Expected Frequency Calculator

Formula

To calculate the Expected Frequency (E):

\[ E = \frac{Ri + Cj}{N} \]

Where:

\( E \) is the expected frequency
\( Ri \) is the total in the ith row
\( Cj \) is the total in the jth column
\( N \) is the grand total

Expected Frequency Definition

Expected frequencies, as opposed to observed frequencies, are theoretical probabilities of certain outcomes occurring. For example, if you were to pick one card from a deck of cards, your expected frequency of getting any given card would be \( \frac{1}{52} = 0.0192 = 1.92\% \). Expected frequencies are most often used when analyzing contingency tables.

Example Calculation

Let's assume the following values:

Total in the ith Row \( Ri \) = 100
Total in the jth Column \( Cj \) = 150
Grand Total \( N \) = 500

Step 1: Use the expected frequency formula:

\[ E = \frac{Ri + Cj}{N} = \frac{100 + 150}{500} = 0.50 \]

The Expected Frequency (E) is 0.50.