The test scores for a math class are shown below.
81,84,82,93,81,85,95,89,86,94
What is the standard deviation of the data set? Roun your answer to the nearest tenth
4.9
5.5
5.3
5.1
Sum = 870
Mean = 870/10 = 87
X Mean X - Mean X - Mean ^ 2
81 87 -6 36
81 87 -6 36
82 87 -5 25
84 87 -3 9
85 87 -2 4
86 87 -1 1
89 87 2 4
93 87 6 36
94 87 7 49
95 87 8 64
Take the sum of all of these ^^^ and you get 264
Divide this by the # of terms, 10, and get 26.4
Your variance = 26.4
The standard deviation is the sqr root of 26.4
This is approximately 5.1
Have a great day
Well, calculating the standard deviation of this dataset seems like a job for a mathematician, not a clown! But since you're here, I'll try to give you a laugh while answering.
Why did the math book get bad test scores?
Because it was feeling a little un-square!
Now, onto the standard deviation. After some mathematical mischief, the correct answer is 5.1. So grab your calculator, but remember, don't divide by zero or try balancing equations with a funny bone!
To calculate the standard deviation of the data set, follow these steps:
Step 1: Find the mean (average) of the data set.
To find the mean, add up all the numbers in the data set and divide the sum by the total number of values.
81 + 84 + 82 + 93 + 81 + 85 + 95 + 89 + 86 + 94 = 870
Mean = 870 / 10 = 87
Step 2: Calculate the squared difference for each data value.
For each data value, subtract the mean from the value and then square the result.
(81 - 87)^2 = 36
(84 - 87)^2 = 9
(82 - 87)^2 = 25
(93 - 87)^2 = 36
(81 - 87)^2 = 36
(85 - 87)^2 = 4
(95 - 87)^2 = 64
(89 - 87)^2 = 4
(86 - 87)^2 = 1
(94 - 87)^2 = 49
Step 3: Find the mean of the squared differences.
Add up all the squared differences and divide the sum by the total number of values.
36 + 9 + 25 + 36 + 36 + 4 + 64 + 4 + 1 + 49 = 260
Mean of squared differences = 260 / 10 = 26
Step 4: Take the square root of the mean of squared differences.
Square root of 26 ≈ 5.1
Therefore, the standard deviation of the data set is approximately 5.1.
To find the standard deviation of a data set, you'll need to do the following steps:
1. Find the mean (average) of the data set.
2. Subtract the mean from each data point and square the result.
3. Find the mean (average) of these squared differences.
4. Take the square root of this mean.
Let's go through the steps:
Step 1: Find the mean
To find the mean of a data set, add up all the numbers and divide the sum by the total number of data points.
81 + 84 + 82 + 93 + 81 + 85 + 95 + 89 + 86 + 94 = 870
The data set has 10 numbers, so the mean is 870/10 = 87.
Step 2: Subtract the mean and square the result
Take each number in the data set and subtract the mean from it. Then square the result.
(81 - 87)^2 = 36
(84 - 87)^2 = 9
(82 - 87)^2 = 25
(93 - 87)^2 = 36
(81 - 87)^2 = 36
(85 - 87)^2 = 4
(95 - 87)^2 = 64
(89 - 87)^2 = 4
(86 - 87)^2 = 1
(94 - 87)^2 = 49
Step 3: Find the mean of the squared differences
Add up all the squared differences from Step 2 and divide the sum by the total number of data points.
36 + 9 + 25 + 36 + 36 + 4 + 64 + 4 + 1 + 49 = 264
The data set has 10 numbers, so the mean of the squared differences is 264/10 = 26.4.
Step 4: Take the square root
Take the square root of the mean of the squared differences from Step 3.
√26.4 ≈ 5.1
Therefore, the standard deviation of the data set is approximately 5.1 (rounded to the nearest tenth).
So, the correct answer is 5.1.
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.