# Algebra II : Algebra II

## Example Questions

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### Example Question #1 : Mean, Standard Deviation, And Normal Distribution

Find the standard deviation of the following set of numbers:

Explanation:

To begin, we must remember the formula for standard deviation:

where is the standard deviation, N is the number of values in our set,   is the value we're currently evaluating in the summation, and is the mean of our set of numbers. All the summation part of the equation means is that we subtract our mean from each number in the set, square that value, and then add all of those values for each number together. So before we find the values that will be added together, we must first find our mean for the set of numbers:

Now we can determine the value for our summation for each number in the set:

Looking at our equation for standard variation, now all we must do is sum all of the values above, divide by N, and take the square root:

### Example Question #100 : Probability

The formula for standard deviation is the following:

.

Where,

,

Five students took a test and recieved the following grades: , , , , . What is the standard deviation of the test grades to the nearest decimal place?

Explanation:

The first step in solving for standrd deviation is to find the mean of the data set.

For this problem:

.

Now we can evaluate the summation:

Now we can rewrite the standard deviation expression:

There are 5 data points, so n = 5

### Example Question #1 : Mean, Standard Deviation, And Normal Distribution

In a normal distribution, what percentage is covered within one standard deviation?

95%

50%

99.7%

68%

34%

68%

Explanation:

By drawing a bell curve, the middle line is 50%. One standard deviation left and right of the middle line is 34% each. That means one standard deviation within is 68%

### Example Question #1 : Mean, Standard Deviation, And Normal Distribution

If the mean is  and the standard deviation is , which of the following is NOT within two standard deviations?

Explanation:

Two standard deviations means to double the standard deviation value.

This means the range is  to

Only  is not in the range.

### Example Question #3 : Mean, Standard Deviation, And Normal Distribution

Ibram was paid $5000 for editing a 2200-page encyclopedia. What was his rate earned per page? Possible Answers:$0.56

$2.27$0.44

$1.27 Correct answer:$2.27

Explanation:

This question is really just asking for the average dollar per page. This could be easily calculated:

However, you might also think of this as a rate problem:

D=RT

Using the information from the question, we can see that D=5000 and T=2200.

This comes out to what we solved above:

### Example Question #5221 : Algebra Ii

Standard Deviation can be calculated from what statistical term?

Quartile

Median

Range

Variance

Mode

Variance

Explanation:

Another way to calculate standard deviation is the square root of variance.

Variance is,

.

Taking the square root of this is how standard deviation can be calculated.

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