Question

The following table gives the frequency distribution of married women by age at a marriage.Calculate the mediange(in years)
15-19
20-24
25-29
30-34
35-39
Frequency:
53
140
98
32
12
Age(in years)
40-44
45-49
50-54
55-59
60 and above
Frequency
9
5
3
3
2

Answer 1

SOLUTION :  

★★Here, the data is not in continuous form( exclusive) so we convert it into continuous form (inclusive).  For this subtract 0.5 from lower limit of each class interval and add 0.5 to upper limit of each class interval.

CUMULATIVE FREQUENCY TABLE is in the attachment.  

Here, n = 357

n/2 = 178.5

Since, the Cumulative frequency just greater than 178.5 is 193 and the corresponding class is 19.5 - 24.5 .Therefore 19.5 - 24.5  is the median class.

Here, l = 19.5 , f = 140 , c.f = 53 ,  h = 5

MEDIAN = l + [(n/2 - cf )/f ] ×h

= 19.5 + [178.5 - 53)/140] × 5

= 19.5 + [125.5 ×5]/140

= 19.5 + 125.5/28

= 19.5 + 4.48

= 23.98

Hence, the Median age is 23.98 years.

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 WILL HELP YOU.  

Answer 2

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Soln:

Lives in hours of is pieces are = 715, 724, 725, 710, 729, 745, 694, 699, 696, 712, 734, 728, 716, 705, 719

Arrange the above data in ascending order = 694, 696, 699, 705, 710, 712, 715, 716, 719, 721, 725, 728, 729, 734, 745

N = 15 (odd)

Median = (N+12)th terms

= (15+12)th terms = 8th terms = 716