Statistics and Probability - Algebra

The first step in calculating standard deviation, or , is to calculate the mean for your sample, or . Remember, to calculate mean, sum your data values and divide by the count, or number of values you have.

Next, we must find the difference between each recorded value and the mean. At the same time, we will square these differences, so it does not matter whether you subtract the mean from the value or vice versa.

We use to represent this, but all it really means is that you square the difference between each value , where is the position of the value you're working with, and the mean, . Then we sum all those differences up (the part that goes , where is your count. just refers to the fact that you start at the first value, so you include them all.)

It's probably easier to do than to think about at first, so let's dive in!

Now, add the deviations, and we're nearly there!

Next, we must divide this number by our :

This number, 43.35, is our variance, or . Since standard variation is , you may have guessed what we must do next. We must take the square root of the summed squares of deviations.

So, our standard deviation is 7 million dollars (remembering to round to the nearest million, per our instructions.)

To find the mode, you must find the most frequent number. Since all of the numbers are never repeated, there is no mode. Thus, our answer is "none".

The mean is the average. The mean can be found by taking the sum of all the numbers (150 + 88 + 141 + 110 + 79 = 568) and then dividing the sum by how many numbers there are (5).

Our answer is 113 3/5, which can be written as a decimal.

Therefore 113 3/5 is equivalent to 113.6, which is our answer.

The outcomes from rolling a die are {1,2,3,4,5,6}.

The mean is (1+2+3+4+5+6)/6 = 3.5.

Rolling the die six million times simply suggests that each number will appear approximately one million times. Since each number is rolled with equal probability, it doesn't matter how many times you perform the experiment; the answer will always remain the same.

To solve, simply use the formula for the range. Thus,

To solve, you must sum up the numbers and divide by the quantity. Thus,

To find the range, simply subtract the smallest number from the largest. Thus,

List the numbers in ascending order: 2,3,4,4,6,8,9,11,13,15,16

The median is the middle number, or 8.

To solve, you must sum up the numbers and divide by the quantity. Thus,

The mean is the average. The mean can be found by taking the sum of all the numbers (150 + 88 + 141 + 110 + 79 = 568) and then dividing the sum by how many numbers there are (5).

Our answer is 113 3/5, which can be written as a decimal.

Therefore 113 3/5 is equivalent to 113.6, which is our answer.

The outcomes from rolling a die are {1,2,3,4,5,6}.

The mean is (1+2+3+4+5+6)/6 = 3.5.

Rolling the die six million times simply suggests that each number will appear approximately one million times. Since each number is rolled with equal probability, it doesn't matter how many times you perform the experiment; the answer will always remain the same.

List the numbers in ascending order: 2,3,4,4,6,8,9,11,13,15,16

The median is the middle number, or 8.

To solve, you must sum up the numbers and divide by the quantity. Thus,

Rearrange the numbers into increasing order.

The number in the center of the set is the median: 243

Add every number together and divide by the total number of numbers in the set (9) to get the following.

The mode of any set of numbers is the number in the set that appears most often. In order to find the mode, it is easier to put the numbers in the set in order from least to greatest. The set we were given is

.

In order from least to greatest, the set is:

Next, we will look through our sequenced set to see if any numbers appear more than one time. In this case, there are several numbers that appear more than once: , , and all appear more than once in our set.

Since we have multiple numbers that appear more than once, now we will look to see how many times each of these numbers appears in the set.

- appears two times

- appears two times

- appears four times

Since appears more times in the set than any other number, is the mode of our set.

The mode of the set is the most repeated number. In this case is the mode because it is in the set 3 times.

Start by putting the numbers in ascending order:

{1, 2, 3, 4, 5, 7, 8, 9, 13, 14, 15}

Once you do that you make your way to the middle number (as that is what the median is) which you find to be .

The mode of the set is the most repeated number. In this case is the mode because it is in the set 3 times.

The mode of the set is the most repeated number. In this case is the mode because it is in the set twice.