Find the range and the standard deviation (correct to two decimal places).
83,96,100,100,103
find the range and standard deviation
Do I that 5 numbers add that divide by 5
for the range I am not sure how to do standard deviation. Thank you
add and divide by 5 gives the mean, not the range
the range is hi-low = 103-83=20
The mean is 96.4
To find the std,
(1) take the difference of each value from the mean
(2) square that difference
(3) add up all those squares
(4) take the square root.
That is the std.
Better review that section again. Visit
http://www.mathsisfun.com/data/standard-deviation.html
for a nice simple explanation and example.
thank you Steve it is appreciated. Thank you very much for the site.
Five staff members have been working in a convenience store for 4, 5, X, 5 and 4 years respectively. Given that the mean of their working experiences is 4.6, find the population standard deviation. (correct to 2 decimal places)
Well, calculating the range is pretty simple! It's just the difference between the highest and lowest values in your set. So, in this case, the range would be 103 (highest value) minus 83 (lowest value), which equals 20.
Calculating the standard deviation is a bit more involved. But fear not, I'm here to help! Here's a breakdown of the steps:
1. Find the mean (average) of your numbers. Simply add them all up and divide the total by the number of values (in this case, 5).
2. Subtract the mean from each number to get the individual deviations. Take each deviation and square it.
3. Find the mean of the squared deviations.
4. Take the square root of the mean of squared deviations to get the standard deviation.
Now, let me crunch the numbers for you real quick...
The mean is: (83 + 96 + 100 + 100 + 103) / 5 = 96.4
The squared deviations are: (16.36, 0, 13.44, 13.44, 39.76)
The mean of squared deviations is: (16.36 + 0 + 13.44 + 13.44 + 39.76) / 5 = 16
And finally, the standard deviation is the square root of 16, which is... drumroll, please... 4.
So, the range is 20 and the standard deviation is 4 (correct to two decimal places). Voilà!
To find the range of a set of numbers, you simply subtract the minimum value from the maximum value. In this case, the minimum value is 83 and the maximum value is 103. Therefore, the range is 103 - 83 = 20.
To calculate the standard deviation, you can follow these steps:
Step 1: Find the mean (average) of the numbers. To do this, add up all the numbers and divide by the total count. In this case, the sum of the numbers is 83 + 96 + 100 + 100 + 103 = 482. Divide this sum by the total count of numbers, which is 5: 482 / 5 = 96.4.
Step 2: Calculate the deviation of each number from the mean. To do this, subtract the mean from each number. Here are the deviations for the given numbers: -13.4, -0.4, 3.6, 3.6, and 6.6.
Step 3: Square each deviation. This is done to eliminate negative values and provide greater emphasis on differences from the mean. The squared deviations for the given numbers are: 179.56, 0.16, 12.96, 12.96, and 43.56.
Step 4: Find the mean of the squared deviations by adding them up and dividing by the total count. The sum of the squared deviations is 179.56 + 0.16 + 12.96 + 12.96 + 43.56 = 249.2. Divide this sum by the total count of numbers, which is 5: 249.2 / 5 = 49.84.
Step 5: Calculate the square root of the mean of the squared deviations. In this case, the square root of 49.84 is approximately 7.06 (rounded to two decimal places).
So, the standard deviation of the given numbers is approximately 7.06.