Let’s say that you work for a news agency, which is conducting an exit poll for the MCD (Municipal Corporation of Delhi) elections. You have been tasked with predicting the winner for ward 75N (Ashok Vihar). You ask 100 randomly selected voters from this ward to name the party they had voted for.
The data thus collected is as given in the following table.
| Contesting Party | Number of Voters |
| BJP | 5 |
| INC | 4 |
From this sample, you have to estimate the percentage of voters that may have voted for BJP.
So, you define X as the proportion of people that voted for BJP. Then, the frequency distribution for X would be as follows:
| x | Frequency |
| 1 | 5 |
| 0 | 4 |
Now, you have to find the mean for X, which is equal to (0 + 0 + 0 + … 42 times) + (1 + 1 + 1 + … 58 times), divided by the total frequency, i.e., 100. So, the mean
= 0.58, or 58%.
Also, you would have to find the standard deviation for this sample of 100 voters. Since the mean is 0.58, the sample’s variance =
= 0.2461. So, the standard deviation is equal to its square root, i.e., 0.496, or 49.6%.