Mean and Mode of grouped data
Complete the table by finding the fill-t Lengths (mm) 25 29 30-34 35-39 Frequency ( . ) Mid-point (xi) Deviation (141.) 2 4044 4549 50-54 55-59 Exam le 32 . 7 10 3 6 ...... The table betow shows the length of 50 pieces of wire used in a physics taboratory. Lengths have been measured to the nearest centimetre. Find the mean by usual method and Coding Method. Lengths (mm) Frequency ( ff) 26 30 4 31 35 10 36 4o 12 41 45 18 46 50 6 V- Solutron We Made ofgroapea' Mommy drktrrutrbn x In order to calculate the mode of grouped data, you need to: 0 Find the modal class. The modal class is the class interval that has the largest frequency. Find the lower class boundary of the modal class (: Lb ) 0 Find the difference of frequency between the modal class to its upper class (= a). c Find the difference of frequency between the modal class to its lower class (= b). I Add the Lb to products Mode = M0 = mm + a (1+!) by C, then add it to A. if" tt+l;I .o Compiete the table by finding the midpoint, deviation and rid! Lengths (mm) Frequency ( ff. ) Mid-point (xi) Deviation (51,-) 2 2529 3034 3539 4044 4549 5054 5559 3. By Coding Method In order to calculate the mean of grouped data by Coding Method, you need to: Find the mid-point of each interval (xi) Find the assumed mean = A H\" the uiwith zero (=0) in the class of A , then fill the uiwith -1, -2, -3, ...to the upper, 1, 2, 3, to the below of the class of A. Multiply he frequency of each interval by its deviation ( j; 1': ) Find the sum of all the products u, Find the sum of all the frequencies Divide the sum of the products fin, by the sum of the frequencies, multiply it with C,then add itto A. Exam ie 31 The foiiowing set of raw data shows the lengths, in mitlimeters, measured to the nearest mm, of 40 leaves taken from plants of a certain species. This is the tabie of frequency distribution. Lengths (mm) Frequency ()2, ) 25 29 2 30 34 4 35 39 7 40 44 10 45 49 8 50 54 6 55 59 3 ' Soiution Lengths (mm) Frequency ( .) Mid-point (xi) 25 29 2 so 34 4 35 39 7 4o 44 10 45 49 8 50 54 5 55 59 3 24 = 2. By Assumed Mean In order to calculate the mean of grouped data by deviation, you need to: 0 Find the mid-point of each interval (xi) Find the assumed mean = A Find the difference between A with xi, we call the deviation (= di) Multiply the frequency of each interval by its deviation (ndj) Find the sum of all the products frail. Find the sum of all the frequencies Divide the sum of the products fludi by the sum of the frequencies, then add it to A . Example 30 The following set of raw data shows the lengths, in millimeters, measured to the nearest mm, of 40 leaves taken from plants of a certain species. This is the table of frequency distribution. Lengths (mm) Solution In this chapter, you will learn: a How to calculate the mean of a grouped frequency distribution. . How to calculate the mean of a grouped frequency distribution using an \"assumed mean" method. 0 How to calculate the mode of a grouped frequency distribution. 0 How to calculate the mode of a grouped frequency distribution using histogram. F. Mean and Mode of grouped data 771a Mean ofgmapaa' data ee 1. In order to calculate the mean of grouped data, you need to: I Find the mid-point of each interval (xi) 0 Multiply the frequency of each interval by its mid-point ( fl. .xl.) 0 Find the sum of all the products fix. 0 Find the sum of all the frequencies I Divide the sum of the products flux: by the sum of the frequencies. Example 29 The following set of raw data shows the lengths, in millimeters, measured to the nearest mm, of 40 leaves taken from plants of a certain species. This is the table of frequency distribution. Calculate the mean. Lengths (mm) Frequency (f1) 25 29 2 3034 .- 45 49 8 -_ 55 59 3 Solution
