You ask 100 randomly selected voters from this ward to name the party they had voted for. Of the 100 voters, 58 voted for AAP and 42 voted for BJP. So, you define X as the proportion of people that voted for AAP. Then, the frequency distribution for X would be as shown in the table given below. X Frequency1 580 42Question 1/3MandatoryComprehensionFind the mean and standard deviation of X.
Question
You ask 100 randomly selected voters from this ward to name the party they had voted for. Of the 100 voters, 58 voted for AAP and 42 voted for BJP. So, you define X as the proportion of people that voted for AAP. Then, the frequency distribution for X would be as shown in the table given below. X Frequency1 580 42Question 1/3MandatoryComprehensionFind the mean and standard deviation of X.
Solution
To find the mean and standard deviation of X, we need to calculate the weighted average of the values in the frequency distribution table.
First, we calculate the product of each value of X with its corresponding frequency. For X = 1, the product is 1 * 58 = 58. For X = 0, the product is 0 * 42 = 0.
Next, we sum up all the products: 58 + 0 = 58.
To find the mean, we divide the sum of the products by the total number of voters: 58 / 100 = 0.58.
To calculate the standard deviation, we need to find the variance first. The variance is the sum of the squared differences between each value of X and the mean, multiplied by their corresponding frequencies.
For X = 1, the squared difference is (1 - 0.58)^2 = 0.1744. The product of the squared difference and the frequency is 0.1744 * 58 = 10.1096.
For X = 0, the squared difference is (0 - 0.58)^2 = 0.3364. The product of the squared difference and the frequency is 0.3364 * 42 = 14.1248.
Next, we sum up all the products: 10.1096 + 14.1248 = 24.2344.
To find the variance, we divide the sum of the products by the total number of voters: 24.2344 / 100 = 0.242344.
Finally, to calculate the standard deviation, we take the square root of the variance: √0.242344 = 0.4923 (rounded to four decimal places).
Therefore, the mean of X is 0.58 and the standard deviation of X is 0.4923.
Similar Questions
Suppose 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. Of the 100 voters, 58 voted for AAP and 42 voted for BJP. So, you define X as the proportion of people that voted for AAP. Then, the frequency distribution for X would be as shown in the table given below. X Frequency1 580 42Question 1/3MandatoryComprehensionFind the mean and standard deviation of X.0.58; 0.2460.58; 0.4960.58; 0.494None of the above
In a certain city, 60% of the registered voters are congress supporters and the rest are BJP supporters. In an assembly election, if 75% of the registered congress supporters and 20% of the registered BJP supporters are expected to vote for candidate A, what percent of the registered voters are expected to vote for candidate A?
Suppose Facebook has launched a new fact-checking feature. It conducts a survey among its user base, wherein it asks them the question ‘Do you find the fact-checking feature useful?’. Out of the 2,500 respondents, 53.2% believe that the feature is useful. If you define X as the proportion of people that find the feature useful, the frequency distribution for X would be as shown in the table given below. X Frequency1 1,3300 1,170Question 2/3MandatorySampling and EstimationSuppose the sample standard deviation is known to be 0.6, what is the interval in which the mean of the sampling distribution of sample size 2,500 will belong at a 99% confidence level?(0.456, 0.608)(0.572, 0.588)(0.493, 0.571)(0.501, 0.563)
A political polling agency wants to take a random sample of registered voters and ask whether or not they will vote for a certain candidate. One plan is to select 400 voters, another plan is to select 1,600 voters.Which one of the following is true regarding the standard deviation of the sampling distribution of the sample proportion, p̂, of "yes" responses? The standard deviation of the sampling distribution will be 4 times smaller with sample size 400. The standard deviation of the sampling distribution will be 4 times larger with sample size 400. The standard deviation of the sampling distribution will be 2 times smaller with sample size 400. The standard deviation of the sampling distribution will be 2 times larger with sample size 400. The standard deviation of the sampling distribution will be the same for both sample sizes.
For the population of scores shown in the frequency distribution table, the mean is ____.X f5 24 13 32 21 2
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.