Final answer:
To calculate the population standard deviation, we find the mean, compute squared deviations, sum them, divide by the number of data points, and then take the square root of the resulting variance. The calculated standard deviation is approximately 7.69, which does not match the given options.
Step-by-step explanation:
To find the population standard deviation of the data set 7, 11, 21, 24, 27, we will follow these steps:
- Calculate the mean (average) of the data set. Mean = (7 + 11 + 21 + 24 + 27) / 5 = 90 / 5 = 18.
- Subtract the mean from each data point and square the result. These are the squared deviations: (7-18)^2 = 121, (11-18)^2 = 49, (21-18)^2 = 9, (24-18)^2 = 36, (27-18)^2 = 81.
- Calculate the sum of the squared deviations. Sum = 121 + 49 + 9 + 36 + 81 = 296.
- Since we are calculating the population standard deviation, divide the sum by the number of data points (N). Variance = 296 / 5 = 59.2.
- Take the square root of the variance to get the standard deviation. Standard deviation = √59.2 ≈ 7.69 (rounded to two decimal places, not found in the given options).
Thus, the correct standard deviation is not listed in the given options. However, since the closest value to 7.69 is 'c' (7.46), there might be a mistake in either the question or the calculation. The true population standard deviation of the given data set is approximately 7.69.