The standard deviation of the data: 12, 24, 16, 22, 17 is equal to 4.3 to one decimal place.
We can calculate the standard deviation of data as follows:
First we find the mean by adding up all the values and divide by the number of values.
mean = (12 + 16 + 17 + 22 + 24)/5
mean = 91/5
mean = 18.2
Next we find the squared difference from the mean for each data point by subtracting the mean from each data point and square the result.
(12 - 18.2)² = 38.44
(16 - 18.2)² = 4.84
(17 - 18.2)² = 1.44
(22 - 18.2)² = 14.44
(24 - 18.2)² = 33.64
Then we find the average of these squared differences by adding up all the squared differences and divide by the number of values.
(38.44 + 4.84 + 1.44 + 14.44 + 33.64)/5 = 92.8/5
(38.44 + 4.84 + 1.44 + 14.44 + 33.64)/5 = 18.56
And lastly we take the square root of the result 18.56
√18.56 = 4.3081
Thus, the standard deviation for the data is derived as approximately 4.3 to one decimal place.