Question

Pocket expenses of a class in a college are shown in the following frequency distribution:

Pocket expenses	0 - 200	200 - 400	400 - 600	600 - 800	800 - 1000	1000 - 1200	1200 - 1400
Number of students	33	74	170	88	76	44	25

Then the median for the above data is?

पर्याय

• 485.07

• 486.01

• 487.06

• 489.03

Answer 1

487.06

Explanation:-

Construct a table as follows:

Class interval	Frequency (fi)	Midpoint (xi)	fixi	cf
0 - 200	33	100	3300	33
200 - 400	74	300	22200	107
400 - 600	170	500	85000	277
600 - 800	88	700	61600	365
800 - 1000	76	900	68400	441
1000 - 1200	44	1100	48400	485
1200 - 1400	25	1300	32500	510
Total	510		321400

Since `N/2=510/2=255`

255 is near to cumulative frequency value 277.

So median class interval is 400 - 600.

`"Median" =l+((N/2-cf)/f)h`

Here,

l = 400

`N/2` = 255

cf = 107

f = 170

h = 100

Therefore,

`"Median" =l+((N/2-cf)/f)h`

`"Median" =400+((255-107)/170)100`

Median = 400 + 87.06

Median = 487.06