Question

Calculate the median for the following data – Class interval 130-139 140-149 150-159 160-169 170-179 180-189 190-199 Frequency 4 9 18 28 24 10 7​

Answer 1

Answer:

166.286

Step-by-step explanation:

Given data

C.I 130−139 140−149 150−159 160−169 170−179 180−189 190−199

Frequency 4 9 18 28 24 10 7

Now we can prepare a table or calculating median

C.I Continous C.I Frequency Cumulative frequency(cf)

130−139 129.5−139.5 4 4

140−149 139.5−149.5 9 4+9=13

150−159 149.5−159.5 18 13+18=31cf

160−169 159.5−169.5 28(f) 31+28=59

170−179 169.5−179.5 24 59+24=83

180−189 179.5−189.5 10 83+10=93

190−199 189.5−199.5 7 93+7=100

Here

N=100

⇒N/2=

2

100

=50

30 median class 159.5−169.5

Because the cf(59) is near to (50)

∴ Lower limit of median

Class(l)=159.5

Class width(h)=10,

cf=preceding cf of median class

f=frequency of median class

∴ Median=l+(

f

N/2−cf

)×h

=159.5+(

28

50−31

)×10

=159.5+

28

19

×10

=159.5+

28

190

=159.5+6.786

(Rounded to one decimal)

Median=166.286≅166.3.