Changes
From Karnataka Open Educational Resources
446 bytes added
, 09:56, 30 October 2019
mLine 1: |
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| =Problem 1= | | =Problem 1= |
− | If n =10, = 12 and | + | If n =10, <math>\bar x </math> = 12 and<br> |
− | <math>\sum{x^2}= 1530 find the standard deviation </math> <br> | + | <math>\sum{x^2}= 1530 find the standard deviation </math> <br> |
| | | |
| =INTERPRETATION OF PROBLEM= | | =INTERPRETATION OF PROBLEM= |
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| {|class="wikitable" | | {|class="wikitable" |
| |- | | |- |
| + | |C.I. |
| |f | | |f |
| |x | | |x |
| |fx | | |fx |
− | |d=frac{x-A}{c} | + | |d=<math>\frac{x-A}{c}</math> |
− | |fx² | + | |fd |
| + | |d² |
| + | |fd² |
| + | |- |
| + | |30-34 |
| + | |4 |
| + | |32 |
| + | |128 |
| + | | -2 |
| + | | -8 |
| + | |4 |
| + | |16 |
| |- | | |- |
− | |03 | + | |34-38 |
− | |07 | + | |7 |
− | |021 | + | |36 |
− | |009 | + | |252 |
− | |0063 | + | | -1 |
| + | | -7 |
| + | |1 |
| + | |7 |
| |- | | |- |
− | |08 | + | |38-42 |
− | |10 | + | |9 |
− | |080 | + | |40 |
− | |064 | + | |360 |
− | |0640 | + | |0 |
| + | |0 |
| + | |0 |
| + | |0 |
| |- | | |- |
− | |13 | + | |42-46 |
− | |15 | + | |11 |
− | |195 | + | |44 |
− | |169 | + | |484 |
− | |2535 | + | |1 |
| + | |11 |
| + | |1 |
| + | |11 |
| |- | | |- |
− | |18 | + | |46-50 |
− | |10 | + | |6 |
− | |180 | + | |48 |
− | |324 | + | |288 |
− | |3240 | + | |2 |
| + | |12 |
| + | |4 |
| + | |24 |
| |- | | |- |
− | |23 | + | |50-54 |
− | |08 | + | |3 |
− | |184 | + | |52 |
− | |529 | + | |156 |
− | |4232 | + | |3 |
| + | |9 |
| + | |9 |
| + | |27 |
| |- | | |- |
| | | | | |
− | |n=50 | + | |n=40 |
− | |Σfx=660 | + | | |
| + | |Σfx=1668 |
| + | | |
| + | |Σfd=17 |
| | | | | |
− | |Σfx²=10710 | + | |Σfd²=85 |
| |} | | |} |
| + | A=assumed average.<br> |
| + | c=4<br> |
| + | d=<math>\frac{x-A}{c}</math>=<math>\frac{32-40}{4}</math>=<math>\frac{-8}{4}=-2</math><br> |
| + | |
| + | assumed mean A=<math>\frac{\sum fx}{n}</math>=<math>\frac{1668}{40}=41.7</math><br> |
| + | |
| + | Varience σ²=[<math>\frac{\sum {fd^2}}{n}-({\frac{\sum fx}{n})^2}]c^2</math> <br> |
| + | |
| + | σ²=[<math>\frac{85}{40}-({\frac{17}{40})^2}]4^2</math> <br> |
| + | |
| + | σ²=[2.125-0.180]16<br> |
| | | |
| + | σ²=[1.945]16<br> |
| | | |
| + | σ²=31.12<br> |
| + | standard deviation, σ=<math>\sqrt{varience}</math> <br> |
| + | σ=<math>\sqrt{31.12}</math> <br> |
| + | σ=5.58 |
| | | |
− | Standard deviation σ=<math>\sqrt{\frac {\sum {fx^2}}{n}-({\frac{\sum fx}{n})^2}}</math> <br>
| + | [[Category:Statistics]] |
− | σ=<math>\sqrt{\frac{10700}{50}-({\frac{660}{50})^2}}</math> <br>
| |
− | σ=<math>\sqrt{214-174.24}</math> <br>
| |
− | σ=<math>\sqrt{39.96}</math> <br>
| |
− | σ=6.3
| |