Mean of grouped data
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This document provides steps for calculating the mean of grouped data: 1. Make a frequency distribution table with class intervals, frequencies, and midpoints. 2. Multiply the midpoint and frequency for each class to calculate the fx value. 3. Use the formula x=fx/n, where f is the frequency, x is the midpoint, and n is the total frequency, to calculate the mean. For example, given data grouped into classes with frequencies totaling 30, the mean was calculated to be 73.97.
Mean of grouped data
- 1. MEAN of Grouped Data By: Maryleigh P. Castillo
- 2. Objectives: • Make frequency distribution table • Compute for the Mean
- 3. Steps in calculating mean of grouped data • Make the frequency distribution table. • Find for the midpoint (x) of each class interval • Multiply the midpoint and the frequency of each class. • Use the formula To calculate the mean from grouped data: 𝑥 = 𝑓𝑥 𝑛 Where: f=class frequency; x=class midpoint; n=sum of frequencies
- 4. Example: Class interval tally frequency 84 – 86 81 – 83 78 – 80 75 – 77 72 – 74 69 – 71 66 – 68 63 - 65 60 -62 72 75 77 67 72 67 82 76 76 70 61 67 84 69 64 78 65 86 73 81 71 63 72 72 83 78 83 80 71 75
- 5. Make the frequency distribution table. Class interval tally frequency 84 – 86 2 81 – 83 4 78 – 80 3 75 – 77 5 72 – 74 5 69 – 71 4 66 – 68 3 63 - 65 3 60 -62 1 N = 30
- 6. Find for the midpoint (x) of each class interval. Class interval Frequency (f) Midpoint (x) 84 – 86 2 85 81 – 83 4 82 78 – 80 3 79 75 – 77 5 77 72 – 74 5 73 69 – 71 4 70 66 – 68 3 67 63 - 65 3 64 60 -62 1 61 N = 30 To find midpoint simply add the lower score and the highest score of each class interval then divide by 2. Do it in every class interval. 𝒙 = 𝑳𝑺 + 𝑯𝑺 𝟐 𝒙 = 𝟖𝟒 + 𝟖𝟔 𝟐 𝒙 = 𝟏𝟕𝟎 𝟐 𝒙 = 𝟖𝟓
- 7. Multiply the midpoint and the frequency of each class. Class interval Frequency (f) Midpoint (x) fx 84 – 86 2 85 170 81 – 83 4 82 328 78 – 80 3 79 237 75 – 77 5 77 385 72 – 74 5 73 365 69 – 71 4 70 280 66 – 68 3 67 201 63 - 65 3 64 192 60 -62 1 61 61 N = 30 𝑓𝑥 = 2219 𝑓𝑥 = 𝑓 𝑥 𝑓𝑥 = 2 85 𝑓𝑥 = 170 𝑓𝑥 = total of fx, just add all the entry in column of fx
- 8. Use the formula To calculate the mean from grouped data: 𝑥 = 𝑓𝑥 𝑛 Where: f=class frequency; x=class midpoint; n=sum of frequencies Class interval Frequency (f) Midpoint (x) fx 84 – 86 2 85 170 81 – 83 4 82 328 78 – 80 3 79 237 75 – 77 5 77 385 72 – 74 5 73 365 69 – 71 4 70 280 66 – 68 3 67 201 63 - 65 3 64 192 60 -62 1 61 61 N = 30 𝑓𝑥 = 2219 𝑥 = 𝑓𝑥 𝑛 𝑥 = 2219 30 𝑥 =73.97 Use always two decimal places