures of Dispersion (Range, Variance & Standard Deviation) Mathematics Grade eleven Unit 5Measures of Dispersion (Range, Variance & Standard Deviation) Grade 11 Mathematics Unit 5 Measures of Dispersion (Range, Variance & Standard Deviation) Grade Eleven Mathematics Unit 5 Measures of Dispersion (Range, Variance & Standard Deviation) Mathematics Grade 11 Unit 5 ACTIVITY 5.5 Grade 11 Mathematics Unit 5 ACTIVITY 5.5 Math's Grade 11 Unit 5 ACTIVITY 5.5 Grade 11 Math's Unit 5 ACTIVITY 5.5 ACTIVITY 5..5 For preparing a development plan of a farmers’ association, researchers collected the following information on the yearly income of 20 farmers. Here are their incomes in Birr 1000. 10 15 20 12 13 20 8 9 10 6 12 13 8 14 5 6 8 20 12 6 a What is the mean yearly income of the farmers? b Does the mean reflect the real living standard of each farmer? c Before using the mean to reach to a conclusion, what other factors should be considered? The degree to which numerical data is spread about an average value is called the variation or dispersion of the data. Range Range is the difference between the maximum and the minimum values in a data set. Range for grouped data is defined as the difference between upper class boundary of the highest class Bu (H) and the lower class boundary of the lowest class BL(L). Example 22 Consider the following data, what is the range of this distribution? Variance and standard deviation Variance is the average of the squared deviation of each item from the mean. Variance for ungrouped data The positive square root of variance is called standard deviation. Steps to calculate variance for ungrouped data a Calculate the mean of the distribution. b Find the deviation of each value from the mean and square it. c Add the squared deviations. d Divide the sum obtained in step 3 by n. Example 23 Find the variance and standard deviation of the following data. Steps to calculate variance from frequency distributions a Find the mean of the distribution. b Find the deviation of each item from the mean and square it. c Multiply the squared deviations by their corresponding frequencies and add. d Divide the sum by i Σ f . Example 24 Find the variance and standard deviation of the following data. Variance for grouped data In a grouped frequency distribution, every class is represented by its class mark or class midpoint. Steps to find variance from a grouped frequency distribution a Find the class mark for each class. b Find the mean of the grouped data. c Find the deviation of each class mark from the mean and square it. d Find the sum of the squared deviations. e Divide the sum obtained in step d by i Σ f . Example 25 Find the variance and standard deviation of the following distribution. Mathematics Grade 11 Unit five Measures of Dispersion (Range, Variance & Standard Deviation) Mathematics Grade Eleven Unit five Measures of Dispersion (Range, Variance & Standard Deviation) Grade 11 Mathematics Unit five Measures of Dispersion (Range, Variance & Standard Deviation) Grade Eleven Mathematics Unit five Measures of Dispersion (Range, Variance & Standard Deviation) Maths Grade 11 Unit Five Measures of Dispersion (Range, Variance & Standard Deviation) Maths Grade Eleven Unit Five Measures of Dispersion (Range, Variance & Standard Deviation) Grade 11 Maths Unit Five Measures of Dispersion (Range, Variance & Standard Deviation) Grade Eleven Maths Unit Five Measures of Dispersion (Range, Variance & Standard Deviation) Maths Grade 11 Unit 5 Measures of Dispersion (Range, Variance & Standard Deviation) Maths Grade eleven Unit 5 Measures of Dispersion (Range, Variance & Standard Deviation) Grade 11 Maths Unit 5 Measures of Dispersion (Range, Variance & Standard Deviation) Grade Eleven Maths Unit 5 Measures of Dispersion (Range, Variance & Standard Deviation) Math's Grade 11 Unit Five Measures of Dispersion (Range, Variance & Standard Deviation) Math's Grade Eleven Unit Five Measures of Dispersion (Range, Variance & Standard Deviation) Grade 11 Math's Unit Five Measures of Dispersion (Range, Variance & Standard Deviation) Grade Eleven Math's Unit Five Measures of Dispersion (Range, Variance & Standard Deviation) Math's Grade 11 Unit 5 Measures of Dispersion (Range, Variance & Standard Deviation) Math's Grade Eleven Unit 5 Measures of Dispersion (Range, Variance & Standard Deviation) Grade 11 Math's Unit 5 Measures of Dispersion (Range, Variance & Standard Deviation) Grade Eleven Math's Unit 5 Measures of Dispersion (Range, Variance & Standard Deviation) Math's Grade 11 Unit 5 Measures of Dispersion (Range, Variance & Standard Deviation) Measures of Dispersion (Range, Variance & Standard Deviation) Ethiopian mathematics Grade 11 Unit 5 Ethiopian Grade 11 Math's Unit 5 #maths , #mathematics ,#exercise , #tutorial ,#example , #unit_4 , #grade11 , #entrance Exam, #example, #mathstricks , #mathematics2 , #math,#chapter5,#Ethiopian,#statisticsandprobability