Calculate the mean and the median for the following continuous frequency distributions.
Class0−1010−2020−3030−4040−5050−6060−70fi68202515104
34.20, 32.4
Class0−1010−2020−3030−4040−5050−6060−70fi68202515104c.fi6143459748488
Mean: To calculate the mean, we calculate n∑i=1xi fi for each observation and divide by n∑i=1fi
n∑i=1xifi=5(6)+15(8)+25(20)+35(25)+45(15)+55(10)+65(40)
=30+120+500+875+675+550+260
=3010
⇒¯x=∑7i−1xifi∑7i=1fi=301088=34.20=mean
Median: To calculate the median for a continuous frequency lies and apply the formula1
Median=l+((N2)−cf× h)
l→ lower limit of median class
N→ sum of frequencies
c → cumulative frequency of class precending median class
f → frequency of median class
h → width of median class
In the given example,
Median class=30-40 {because(882)thterm lies in 30−40 class}
⇒ l=30
N=∑7i=1fi=88
C=34
f=25
h=10
∴ Median=M=30+ =((802)−3425)× 10
=30+(625)10=30+24=32.4.