Q.
The following data give the distribution of heights of students:
Height
(in cm)
160
150
152
161
156
154
155
Number of students
12
8
4
4
3
3
7
The median of the distribution is
| Height (in cm) | 160 | 150 | 152 | 161 | 156 | 154 | 155 |
| Number of students | 12 | 8 | 4 | 4 | 3 | 3 | 7 |
Solution:
Arranging the data in ascending order of magnitude, we obtain
Height
(in cm)
150
152
154
155
156
160
161
Number of students
8
4
3
7
3
12
4
Cumulative frequency
8
12
15
22
25
37
41
Here, the total number of items is 41 , i.e., an odd number.
Hence, the median is th i.e., 21 st item.
From cumulative frequency table, we find that the median, i.e. 21st item is 155
(All items from 16 th to 22 nd are equal, each 155 )
| Height (in cm) | 150 | 152 | 154 | 155 | 156 | 160 | 161 |
| Number of students | 8 | 4 | 3 | 7 | 3 | 12 | 4 |
| Cumulative frequency | 8 | 12 | 15 | 22 | 25 | 37 | 41 |