Line 1: |
Line 1: |
| =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= |
Line 24: |
Line 24: |
| | | |
| =Problem 2= | | =Problem 2= |
| + | Problem No.1 of excercise No.6.1 <br> |
| Find the Standard deviation for the following data. | | Find the Standard deviation for the following data. |
| {|class="wikitable" | | {|class="wikitable" |
Line 99: |
Line 100: |
| σ=<math>\sqrt{39.96}</math> <br> | | σ=<math>\sqrt{39.96}</math> <br> |
| σ=6.3 | | σ=6.3 |
| + | |
| + | =Problem 3= |
| + | Problem No.5 of excercise No.6.3 <br> |
| + | Find the varience and Standard deviation for the following data. |
| + | {|class="wikitable" |
| + | |- |
| + | |class intervals(CI) |
| + | |30-34 |
| + | |34-38 |
| + | |38-42 |
| + | |42-46 |
| + | |46-50 |
| + | |50-54 |
| + | |- |
| + | |freequency(f) |
| + | |04 |
| + | |07 |
| + | |09 |
| + | |11 |
| + | |06 |
| + | |03 |
| + | |} |
| + | |
| + | =INTERPRETATION OF PROBLEM= |
| + | |
| + | =Previous knowledge= |
| + | |
| + | =Solution:= |
| + | {|class="wikitable" |
| + | |- |
| + | |C.I. |
| + | |f |
| + | |x |
| + | |fx |
| + | |d=<math>\frac{x-A}{c}</math> |
| + | |fd |
| + | |d² |
| + | |fd² |
| + | |- |
| + | |30-34 |
| + | |4 |
| + | |32 |
| + | |128 |
| + | | -2 |
| + | | -8 |
| + | |4 |
| + | |16 |
| + | |- |
| + | |34-38 |
| + | |7 |
| + | |36 |
| + | |252 |
| + | | -1 |
| + | | -7 |
| + | |1 |
| + | |7 |
| + | |- |
| + | |38-42 |
| + | |9 |
| + | |40 |
| + | |360 |
| + | |0 |
| + | |0 |
| + | |0 |
| + | |0 |
| + | |- |
| + | |42-46 |
| + | |11 |
| + | |44 |
| + | |484 |
| + | |1 |
| + | |11 |
| + | |1 |
| + | |11 |
| + | |- |
| + | |46-50 |
| + | |6 |
| + | |48 |
| + | |288 |
| + | |2 |
| + | |12 |
| + | |4 |
| + | |24 |
| + | |- |
| + | |50-54 |
| + | |3 |
| + | |52 |
| + | |156 |
| + | |3 |
| + | |9 |
| + | |9 |
| + | |27 |
| + | |- |
| + | | |
| + | |n=40 |
| + | | |
| + | |Σfx=1668 |
| + | | |
| + | |Σfd=17 |
| + | | |
| + | |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 |
| + | |
| + | [[Category:Statistics]] |