Answer :
Final answer:
To find the variance and standard deviation, calculate the sample mean, determine squared differences, sum them, divide by n-1 for variance, and square root the variance for standard deviation. Use a calculator or software for precision.
Explanation:
To calculate the variance and standard deviation for a set of data, you first need to find the mean (average) of the sample. Then, you subtract the mean from each data point and square the result to find the squared differences. Add all the squared differences together to get the sum of squared differences. Divide this sum by the number of data points minus one (n-1) to get the sample variance. The standard deviation is then the square root of the variance.
Step-by-Step Calculation:
- Find the mean: (81.2 + 86.4 + 59.1 + 45.4 + 73.5 + 62.4) / 6 = 68.17.
- Calculate each data point's squared difference from the mean.
- Add all squared differences to get the sum of squared differences.
- Divide by the number of data points minus one: Sum of squared differences / 5 = variance.
- Take the square root of variance to get standard deviation.
Remember to use a graphing calculator or computer software for accuracy and to avoid rounding intermediate calculations. Round your final answers to the nearest tenth.
