1. Find missing frequency from the following data
| Class | Frequency |
| 5 - 10 | 11 |
| 10 - 15 | 20 |
| 15 - 20 | 35 |
| 20 - 25 | 20 |
| 25 - 30 | a |
| 30 - 35 | 6 |
mean = 18.1
Solution:
Class
`(1)` | Frequency `(f)`
`(2)` | Mid value `(x)`
`(3)` | `d=(x-A)/h=(x-27.5)/5`
`A=27.5,h=5`
`(4)` | `f*d`
`(5)=(2)xx(4)` |
| 5 - 10 | 11 | 7.5 `7.5=(5+10)/2` | -4 `d=(7.5-27.5)/5=(-20)/5=-4`
`d=(x-27.5)/5` | `-44` `-44=11xx-4`
`(5)=(2)xx(4)` |
| 10 - 15 | 20 | 12.5 `12.5=(10+15)/2` | -3 `d=(12.5-27.5)/5=(-15)/5=-3`
`d=(x-27.5)/5` | `-60` `-60=20xx-3`
`(5)=(2)xx(4)` |
| 15 - 20 | 35 | 17.5 `17.5=(15+20)/2` | -2 `d=(17.5-27.5)/5=(-10)/5=-2`
`d=(x-27.5)/5` | `-70` `-70=35xx-2`
`(5)=(2)xx(4)` |
| 20 - 25 | 20 | 22.5 `22.5=(20+25)/2` | -1 `d=(22.5-27.5)/5=(-5)/5=-1`
`d=(x-27.5)/5` | `-20` `-20=20xx-1`
`(5)=(2)xx(4)` |
| 25 - 30 | a | 27.5 `27.5=(25+30)/2` | 0 `d=(27.5-27.5)/5=(0)/5=0`
`d=(x-27.5)/5` | `0` `0=axx0`
`(5)=(2)xx(4)` |
| 30 - 35 | 6 | 32.5 `32.5=(30+35)/2` | 1 `d=(32.5-27.5)/5=(5)/5=1`
`d=(x-27.5)/5` | `6` `6=6xx1`
`(5)=(2)xx(4)` |
| --- | --- | --- | --- | --- |
| `n=92+a` | ----- | ----- | `sum f*d=-188` |
Mean `bar x = A + (sum fd)/n * h`
`18.1 = 27.5 + (-188)/(92+a) * 5`
`-9.4 = (-188)/(92+a) * 5`
`92+a = (-188)/(-9.4) * 5`
`92+a = 100`
`a = 100 - 92`
`a = 8`
Thus, the missing frequency is `8`.
2. Find missing frequency from the following data
| Class | Frequency |
| 100 - 110 | 100 |
| 110 - 120 | 130 |
| 120 - 130 | 71 |
| 130 - 140 | 20 |
| 140 - 150 | ? |
| 150 - 160 | 50 |
mean = 123
Solution:
Class
`(1)` | Frequency `(f)`
`(2)` | Mid value `(x)`
`(3)` | `d=(x-A)/h=(x-145)/10`
`A=145,h=10`
`(4)` | `f*d`
`(5)=(2)xx(4)` |
| 100 - 110 | 100 | 105 | -4 | `-400` |
| 110 - 120 | 130 | 115 | -3 | `-390` |
| 120 - 130 | 71 | 125 | -2 | `-142` |
| 130 - 140 | 20 | 135 | -1 | `-20` |
| 140 - 150 | a | 145 | 0 | `0` |
| 150 - 160 | 50 | 155 | 1 | `50` |
| --- | --- | --- | --- | --- |
| `n=371+a` | ----- | ----- | `sum f*d=-902` |
Mean `bar x = A + (sum fd)/n * h`
`123=145 + (-902)/(371+a) * 10`
`-22 = (-902)/(371+a) * 10`
`371+a = (-902)/(-22) * 10`
`371+a=410`
`a=410 - 371`
`a=39`
Thus, the missing frequency is `39`.
3. Find missing frequency from the following data
| Class | Frequency |
| 0 - 10 | 4 |
| 10 - 20 | 4 |
| 20 - 30 | 9 |
| 30 - 40 | ? |
| 40 - 50 | 12 |
| 50 - 60 | 6 |
| 60 - 70 | 3 |
| 70 - 80 | 2 |
mean = 37
Solution:
Class
`(1)` | Frequency `(f)`
`(2)` | Mid value `(x)`
`(3)` | `d=(x-A)/h=(x-35)/10`
`A=35,h=10`
`(4)` | `f*d`
`(5)=(2)xx(4)` |
| 0 - 10 | 4 | 5 | -3 | `-12` |
| 10 - 20 | 4 | 15 | -2 | `-8` |
| 20 - 30 | 9 | 25 | -1 | `-9` |
| 30 - 40 | a | 35 | 0 | `0` |
| 40 - 50 | 12 | 45 | 1 | `12` |
| 50 - 60 | 6 | 55 | 2 | `12` |
| 60 - 70 | 3 | 65 | 3 | `9` |
| 70 - 80 | 2 | 75 | 4 | `8` |
| --- | --- | --- | --- | --- |
| `n=40+a` | ----- | ----- | `sum f*d=12` |
Mean `bar x = A + (sum fd)/n * h`
`37=35 + (12)/(40+a) * 10`
`2 = (12)/(40+a) * 10`
`40+a = (12)/(2) * 10`
`40+a=60`
`a=60 - 40`
`a=20`
Thus, the missing frequency is `20`.
This material is intended as a summary. Use your textbook for detail explanation.
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