Discuss the concept of expected frequencies and summarize th

Discuss the concept of expected frequencies and summarize the steps involved in computing them.

Solution

Expected frequency is defined as the number of times an event is presumed to happen in a given number of trials. Suppose there were a total of 5 events and each event has equal probability of occurence. Then for a total of 10 trials, the expected frequency of each event will be 2 times.

Now consider a more complex situation. Consider two sets of events (Say {A,B,C} and {P,Q,R}) with each intersection of events having equal probability of occurence. Thus for a total of 45 trials the expected frequency of A and P to occur in unision will be 5 times. One alternate way to see this is A is expected to occur 15 times, P is also expected to occur 15 times. The number of ways A and P occur in unision will be given by,

Expected occurence of A and P = (Expected occurence of A)*(Expected occurrence of P)/(Total Number of trials)

Now this last formula that we have used here can be used for the cases where the events do not have same probability of occurrence. Thus this is the generalised form of calculating expected frequency.

For finding the expected frequency write the observed frequencies in a table. Find the row total and column totals and grand total. Expected frequency of any cell will be given by , (row total)*(column total)/(grand total).