Median of grouped data
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This document provides steps for calculating the median of grouped data: 1. Create a frequency distribution table with class intervals, frequencies, and cumulative frequencies. 2. Find the median class by calculating N/2, where N is the total number of data points. 3. The median is calculated using the formula: x = L + (n2 - F2)/f2 * i, where L is the lower limit of the median class, n2 is the median class, F2 is the cumulative frequency before the median class, f2 is the frequency of the median class, and i is the class interval.
Median of grouped data
- 1. MEDIAN of Grouped Data By: Maryleigh P. Castillo
- 2. Objectives: • Make frequency distribution table • Compute for the Median
- 3. Steps in calculating Median of grouped data • Make the frequency distribution table. • Make a column for the less than cumulative frequency (<cf) • Find for the median class using 𝑚𝑑 𝑐𝑙𝑎𝑠𝑠 = 𝑁 2 • Locate the median class in your table by looking at the cumulative frequency where it lies, then put markings in the class. • Calculate the median from grouped data: 𝑥 = 𝐿 + 𝑛 2 − 𝐹2 𝑓2 𝑖 Where: L=exact lower limit of the interval where the median lies 𝑛 2 = 𝑚𝑒𝑑𝑖𝑎𝑛 𝑐𝑙𝑎𝑠𝑠; i=class interval; 𝑓2=frequency of median class 𝐹2=cumulative frequency up to the class immediately preceding the median class
- 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. Make a column for the less than cumulative frequency (<cf) Class interval f <cf 84 – 86 2 30 81 – 83 4 28 78 – 80 3 24 75 – 77 5 21 72 – 74 5 16 69 – 71 4 11 66 – 68 3 7 63 - 65 3 4 60 -62 1 1 N = 30 To find the cumulative frequency start at the bottom by copying the frequency in the lowest class interval. Then to get the next cumulative frequency simply add the preceding frequency. 1 + 3 = 4 4 + 3 = 7 7 + 4 = 11
- 7. Find for the median class using 𝑚𝑑 𝑐𝑙𝑎𝑠𝑠 = 𝑁 2 Class interval f <cf 84 – 86 2 30 81 – 83 4 28 78 – 80 3 24 75 – 77 5 21 72 – 74 5 16 69 – 71 4 11 66 – 68 3 7 63 - 65 3 4 60 -62 1 1 N = 30 𝑚𝑑 𝑐𝑙𝑎𝑠𝑠 = 𝑁 2 𝑚𝑑 𝑐𝑙𝑎𝑠𝑠 = 30 2 𝒎𝒅 𝒄𝒍𝒂𝒔𝒔 = 𝟏𝟓
- 8. Locate the median class in your table by looking at the cumulative frequency where it lies, then put markings in the class. Class interval f <cf 84 – 86 2 30 81 – 83 4 28 78 – 80 3 24 75 – 77 5 21 72 – 74 5 16 69 – 71 4 11 66 – 68 3 7 63 - 65 3 4 60 -62 1 1 N = 30 𝒎𝒅 𝒄𝒍𝒂𝒔𝒔 = 𝟏𝟓 Note: when the computed md class is not present in the <cf column, choose the number higher than but nearer the computed md class. In this case the computed md class which is 15 is not present In the <cf column, so we will choose the number higher to It which is 16. Put markings in the class where It lies.
- 9. Calculate the median from grouped data. Class interval f <cf 84 – 86 2 30 81 – 83 4 28 78 – 80 3 24 75 – 77 5 21 72 – 74 5 16 69 – 71 4 11 66 – 68 3 7 63 - 65 3 4 60 -62 1 1 N = 30 𝑥 = 𝐿 + 𝑛 2 − 𝐹2 𝑓2 𝑖 Where: L=exact lower limit of the class interval where the median class lies 𝑛 2 = 𝑚𝑒𝑑𝑖𝑎𝑛 𝑐𝑙𝑎𝑠𝑠; i=class interval; 𝑓2=frequency of median class 𝐹2=cumulative frequency up to the class immediately preceding the median class L = LS of the md class – 0.5 L = 72 – 0.5 L = 71.5
- 10. Calculate the median from grouped data. Class interval f <cf 84 – 86 2 30 81 – 83 4 28 78 – 80 3 24 75 – 77 5 21 72 – 74 5 16 69 – 71 4 11 66 – 68 3 7 63 - 65 3 4 60 -62 1 1 N = 30 𝑥 = 𝐿 + 𝑛 2 − 𝐹2 𝑓2 𝑖 Where: L=exact lower limit of the class interval where the median class lies 𝑛 2 = 𝑚𝑒𝑑𝑖𝑎𝑛 𝑐𝑙𝑎𝑠𝑠; i=class interval; 𝑓2=frequency of median class 𝐹2=cumulative frequency up to the class immediately preceding the median class L = 71.5 𝑛 2 = 15 𝑖 = 3 𝐹2 = 11 𝑓2 = 5
- 11. Calculate the median from grouped data. Class interval f <cf 84 – 86 2 30 81 – 83 4 28 78 – 80 3 24 75 – 77 5 21 72 – 74 5 16 69 – 71 4 11 66 – 68 3 7 63 - 65 3 4 60 -62 1 1 N = 30 𝑥 = 𝐿 + 𝑛 2 − 𝐹2 𝑓2 𝑖 L = 71.5 𝐹2 = 11 𝑖 = 3 𝑛 2 = 15 𝑓2 = 5 𝑥 = 71.5 + 15 − 11 5 3 𝑥 =73.9 Note: The median must be in two decimal places only. And also the answer in the median must lies in the median class.