Find the standard deviation of the sample data set. 51 64 35 74 42 62 34 39 52 77 (1 point) Responses 3.8 3.8 15.7 15.7 247.3 247.3 14.9
To find the standard deviation of a sample data set, you can follow these steps:
1. Find the mean of the data set:
mean = (51 + 64 + 35 + 74 + 42 + 62 + 34 + 39 + 52 + 77) / 10 = 50
2. Subtract the mean from each data point and square the result:
(51 - 50)^2 = 1
(64 - 50)^2 = 196
(35 - 50)^2 = 225
(74 - 50)^2 = 576
(42 - 50)^2 = 64
(62 - 50)^2 = 144
(34 - 50)^2 = 256
(39 - 50)^2 = 121
(52 - 50)^2 = 4
(77 - 50)^2 = 729
3. Calculate the sum of the squared differences:
1 + 196 + 225 + 576 + 64 + 144 + 256 + 121 + 4 + 729 = 2566
4. Divide the sum by (n-1) where n is the number of data points:
2566 / (10-1) = 2566 / 9 = 284.89
5. Take the square root of the result to find the standard deviation:
sqrt(284.89) ≈ 16.88
So, the standard deviation of the sample data set is approximately 16.88.
To find the standard deviation of a sample data set, follow these steps:
1. Find the mean: Add up all the numbers in the data set and divide the sum by the number of values. In this case, the sum of the values is 51+64+35+74+42+62+34+39+52+77 = 530. Since there are 10 values, the mean is 530/10 = 53.
2. Find the deviations: Subtract the mean from each individual value to get the deviations. The deviations for this data set are:
51 - 53 = -2
64 - 53 = 11
35 - 53 = -18
74 - 53 = 21
42 - 53 = -11
62 - 53 = 9
34 - 53 = -19
39 - 53 = -14
52 - 53 = -1
77 - 53 = 24
3. Square the deviations: Square each of the deviations from the previous step. The squared deviations are:
(-2)^2 = 4
11^2 = 121
(-18)^2 = 324
21^2 = 441
(-11)^2 = 121
9^2 = 81
(-19)^2 = 361
(-14)^2 = 196
(-1)^2 = 1
24^2 = 576
4. Find the mean of the squared deviations: Add up all the squared deviations and divide by the number of values. The sum of the squared deviations is 4+121+324+441+121+81+361+196+1+576 = 2226. Since there are 10 values, the mean squared deviation is 2226/10 = 222.6.
5. Find the square root of the mean squared deviation: Take the square root of the mean squared deviation to get the standard deviation. The square root of 222.6 is approximately 14.9.
Therefore, the standard deviation of the sample data set is 14.9.
To find the standard deviation of a sample data set, you can follow these steps:
1. Find the mean of the data set. The mean is calculated by adding up all the numbers and dividing the sum by the total number of data points. In this case, the sum of the numbers is:
51 + 64 + 35 + 74 + 42 + 62 + 34 + 39 + 52 + 77 = 530
Since there are 10 data points, the mean is 530/10 = 53.
2. Calculate the deviation of each data point from the mean. To do this, subtract the mean from each data point. The deviations for the given data set are:
51 - 53 = -2
64 - 53 = 11
35 - 53 = -18
74 - 53 = 21
42 - 53 = -11
62 - 53 = 9
34 - 53 = -19
39 - 53 = -14
52 - 53 = -1
77 - 53 = 24
3. Square each deviation. This is done to ensure that all deviations are positive and to emphasize larger deviations. The squared deviations for the given data set are:
(-2)^2 = 4
11^2 = 121
(-18)^2 = 324
21^2 = 441
(-11)^2 = 121
9^2 = 81
(-19)^2 = 361
(-14)^2 = 196
(-1)^2 = 1
24^2 = 576
4. Calculate the variance. The variance is the average of the squared deviations. To find the variance, add up all the squared deviations and divide by the total number of data points. In this case, the sum of the squared deviations is:
4 + 121 + 324 + 441 + 121 + 81 + 361 + 196 + 1 + 576 = 2226
Since there are 10 data points, the variance is 2226/10 = 222.6.
5. Finally, calculate the standard deviation. The standard deviation is the square root of the variance. In this case, the standard deviation is:
√222.6 ≈ 14.9
Therefore, the standard deviation of the given sample data set is approximately 14.9.