Question

A six-sided die has one 1, two 3 's, two 4's and one 6 . The mean and the standard deviation of the score on this die are 3.5 and 1.5 , respectively. What are the mean and the standard deviation function.

Answer 1

The mean function calculates the average of a set of numbers, and the standard deviation function measures how spread out the data is.

Step-by-step explanation:

Mean Function:

The mean function calculates the average of a set of numbers. In this case, we have a six-sided die with values 1, 3, 3, 4, 4, and 6. To find the mean, we add up all the numbers and divide by the total number of values:

(1 + 3 + 3 + 4 + 4 + 6) / 6 = 3.5

Standard Deviation Function:

The standard deviation function measures how spread out the data is. To find the standard deviation, we follow these steps:

1. Calculate the mean (in this case, 3.5).
2. Subtract the mean from each value, square the result, and sum up all the squared values.
3. Divide the sum by the total number of values (in this case, 6).
4. Take the square root of the result.

This gives us the standard deviation:

sqrt(((1-3.5)^2 + (3-3.5)^2 + (3-3.5)^2 + (4-3.5)^2 + (4-3.5)^2 + (6-3.5)^2)/6) = 1.5