Question

Observe the following frequency distribution table. It shows the distances
travelled by 60 public transport buses in a day. Find the median of the
distance travelled.​

Answer 1

Answer:

here is the sol.

...............

Answer 2

Median of the  distance traveled = 224.12

Step-by-step explanation:

Daily distance           No. of buses           C.I.               f

travelled (in km)           (C.F.)

200 - 209                         4              199.5 - 209.5        4

210 - 219                          14             209.5 - 219.5       18 ⇒ cf

220 - 229                       26⇒ f        219.5 - 229.5       44

230 - 239                        10             229.5 - 239.5       54

240 - 249                         6              239.5 - 249.5       60

To find median class

= value of $(\frac{n}{2})^{th}$ observation

= value of $(\frac{60}{2})^{th}$ observation

= value of 30th observation

First 18 scores are less than 219.5 and remaining, 30 - 18 = 12 are in the class 219.5 - 229.5. Therefore, 219.5 - 229.5 is the median class.

The cumulative frequency of the class 219.5 - 229.5 is 44.

In the formula

Median  $M=L+\frac{\frac{n}{2}-cf }{f}\times c$

L = Lower boundary point of median class = 219.5

n = total frequency = 60

cf = cumulative frequency of the class preceding the median class = 18

f = frequency of median class = 26

c = class length of median class = 10

$Median=219.5+\frac{\frac{60}{2}-18 }{26}\times 10$

            = $219.5+\frac{30-18}{26}\times 10$

            = 219.5 + 4.62

            = 224.12

Median of the distance traveled = 224.12

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