Question : Heights of 50 students of class X of a school are recorded and the following data is obtained :
| Height (in cm) | 130-135 | 135-140 | 140-145 | 145-150 | 150-155 | 155-160 |
| No. of Students | 4 | 11 | 12 | 7 | 10 | 6 |
Find the median height of the students.
Doubt by CBSE 2022
Solution :
| Height (in cm) [C.I.] | No. of Students (fi) | Cumulative Frequency (CF) |
| 130-135 | 4 | 4 |
| 135-140 | 11 | 15 |
| 140-145 | 12 | 27 |
| 145-150 | 7 | 34 |
| 150-155 | 10 | 44 |
| 155-160 | 6 | 50 |
| n = Σfi = 50 |
Total number of students = n = Σfi = 50
n/2 = 50/2 = 25
Median Class = 140-145
Lower Limit of the Median Class (l) = 140
Class Size (h) = 145-140 = 5
f = 12
CF = 15
Median = l+[(n/2-CF)/f]×h
Median = 140+[(25-15)/12]×5
Median = 140+[10/12]×5
Median = 140+50/12
Medina = 140+4.166
Median = 144.166
Median = 144.167
Median = 144.17
Hence, the required median height of students is 144.17 cm