Final answer:
To calculate the standard deviation of the given numbers, substitute the values of a into the formula and calculate the standard deviation for each case.
Step-by-step explanation:
To calculate the standard deviation of a set of numbers, follow these steps:
- Find the mean of the numbers.
- Subtract the mean from each number to get the deviation.
- Square each deviation.
- Find the mean of the squared deviations.
- Take the square root of the mean of the squared deviations to get the standard deviation.
In this question, we have the four numbers 140 - a. To calculate the standard deviation, we need the value of a. Let's substitute the different options for a into the formula and calculate the standard deviation in each case.
A) a = 145:
140 - 145 = -5
Standard Deviation = √((-5² + 0² + 5² + 10²)/4) = √(100/4) = √25 = 5
B) a = 140:
140 - 140 = 0
Standard Deviation = √((0² + 0² + 5² + 10²)/4) = √(125/4) = √31.25 ≈ 5.59
C) a = 135:
140 - 135 = 5
Standard Deviation = √((5² + 0² + 5² + 10²)/4) = √(150/4) = √37.5 ≈ 6.12
D) a = 130:
140 - 130 = 10
Standard Deviation = √((10² + 0² + 5² + 10²)/4) = √(225/4) = √56.25 ≈ 7.50
Therefore, the standard deviation for each value of a is:
A) a = 145: 5
B) a = 140: 5.59
C) a = 135: 6.12
D) a = 130: 7.50