Answer :
Final answer:
The mean of the data set is 16.4125, the median is 18.3, the mode is 10.1, the variance is 29.168786, and the standard deviation is approximately 5.401558.
Explanation:
To calculate the mean, you add up all the numbers and then divide by the count of the numbers. For the given data set (10.1, 20.2, 16.7, 9.9, 10.1, 24.4, 19.9, 20.0), the mean would be calculated as follows:
(10.1 + 20.2 + 16.7 + 9.9 + 10.1 + 24.4 + 19.9 + 20.0) ÷ 8 = 131.3 ÷ 8 = 16.4125
The median is the middle value when the numbers are put in order. Ordering the numbers (9.9, 10.1, 10.1, 16.7, 19.9, 20.0, 20.2, 24.4), the median is the average of the middle two numbers since there is an even count. Thus, (16.7 + 19.9) ÷ 2 = 18.3.
The mode is the number which appears most often. Here it is 10.1, as it appears twice.
To find the variance and standard deviation, first calculate the deviations from the mean, square them, add them up, and divide by the count of numbers minus one for the variance. Then take the square root of the variance for the standard deviation:
- Deviations from mean: (10.1 - 16.4125)^2, (20.2 - 16.4125)^2, ...
- Square deviations: 40.179025, 14.364225, ...
- Sum of squared deviations: 204.1815
- Variance (σ^2): 204.1815 ÷ (8 - 1) = 29.168786
- Standard deviation (σ): √29.168786 = 5.401558
