What is the stardard deviation using the rull of thumb for each set of numbers: 57,61,57,57,58,57,61
61,52,69,64,46,554,47
132.8460441
Provided your 554 is correct.
Rule of Thumb
Range/4 = approx. SD
You can do the calculations.
To calculate the standard deviation using the "rule of thumb," you need to follow these steps:
Step 1: Calculate the mean (average) of the given set of numbers.
To find the mean, sum up all the numbers in the set, and then divide the sum by the total number of elements in the set.
For the given set of numbers: 57, 61, 57, 57, 58, 57, 61, 52, 69, 64, 46, 554, 47,
Sum = 57 + 61 + 57 + 57 + 58 + 57 + 61 + 52 + 69 + 64 + 46 + 554 + 47 = 788.
Total number of elements = 13.
Mean = Sum / Total number of elements = 788 / 13 = 60.6154 (rounded to four decimal places).
Step 2: Calculate the difference between each number and the mean.
To do this, subtract the mean from each number in the set.
The differences for the given set of numbers are:
57 - 60.6154 = -3.6154
61 - 60.6154 = 0.3846
57 - 60.6154 = -3.6154
57 - 60.6154 = -3.6154
58 - 60.6154 = -2.6154
57 - 60.6154 = -3.6154
61 - 60.6154 = 0.3846
52 - 60.6154 = -8.6154
69 - 60.6154 = 8.3846
64 - 60.6154 = 3.3846
46 - 60.6154 = -14.6154
554 - 60.6154 = 493.3846
47 - 60.6154 = -13.6154
Step 3: Square each difference.
To eliminate the negative values introduced in Step 2, square each difference.
The squared differences for the given set of numbers are:
(-3.6154)^2 = 13.0655
0.3846^2 = 0.1481
(-3.6154)^2 = 13.0655
(-3.6154)^2 = 13.0655
(-2.6154)^2 = 6.8419
(-3.6154)^2 = 13.0655
0.3846^2 = 0.1481
(-8.6154)^2 = 74.2689
8.3846^2 = 70.2670
3.3846^2 = 11.4339
(-14.6154)^2 = 213.6100
493.3846^2 = 243459.0071
(-13.6154)^2 = 185.1444
Step 4: Calculate the variance.
The variance is the average of the squared differences. To find it, sum up all the squared differences from Step 3 and divide by the total number of elements.
Sum of squared differences = 13.0655 + 0.1481 + 13.0655 + 13.0655 + 6.8419 + 13.0655 + 0.1481 + 74.2689 + 70.2670 + 11.4339 + 213.6100 + 243459.0071 + 185.1444 = 243999.4218.
Variance = Sum of squared differences / Total number of elements = 243999.4218 / 13 = 18769.1863 (rounded to four decimal places).
Step 5: Calculate the standard deviation.
The standard deviation is the square root of the variance. To find it, take the square root of the variance calculated in Step 4.
Standard Deviation = √Variance = √18769.1863 ≈ 137.0207 (rounded to four decimal places).
Therefore, the standard deviation of the given set of numbers using the "rule of thumb" is approximately 137.0207.