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
16.4 is a typical value for the data set. 3.0 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 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 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 between any pair of values in the data set.
To find the mean of the data set, we sum up all the values and divide by the total number of values:
(11 + 14 + 15 + 15 + 16 + 16 + 17 + 18 + 19 + 23) / 10 = 164 / 10 = 16.4
To find the standard deviation, we follow these steps:
1. Find the difference between each value and the mean, square it, and sum them all up:
(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 = 234.4
2. Divide by the number of values, subtract 1, and take the square root:
ā(234.4 / 9) ā 3.0
Therefore, the mean is 16.4 and the standard deviation is approximately 3.0.
Based on this information, 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.