Final answer:
The range is 62, variance is 85.94, and standard deviation of the given data is 9.27, to calculate this, first calculate the mean. Then, find the difference between the largest and smallest numbers to find the range. Calculate the squared difference between each number and the mean to determine the variance. Finally, take the square root of the variance to find the standard deviation.
Step-by-step explanation:
To find the range, variance, and standard deviation of the given data, we first need to calculate the mean. The mean is the sum of all the numbers divided by the total count of numbers. In this case, the mean is (60+20+40+40+45+12+34+51+30+70+42+31+69+32+8+18+50) / 17 = 38.29.
Next, we calculate the range, which is the difference between the largest and smallest numbers. In this case, the range is 70 - 8 = 62.
To calculate the variance, we need to find the squared difference between each number and the mean, sum up the squared differences, and then divide by the total count of numbers. The variance is the measure of how spread out the numbers are from the mean. The formula for variance is (∑(x - mean)^2) / n. Using this formula, we get the variance as (1461.06) / 17 ≈ 85.94.
Finally, the standard deviation is the square root of the variance. It tells us how much the data deviates from the mean. The standard deviation formula is √variance. In this case, the standard deviation is √85.94 ≈ 9.27.