Find the standard deviation using the rule of thumb for each of the data sets
57,61,57,57,58,57,61
61,52,69,64,46,54,47
The standard deviation is approximately 1/4 the range; therefore, determine the difference between the highest and lowest value in each data set, then divide by 4. This is a rough estimate, but if you actually calculate the standard deviation and it's way off the estimate, then you may need to redo your calculations.
I hope this will help get you started.
Find the standard deviation using the rule of thumb for each of the data sets
57,61,57,57,58,57,61
61,52,69,64,46,54,47
first 7 is 1
second 7 is 5.75
To find the standard deviation using the rule of thumb, you need to follow these steps:
1. Find the mean of the data set.
2. Subtract the mean from each number in the data set to get the deviations.
3. Square each deviation.
4. Find the mean of the squared deviations.
5. Take the square root of the mean of squared deviations to get the standard deviation.
Let's calculate the standard deviation for each data set:
1. For the first data set: 57, 61, 57, 57, 58, 57, 61
Step 1: Calculate the mean:
(57 + 61 + 57 + 57 + 58 + 57 + 61) / 7 = 408 / 7 = 58.29 (rounded to two decimal places)
Step 2: Calculate the deviations:
57 - 58.29 = -1.29
61 - 58.29 = 2.71
57 - 58.29 = -1.29
57 - 58.29 = -1.29
58 - 58.29 = -0.29
57 - 58.29 = -1.29
61 - 58.29 = 2.71
Step 3: Square each deviation:
(-1.29)^2 = 1.66
(2.71)^2 = 7.34
(-1.29)^2 = 1.66
(-1.29)^2 = 1.66
(-0.29)^2 = 0.08
(-1.29)^2 = 1.66
(2.71)^2 = 7.34
Step 4: Find the mean of the squared deviations:
(1.66 + 7.34 + 1.66 + 1.66 + 0.08 + 1.66 + 7.34) / 7 = 21.84 / 7 = 3.12 (rounded to two decimal places)
Step 5: Take the square root of the mean of squared deviations:
√3.12 ≈ 1.77 (rounded to two decimal places)
The standard deviation for the first data set is approximately 1.77 using the rule of thumb.
2. For the second data set: 61, 52, 69, 64, 46, 54, 47
You can follow the same steps as before to calculate the standard deviation for this data set.