the test scores fpr a math class are shown below. 83, 85, 82, 93, 83, 84, 95, 87, 86, 94 what is the standard deviation of this data set?
The standard deviation of this data set is approximately 4.24.
To find the standard deviation of a data set, you can follow these steps:
Step 1: Find the mean of the data set.
Step 2: Subtract the mean from each individual data point.
Step 3: Square each result from step 2.
Step 4: Find the mean of the squared values from step 3.
Step 5: Take the square root of the mean found in step 4.
Let's calculate the standard deviation for the given data set.
Step 1: Find the mean
Mean (μ) = (83 + 85 + 82 + 93 + 83 + 84 + 95 + 87 + 86 + 94) / 10 = 872 / 10 = 87.2
Step 2: Subtract the mean from each data point
(83 - 87.2) = -4.2
(85 - 87.2) = -2.2
(82 - 87.2) = -5.2
(93 - 87.2) = 5.8
(83 - 87.2) = -4.2
(84 - 87.2) = -3.2
(95 - 87.2) = 7.8
(87 - 87.2) = -0.2
(86 - 87.2) = -1.2
(94 - 87.2) = 6.8
Step 3: Square each result
(-4.2)^2 = 17.64
(-2.2)^2 = 4.84
(-5.2)^2 = 27.04
(5.8)^2 = 33.64
(-4.2)^2 = 17.64
(-3.2)^2 = 10.24
(7.8)^2 = 60.84
(-0.2)^2 = 0.04
(-1.2)^2 = 1.44
(6.8)^2 = 46.24
Step 4: Find the mean of the squared values
Mean of squared values = (17.64 + 4.84 + 27.04 + 33.64 + 17.64 + 10.24 + 60.84 + 0.04 + 1.44 + 46.24) / 10 = 220.7 / 10 = 22.07
Step 5: Take the square root of the mean found in step 4
Standard Deviation (σ) = sqrt(22.07) ≈ 4.70
Therefore, the standard deviation of the given data set is approximately 4.70.