What is the standard deviation to two decimal places for the following data:
4 6 7 4 5
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.
Standard deviation = square root of variance
I'll let you do the calculations.
To find the standard deviation of a set of data, you can follow these steps:
Step 1: Calculate the mean of the data set.
Add up all the values in the data set and divide the sum by the total number of values.
For the given data set (4, 6, 7, 4, 5):
Mean = (4 + 6 + 7 + 4 + 5) / 5 = 26 / 5 = 5.2
Step 2: Subtract the mean from each data point and square the result.
For each value in the data set, subtract the mean obtained in Step 1 and then square the result.
(4 - 5.2)² = 1.44
(6 - 5.2)² = 0.64
(7 - 5.2)² = 3.24
(4 - 5.2)² = 1.44
(5 - 5.2)² = 0.04
Step 3: Calculate the mean of the squared values obtained in Step 2.
Add up all the squared values and divide the sum by the total number of values.
Mean of squared values = (1.44 + 0.64 + 3.24 + 1.44 + 0.04) / 5 = 6.8 / 5 = 1.36
Step 4: Take the square root of the result obtained in Step 3 to find the standard deviation.
Standard Deviation = √(mean of squared values)
Standard Deviation = √1.36 = 1.17 (rounded to two decimal places)
Therefore, the standard deviation for the given data set (4, 6, 7, 4, 5) is approximately 1.17 when rounded to two decimal places.