Final answer:
To find the mean, variance, and standard deviation, calculate the midpoint for each class interval. Multiply each midpoint by its frequency and sum up the results to find the mean. Find the squared deviations from the mean, multiply them by their frequency, and sum up the results to find the variance. Finally, take the square root of the variance to find the standard deviation.
Step-by-step explanation:
To find the mean, variance, and standard deviation, we first need to calculate the midpoint for each class interval. The midpoint is calculated by adding the lower and upper class boundaries and dividing by 2. For the first class interval, the midpoint is (15.5 + 20.5) / 2 = 18. For the second class interval, the midpoint is (20.5 + 25.5) / 2 = 23. For the third class interval, the midpoint is (25.5 + 30.5) / 2 = 28. For the fourth class interval, the midpoint is (30.5 + 35.5) / 2 = 33. For the fifth class interval, the midpoint is (35.5 + 40.5) / 2 = 38.
The frequency is given as the number of CEOs in each class interval. The sum of the frequencies is 13 + 6 + 4 + 1 + 1 = 25.
To find the mean, we multiply each midpoint by its frequency and sum up the results. Then, we divide the sum by the total frequency. The mean is (18 * 13 + 23 * 6 + 28 * 4 + 33 * 1 + 38 * 1) / 25 = 22.44 million dollars.
To find the variance, we first need to find the squared deviations from the mean for each midpoint. We multiply each squared deviation by its frequency and sum up the results. Then, we divide the sum by the total frequency. The variance is ((18 - 22.44)^2 * 13 + (23 - 22.44)^2 * 6 + (28 - 22.44)^2 * 4 + (33 - 22.44)^2 * 1 + (38 - 22.44)^2 * 1) / 25 = 51.5416 million dollars squared.
To find the standard deviation, we take the square root of the variance. The standard deviation is √(51.5416) = 7.18 million dollars.