What is the standard deviation of the given data set? Round to the nearest tenth.
5, 10, 7, 12, 0, 20, 15, 22, 8, 2
A
6
B
6.89
C
6.892
D
6.9
To calculate the standard deviation, we first need to find the mean of the data set.
Mean = (5 + 10 + 7 + 12 + 0 + 20 + 15 + 22 + 8 + 2) / 10 = 10.1
Next, we subtract the mean from each number in the data set, square the result, and then find the mean of those squared differences.
(5 - 10.1)^2 = 26.01
(10 - 10.1)^2 = 0.01
(7 - 10.1)^2 = 9.61
(12 - 10.1)^2 = 3.61
(0 - 10.1)^2 = 102.01
(20 - 10.1)^2 = 98.01
(15 - 10.1)^2 = 23.41
(22 - 10.1)^2 = 141.61
(8 - 10.1)^2 = 4.41
(2 - 10.1)^2 = 65.61
Mean of squared differences = (26.01 + 0.01 + 9.61 + 3.61 + 102.01 + 98.01 + 23.41 + 141.61 + 4.41 + 65.61) / 10 = 47.2
Finally, we take the square root of the mean of squared differences to get the standard deviation.
Standard deviation = √47.2 ≈ 6.9
Therefore, the correct answer is D. 6.9.
Which is an example of qualitative data?
A
the number of textbooks in a classroom
B
the condition of the textbooks in a classroom
C
the ID numbers of the textbooks in a classroom
D
the number of pencil marks in the textbooks in a classroom
B
the condition of the textbooks in a classroom
To find the standard deviation of a data set, you can follow these steps:
Step 1: Find the mean (average) of the data set.
To find the mean, you add up all the numbers and then divide by the total number of values.
Mean = (5 + 10 + 7 + 12 + 0 + 20 + 15 + 22 + 8 + 2) / 10
Mean = 101/10
Mean = 10.1
Step 2: Find the deviation of each value from the mean.
Subtract the mean from each value in the data set, and then square the result.
(5 - 10.1)^2 = 26.01
(10 - 10.1)^2 = 0.01
(7 - 10.1)^2 = 9.61
(12 - 10.1)^2 = 3.61
(0 - 10.1)^2 = 102.01
(20 - 10.1)^2 = 98.01
(15 - 10.1)^2 = 24.01
(22 - 10.1)^2 = 140.41
(8 - 10.1)^2 = 4.41
(2 - 10.1)^2 = 64.81
Step 3: Find the mean of the squared deviations.
Add up all the squared deviations and then divide by the total number of values.
Mean of Squared Deviations = (26.01 + 0.01 + 9.61 + 3.61 + 102.01 + 98.01 + 24.01 + 140.41 + 4.41 + 64.81) / 10
Mean of Squared Deviations = 532.9 / 10
Mean of Squared Deviations = 53.29
Step 4: Find the square root of the mean of the squared deviations to get the standard deviation.
Square root of the Mean of Squared Deviations = √53.29
Standard Deviation ≈ 7.3
Therefore, the standard deviation of the given data set (rounded to the nearest tenth) is approximately 7.3.
To find the standard deviation of a data set, you can follow these steps:
1. Calculate the mean (average) of the data set.
2. Subtract the mean from each data point, and square the result.
3. Calculate the mean of the squared differences.
4. Take the square root of the mean squared differences.
Let's perform these steps for the given data set:
1. Calculate the mean:
(5 + 10 + 7 + 12 + 0 + 20 + 15 + 22 + 8 + 2) / 10 = 9.1
2. Subtract the mean from each data point, and square the result:
(5-9.1)^2, (10-9.1)^2, (7-9.1)^2, (12-9.1)^2, (0-9.1)^2, (20-9.1)^2, (15-9.1)^2, (22-9.1)^2, (8-9.1)^2, (2-9.1)^2
= 18.81, 0.81, 4.41, 6.76, 82.81, 121.00, 32.41, 157.61, 1.21, 48.41
3. Calculate the mean of the squared differences:
(18.81 + 0.81 + 4.41 + 6.76 + 82.81 + 121.00 + 32.41 + 157.61 + 1.21 + 48.41) / 10
= 473.13 / 10
= 47.313
4. Take the square root of the mean squared differences:
sqrt(47.313) ≈ 6.9
So, the standard deviation of the given data set is approximately 6.9.
Therefore, the correct answer is Option D: 6.9.