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Find missing frequency, {{40-59,60-79,80-99,100-119,120-139},{50,?,500,?,50}},median=87.50,N=1000

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Your problem `->` missing frequency, {{40-59,60-79,80-99,100-119,120-139},{50,?,500,?,50}},median=87.50,N=1000


Class
`(1)`
Frequency `(f)`
`(2)`
`cf`
`(3)`
40-5950 50 `50=0+50`
`(3)=`Previous `(3)+(2)`
60-79a 50 + a `50 + a=50+a`
`(3)=`Previous `(3)+(2)`
80-99500 550 + a `550 + a=50 + a+500`
`(3)=`Previous `(3)+(2)`
100-119b 550 + a + b `550 + a + b=550 + a+b`
`(3)=`Previous `(3)+(2)`
120-13950 600 + a + b `600 + a + b=550 + a + b+50`
`(3)=`Previous `(3)+(2)`
---------
--`n=1000`
`n=a + b + 600`


`n=1000`

`a+b+600=1000`

`a+b=400 ->(1)`

To find median class
Here, median is `87.5`.

`:.` The median class is `79.5 - 99.5`.

Now,
`:. L = `lower boundary point of median class `=79.5`

`:. n = `Total frequency `=1000`

`:. cf = `Cumulative frequency of the class preceding the median class `=50 + a`

`:. f = `Frequency of the median class `=500`

`:. c = `class length of median class `=20`

Median `M = L + (( n)/2 - cf)/f * c`

`87.5=79.5 + (( 1000)/2 - (50 + a))/500 * 20`

`87.5 - 79.5=(500 - (50 + a))/500 * 20`

`8 = (-a+450)/500 * 20`

`8*500=(-a+450)*20`

`4000=-20a+9000`

`20a=5000`

`a=5000/20`

`a=250`

Substituting in `(1)`

`250 + b = 400`

`b = 400 - 250`

`b = 150`

Thus, the missing frequencies are `250` and `150` respectively.






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