Question

5. Compute Median from the following data:
Mid-values:
37.5
42.5
47.5
52.5
57.5
Frequency:
30
20
15
13
22​

Answer 1

Answer:

153.80

Explanation:

Here we are given the mid-values. So, should first find the upper and lower limits of the various classes. The difference between two consecutive values is h=125−115=10.  

∴ Lower limit of a class = Mid-value- h/2, Upper limit = Mid-value + h/2.

Calculation of Median  

Mid-value Class groups Frequency Cumulative Frequency

115                   110-120                6                          6

125             120-130       25                          31

135             130-140       48                  79

145       140-150       72                  151

155       150-160        116                  267

165       160-170       60                  327

175       170-180      38                  365

185       180-190      22                  387

195              190-200        3                  390

N=∑f  i  =390

We have,

N=390

∴2N = 2/390

​   =195

The cumulative frequency just greater than N/2 i.e.195 is 267 and the corresponding class is 150−160. So, 150−160 is the median class.

∴l=150,f=116,h=10,F=151

Now,  

Median =l+  f 2 N −F ×h

⇒Median=150+  116 /195−151 ×10

=153.80