compute the median from the following data (a). weight more than 20, 30, 40, 50, 60, 70, 80 and (b). number of students 40, 37, 32, 20, 11, 4, 0
Answers
Answer:
From the table, Here, n = 250
n/2 = 125
Since, the Cumulative frequency just greater than 125 is 127 and the corresponding class is 50 - 60 . Therefore 50 - 60 is the median class.
Here, l = 50 , f = 31 , c.f = 96 , h = 10
MEDIAN = l + [(n/2 - cf )/f ] ×h
= 50 + [125 - 96)/31] × 10
= 50 + (29/31)×10
= 50 + ( 290/31)
= 50 + 9.35
= 59.35
Hence, the Median is 59.35.
MEDIAN: Median is defined as the middle most or the Central observation , when the observations are arranged either in ascending or descending order of their magnitudes.
★★Median is that value of the given observation which divides it into exactly two parts.i.e 50% of the observations lie below the median and the remaining are above the median.
MEDIAN for the GROUPED data :
For this we find the Cumulative frequency(cf) of all the classes and n/2 , where n = number of observations.
Now find the class whose Cumulative frequency is greater than and nearest to n/2 and this class is called median class,then use the following formula calculating the median.
MEDIAN = l + [(n/2 - cf )/f ] ×h
Where,
l = lower limit of the median class
n = number of observations
cf = cumulative frequency of class interval preceding the median class
f = frequency of median class
h = class size
★★ CUMULATIVE FREQUENCY:
Cumulative frequency is defined as a consecutive sum of frequencies.
**The Cumulative frequency of first observation is the same as its frequency since there is no frequency before it.
HOPE THIS ANSWER HELPS YOU BUDDY!
CUMMUTATIVE FREQUENCT TABLE IN THE ATTACHED FILE!
