Median of grouped data

for senior high school

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 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: Where : L=exact lower limit of the interval where the median lies ; i =class interval; =frequency of median class =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   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  

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 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 Where : L=exact lower limit of the class interval where the median class lies ; i =class interval; =frequency of median class =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 Where : L=exact lower limit of the class interval where the median class lies ; i =class interval; =frequency of median class =cumulative frequency up to the class immediately preceding the median class   L = 71.5 = 11 = 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 L = 71.5 = 11 = 5 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.