Find the mean and standard deviation for the following data set. Round to the nearest tenth.
11, 14, 15, 15, 16, 16, 17, 18, 19, 23
Use the mean and standard deviation to select the correct statement.
(1 point)
Responses
16.6 is a typical value for the data set. 3.7 is the typical distance that a value in the data set is from 16.6.
16.6 is a typical value for the data set. 3.7 is the typical distance that a value in the data set is from 16.6.
16.4 is a typical value for the data set. 3.0 is the typical distance that a value in the data set is from 16.4.
16.4 is a typical value for the data set. 3.0 is the typical distance that a value in the data set is from 16.4.
16.6 is a typical value for the data set. 3.7 is the typical distance between any pair of values in the data set.
16.6 is a typical value for the data set. 3.7 is the typical distance between any pair of values in the data set.
16.4 is a typical value for the data set. 3.0 is the typical distance between any pair of values in the data set.
To find the mean, we add all the values together and divide by the number of values:
(11 + 14 + 15 + 15 + 16 + 16 + 17 + 18 + 19 + 23) / 10 = 164 / 10 = 16.4
To find the standard deviation, we first need to find the variance. We subtract the mean from each value, square the result, add up all the squared results, divide by the number of values, and then take the square root of that result:
Variance = [(11-16.4)^2 + (14-16.4)^2 + (15-16.4)^2 + (15-16.4)^2 + (16-16.4)^2 + (16-16.4)^2 + (17-16.4)^2 + (18-16.4)^2 + (19-16.4)^2 + (23-16.4)^2] / 10
Variance = [27.04 + 6.76 + 2.56 + 2.56 + 0.36 + 0.36 + 0.36 + 3.24 + 6.76 + 41.6] / 10
Variance = 91.3 / 10 = 9.13
Standard Deviation = sqrt(9.13) = 3.0
Therefore, the correct statement is:
16.4 is a typical value for the data set. 3.0 is the typical distance that a value in the data set is from 16.4.
is this right?
I apologize for the error in my previous response. Let me correct the calculations:
Mean:
(11 + 14 + 15 + 15 + 16 + 16 + 17 + 18 + 19 + 23) / 10 = 164 / 10 = 16.4
Variance:
Calculate the squared difference between each value and the mean, sum them up, and divide by the number of values to get the variance:
Variance = [(11-16.4)^2 + (14-16.4)^2 + (15-16.4)^2 + (15-16.4)^2 + (16-16.4)^2 + (16-16.4)^2 + (17-16.4)^2 + (18-16.4)^2 + (19-16.4)^2 + (23-16.4)^2] / 10
Variance = [27.04 + 6.76 + 2.56 + 2.56 + 0.36 + 0.36 + 0.36 + 3.24 + 6.76 + 41.6] / 10
Variance = 91 / 10 = 9.1
Standard Deviation:
Standard Deviation = sqrt(9.1) = 3.0
Therefore, the correct statement is:
16.4 is a typical value for the data set. 3.0 is the typical distance that a value in the data set is from 16.4.