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From Karnataka Open Educational Resources
Activity- statistics problems (view source)
Revision as of 09:56, 30 October 2019
, 09:56, 30 October 2019added Category:Statistics using HotCat
=Problem 1=
=Problem 1=
If n =10, = 12 and = 1530 find coefficient of variation
If n =10, <math>\bar x </math> = 12 and<br>
==INTERPRETATION OF PROBLEM==
<math>\sum{x^2}= 1530 find the standard deviation </math> <br>
==Previous knowledge==
==Solution==
=INTERPRETATION OF PROBLEM=
<math>\frac{\sum_{}^{}x}{n}=\bar x </math>
=Previous knowledge=
=Solution:=
<math>\frac{\sum x}{n}=\bar x </math> <br>
<math>\sum {x} ={\bar x \times {n}} </math> <br>
<math>\sum {x} ={12 \times {10}} </math> <br>
<math>\sum {x} =120 </math> <br>
σ=<math>\sqrt{\frac {\sum {x^2}}{n}-({\frac{\sum x}{n})^2}}</math> <br>
σ=<math>\sqrt{\frac{1530}{10}-{144}}</math> <br>
σ=<math>\sqrt{\frac{1530}{10}-{144}}</math> <br>
σ=<math>\sqrt{153-144}</math> <br>
σ=<math>\sqrt{9}</math> <br>
σ=3
=Problem 2=
Problem No.1 of excercise No.6.1 <br>
Find the Standard deviation for the following data.
{|class="wikitable"
|-
|x
|03
|08
|13
|18
|23
|-
|f
|07
|10
|15
|10
|08
|}
=INTERPRETATION OF PROBLEM=
=Previous knowledge=
=Solution:=
{|class="wikitable"
|-
|x
|f
|fx
|x²
|fx²
|-
|03
|07
|021
|009
|0063
|-
|08
|10
|080
|064
|0640
|-
|13
|15
|195
|169
|2535
|-
|18
|10
|180
|324
|3240
|-
|23
|08
|184
|529
|4232
|-
|
|n=50
|Σfx=660
|
|Σfx²=10710
|}
Standard deviation σ=<math>\sqrt{\frac {\sum {fx^2}}{n}-({\frac{\sum fx}{n})^2}}</math> <br>
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
=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]]
