A sample of n = 5 college students yielded the following observations on number of traffic citations for a moving violation during the previous year.
Calculate s2 and s. (Round all answers to four decimal places.)
s2 = 1
s = 2
Observations not cited.
Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance (s^2).
Standard deviation = square root of variance
If s^2 = 1, s ≠ 2.
To calculate s^2 (squared) and s (standard deviation) for the given data, you will need to follow these steps:
Step 1: Find the mean (average) of the data.
To find the mean, sum up all the observations and divide by the total number of observations.
For example, if the given data is 1, 2, 3, 4, 5, the mean will be calculated as follows:
Mean = (1 + 2 + 3 + 4 + 5) / 5 = 15 / 5 = 3.
Step 2: Find the squared deviation for each observation.
Subtract the mean from each observation and square the result.
Squared Deviation = (Observation - Mean)^2.
For example, if the given data is 1, 2, 3, 4, 5, and the mean is 3, the squared deviations will be calculated as follows:
(1 - 3)^2 = 4
(2 - 3)^2 = 1
(3 - 3)^2 = 0
(4 - 3)^2 = 1
(5 - 3)^2 = 4.
Step 3: Find the sum of squared deviations.
Add up all the squared deviations calculated in step 2.
For example, sum of squared deviations = 4 + 1 + 0 + 1 + 4 = 10.
Step 4: Calculate s^2.
The formula for s^2 (squared) is the sum of squared deviations divided by (n - 1).
s^2 = Sum of squared deviations / (n - 1).
For example, s^2 = 10 / (5 - 1) = 10 / 4 = 2.5.
Step 5: Calculate s (standard deviation).
The standard deviation (s) is the square root of s^2.
s = Square root of s^2.
For example, s = Square root of 2.5 = 1.5811.
Therefore, the calculated values are:
s^2 = 2.5 (rounded to 4 decimal places)
s = 1.5811 (rounded to 4 decimal places).