Find the median:
Class Interval Frequency
160-162 15
163-165 118
166-168 142
169-171 127
172-174 18
Answer :
We form our data table :
So,
Mean =
So,
Median group = 166 - 168
And
We know Median =
Here
L = The lower class boundary of the group containing the median = 166
n = The total number of data = 420
cfb = The cumulative frequency of the groups before the median group = 133
fm = The frequency of the median group = 142
w = The group width = 3
So,
Median =
We form our data table :
Class interval | Mid point ( x ) | Frequency ( f ) | fx | cumulative frequency cfb |
160 - 162 | 161 | 15 | 2415 | 15 |
163 - 165 | 164 | 118 | 19352 | 15 + 118 = 133 |
166 - 168 | 165 | 142 | 23430 | 133 + 142 = 275 |
169 - 171 | 170 | 127 | 21590 | 275 + 127 = 402 |
172 - 174 | 173 | 18 | 3114 | 402 + 18 = 420 |
f = 420 | fx = 69901 |
So,
Mean =
So,
Median group = 166 - 168
And
We know Median =
Here
L = The lower class boundary of the group containing the median = 166
n = The total number of data = 420
cfb = The cumulative frequency of the groups before the median group = 133
fm = The frequency of the median group = 142
w = The group width = 3
So,
Median =