Find the mean, median and mode of the following data:
Class0−5050−100100−150150−200200−250250−300300−350Frequency2356531
Class0−5050−100100−150150−200200−250250−300300−350Frequency2356531cf251016212425
N = 25 ⇒ N2=12.5
Median class = 150 - 200
Here, l = 150, f = 6, F = 10, h = 50
Median class = 150 - 200
Here, l = 150, f = 6, F = 10 , h = 50
Median = l +(N2−Ff)× h
= 150 + (12.5−106) × 50
= 150 + 20.83 = 170.83
Modal class = 150 -200
l = 150. f1 = 5 f2= 5 f = 6 h = 50
Mode = l + f−f12f−f1−f2 × h
Mode = 150+ 6−512−5−5 × 50
Mode = 150+ 25 = 175
By empirical formula;
Mode = 3 median - 2 mean
175 = 3 × 170.83 - 2mean
mean = 168.74
Hence, mean = 168.74, median = 170.83, Mode = 175