The test scores for a math class are shown below
83,85,82,93,83,84,95,87,86,94
what is the standard deviation of the data set?
4.6
That's wrong
takes too long
calculate mean, the sum/10
calculate (x-mean)^2 for each x
add them
divide by 10
take the square root
To find the standard deviation of a data set, you can follow these steps:
1. Calculate the mean:
- Add up all the numbers in the data set.
- Divide the sum by the total number of data points.
Let's calculate the mean of the given data set:
(83 + 85 + 82 + 93 + 83 + 84 + 95 + 87 + 86 + 94) / 10 = 872 / 10 = 87.2
The mean is 87.2.
2. Calculate the deviations:
- Take each data point and subtract the mean from it.
- Square each deviation.
Let's calculate the deviations for each data point:
(83 - 87.2)^2 = (-4.2)^2 = 17.64
(85 - 87.2)^2 = (-2.2)^2 = 4.84
(82 - 87.2)^2 = (-5.2)^2 = 27.04
(93 - 87.2)^2 = (5.8)^2 = 33.64
(83 - 87.2)^2 = (-4.2)^2 = 17.64
(84 - 87.2)^2 = (-3.2)^2 = 10.24
(95 - 87.2)^2 = (7.8)^2 = 60.84
(87 - 87.2)^2 = (-0.2)^2 = 0.04
(86 - 87.2)^2 = (-1.2)^2 = 1.44
(94 - 87.2)^2 = (6.8)^2 = 46.24
3. Calculate the variance:
- Add up all the squared deviations.
- Divide the sum by the total number of data points.
Let's calculate the variance:
(17.64 + 4.84 + 27.04 + 33.64 + 17.64 + 10.24 + 60.84 + 0.04 + 1.44 + 46.24) / 10 = 219.16 / 10 = 21.916
The variance is 21.916.
4. Calculate the standard deviation:
- Take the square root of the variance.
Let's calculate the standard deviation:
√21.916 ≈ 4.68
Therefore, the standard deviation of the given data set is approximately 4.68.