Final answer:
To calculate the standard deviation of a data set, follow these steps: find the mean, subtract the mean from each value and square the result, add up all the squared differences, divide the sum by the number of values, and take the square root of the result. Applying these steps to the given data set, the standard deviation is approximately 8.57.
Step-by-step explanation:
To calculate the standard deviation of a data set, follow these steps:
Find the mean of the data set. Add up all the values and divide by the total number of values.
Subtract the mean from each value in the data set and square the result.
Add up all the squared differences found in step 2.
Divide the sum of squared differences by the total number of values in the data set (n).
Take the square root of the result from step 4.
Applying these steps to the given data set: 59, 92, 66, 46, 90, 98, 95, 79, 70, 92, 75, 90, 63, 80, 92, 89, 85, 79, 63:
1. The mean = (59+92+66+46+90+98+95+79+70+92+75+90+63+80+92+89+85+79+63)/19 = 79
2. Subtracting the mean from each value and squaring the result:
(59-79)^2, (92-79)^2, (66-79)^2, (46-79)^2, (90-79)^2, (98-79)^2, (95-79)^2, (79-79)^2, (70-79)^2, (92-79)^2, (75-79)^2, (90-79)^2, (63-79)^2, (80-79)^2, (92-79)^2, (89-79)^2, (85-79)^2, (79-79)^2, (63-79)^2
3. Adding up all the squared differences = 1398
4. Calculating the variance = 1398/19 = 73.5789
5. Taking the square root of the variance to find the standard deviation: √73.5789 = 8.57
Therefore, the standard deviation of the given data set is approximately 8.57.