Answer :
The standard deviation of the flower counts on Peter's rose bushes can be calculated by first finding the mean of the counts, then finding the mean of the square of the differences between each count and the mean, and finally taking the square root of that number. This involves the use of basic arithmetic, squaring, and square roots.
To calculate the standard deviation of a set of numbers, you have to follow these steps:
Calculate the mean of the numbers. This is done by adding them all together and then dividing by the number of numbers.
Subtract the mean from each number to get the list of deviations.
Square each deviation.
Get the mean of these squared deviations.
Finally, take the square root of that mean. That gives you the standard deviation.
So, in Peter's case, the numbers are the counts of flowers on each bush. The steps would look like this:
Sum of flower counts = 9+2+5+4+12+7+8+11+9+3+7+4+12+5+4 = 95. Therefore, mean = 95/15 = 6.33
Subtract the mean from each count to get the deviations and then square. For instance, for the first bush, (9-6.33)^2 = 7.11. Do this for all bushes.
Then, find the mean of those squared deviations, which would be the variance.
Finally, find the square root of the variance to find the standard deviation.
Learn more about standard deviation here:
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