Question

Calculate the median from the following data:

Height (in cm)	135 – 140	140 – 145	145 – 150	150 – 155	155 – 160	160 – 165	165 – 170	170 – 175
Frequency	6	10	18	22	20	15	6	3

Answer 1

Class	Frequency (f)	Cumulative Frequency (cf)
135 – 140	6	6
140 – 145	10	16
145 – 150	18	34
150 – 155	22	56
155 – 160	20	76
160 – 165	15	91
165 – 170	6	97
170 – 175	3	100
	N = Σ𝑓 = 100

Now, N = 100
`⇒ N/2` = 50.
The cumulative frequency just greater than 50 is 56 and the corresponding class is 150 - 155.
Thus, the median class is 150 – 155.
∴ l = 150, h = 5, f = 22, cf = c.f. of preceding class = 34 and `N/2` = 50.
Now,
Median, `M = l + {h×((N/2−cf)/f)}`
                   `= 150 + {5 × ((50 − 34)/22)}`
                    = 150 + 3.64
                    = 153.64
Hence, the median = 153.64.