Final answer:
To find the standard deviation of the sample data (55, 53, 76, 52, 91), calculate the mean, then find the deviations, square them, sum them, divide by n-1, and take the square root. The sample standard deviation is approximately 17.39.
Step-by-step explanation:
To find the standard deviation of the set of sample data (55, 53, 76, 52, 91), you would follow these steps:
- Calculate the mean (average) of the numbers.
- Subtract the mean from each number to find the deviation of each number from the mean.
- Square each of the deviations.
- Find the sum of the squared deviations.
- Divide this sum by the sample size minus one (which is the degrees of freedom for a sample standard deviation).
- Take the square root of the result from step 5 to get the sample standard deviation.
Here, the mean (step 1) is Σx/n = (55+53+76+52+91)/5 = 327/5 = 65.4.
Next, calculate the deviations (step 2), square them (step 3), and sum them up (step 4):
(55-65.4)^2 = 108.16
(53-65.4)^2 = 153.76
(76-65.4)^2 = 112.36
(52-65.4)^2 = 179.56
(91-65.4)^2 = 655.36
The sum of these values is 1209.2.
Divide by the degrees of freedom, which is n-1 (step 5). With five numbers, we have n-1 = 4 degrees of freedom, so 1209.2 / 4 = 302.3.
Finally, take the square root of 302.3 to get the sample standard deviation (step 6), which is approximately √302.3 = 17.39 when rounded to two decimal places.