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Chi Square Calculator
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 Chi Square Calculator (or Chi Square Test Calculator or Chi Squared Calculator) is an online tool used to test the cumulative probability on the basis of chi-square statistics, which is used to find out whether the distribution of given category variables are differ from one another or not.chi-square value can be calculated when observed frequency and expected frequency of a corresponding data is known. Chi square is denoted by $\chi^{2}$ Chi-Square Test Formula$\chi^{2}$ = $\sum$ $\frac{(O - E)^{2}}{E}$where, $\chi^{2}$ = Chi-square valueO = Observed frequency for each category E = Expected frequency for each category.

## Step by Step Calculation

Step 1 :

Observed the given observed frequency and expected frequency.

Step 2 :

To find the chi-square value, apply the formula

chi-square value($\chi^{2}$) = $\sum$ $\frac{(O - E)^{2}}{E}$
where,
$\chi^{2}$ = Chi-square value
O = Observed frequency for each category
E = Expected frequency for each category.

## Example Problems

1. ### Calculate the chi-square value, if observed frequency is 5 and expected frequency is 10?

Step 1 :

Given observed frequency = 5
and expected frequency = 10

Step 2 :

chi-square value($\chi^{2}$) = $\frac{(5 - 10)^{2}}{10}$
$\chi^{2}$ = $\frac{(-5)^{2}}{10}$

$\chi^{2}$ = $\frac{25}{10}$

$\chi^{2}$ = 2.5

chi-square value($\chi^{2}$) = 2.5

2. ### Calculate the chi-square value for the following data.          Color Red Green Yellow Observed Frequency  15  10  20 Expected Frequency  20  5  30

Step 1 :

So, for the color red: (Observed frequency - Expected frequency)2 = (15 - 20)2 = 25

So, for the color green: (Observed frequency - Expected frequency)2 = (10 - 5)2 = 25

So, for the color yellow: (Observed frequency - Expected frequency)2 = (20 - 30)2 = 100

Step 2 :

Chi-square value for the color red: $\frac{(O - E)^{2}}{E}$

$\Rightarrow$ $\frac{25}{20}$

$\Rightarrow$ 1.25

Chi-square value for the color green: $\frac{(O - E)^{2}}{E}$

$\Rightarrow$ $\frac{25}{5}$

$\Rightarrow$ 5

Chi-square value for the color yellow: $\frac{(O - E)^{2}}{E}$

$\Rightarrow$ $\frac{100}{30}$

$\Rightarrow$ 3.333

So, the chi-square value for the given data is given by = 1.25 + 5 + 3.333

chi-square value($\chi^{2}$) = 9.58300