Explanation:
To find the range, we need to subtract the smallest value from the largest value in the dataset:
Range = Largest value - Smallest value
Range = 92 - 3
Range = 89
To find the variance and standard deviation, we need to calculate the mean first:
Mean = (Sum of all values) / (Number of values)
Mean = (92+19+41+24+75+53+70+3+67+64+9) / 11
Mean = 45.09 (rounded to two decimal places)
Next, we need to calculate the variance:
Variance = (Sum of squared differences from the mean) / (Number of values - 1)
Variance = [(92-45.09)^2 + (19-45.09)^2 + (41-45.09)^2 + (24-45.09)^2 + (75-45.09)^2 + (53-45.09)^2 + (70-45.09)^2 + (3-45.09)^2 + (67-45.09)^2 + (64-45.09)^2 + (9-45.09)^2] / (11-1)
Variance = 1071.45 (rounded to two decimal places)
Finally, we can calculate the standard deviation by taking the square root of the variance:
Standard deviation = Square root of variance
Standard deviation = Square root of 1071.45
Standard deviation = 32.74 (rounded to two decimal places)
The range tells us the difference between the highest and lowest values in the dataset, which in this case is 89. The variance and standard deviation tell us how spread out the data is from the mean. The higher the variance and standard deviation, the more spread out the data is. In this case, the variance and standard deviation are both relatively high, indicating that the data is fairly spread out.