Basic Statistics - Math

A normal distribution is one in which the values are evenly distributed both above and below the mean. A population has a precisely normal distribution if the mean, mode, and median are all equal. For the population of 3,4,5,5,5,6,7, the mean, mode, and median are all 5.

In a normal distribution, the number of values within one positive standard deviation of the mean is equal to the number of values within one negative standard deviation of the mean. The reason for this is that the values below the population mean exactly parallel the values above the mean.

A -score indicates whether a particular value is typical for a population or data set. The closer the -score is to 0, the closer the value is to the mean of the population and the more typical it is. The -score is calculated by subtracting the mean of a population from the particular value in question, then dividing the result by the population's standard deviation.

The -score indicates how close a particular value is to the population mean and whether the value is above or below the mean. A positive -score is always above the mean and a negative -score is always below it. Here, we know the value is below the mean because we have a negative -score.

A Z-score indicates whether a particular value is typical for a population or data set. The closer the Z-score is to 0, the closer the value is to the mean of the population and the more typical it is. The Z-score is calculated by subtracting the mean of a population from the particular value in question, then dividing the result by the population's standard deviation.

Standard deviation is essentially the average distance from the mean of a group of numbers. There are a number of steps in computing standard deviation, but the steps are not too complicated if you take them one at a time. First, find the mean of the values. Second, subtract the mean from the first value and square the result. Do this for all remaining values. Third, add these results together. Fourth, divide this value by the number of values. Finally, find the square root of the result.

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There are five steps to finding the standard deviation of a group of values. First, find the mean of the values. Second, subtract the mean from the first value and square the result. Do this for all remaining values. Third, add these results together. Fourth, divide this value by the number of values minus one. Finally, find the square root of the result.

Probability of drawing first ace of hearts:

Probability of drawing second ace of hearts:

Multiply both probabilities by each other:

Start with 52 cards, probability of drawing first king:

Now you have 51 cards. Probability of drawing second king:

Now you have 50 cards. Probability of drawing third king:

Multiply all probabilities:

There are cards in a standard deck: cards in suits. There are face cards (King, Queen, Jack) in each suit, so there are total face cards.

Thus the probability of choosing a single face card is or .

In a standard deck of cards:

A normal distribution is one in which the values are evenly distributed both above and below the mean. A population has a precisely normal distribution if the mean, mode, and median are all equal. For the population of 3,4,5,5,5,6,7, the mean, mode, and median are all 5.

In a normal distribution, the number of values within one positive standard deviation of the mean is equal to the number of values within one negative standard deviation of the mean. The reason for this is that the values below the population mean exactly parallel the values above the mean.

Variation measures the average difference between values within a group. The process is not complicated but there are four steps that can take time. First, find the mean of the values. Second, subtract the mean from the first value and square the result. Do this for all remaining values. Third, add these results together. Fourth, divide this value by the number of values in the group minus one (in this case, there are four days).

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Note that to find the standard deviation, we would simply take one additional step of finding the square root of the variance.

This question illustrates the close relationship between the concepts of variance and standard deviation. We can find variance even though we do not know the values in the population if we know the standard deviation. Simply square the standard deviation to find the variance.

There are four steps to finding the variance of values within a group. First, find the mean of the values. Second, subtract the mean from the first value and square the result. Do this for all remaining values. Third, add these results together. Fourth, divide the result by the number of values in the group minus one (in this case, there are seven days, so you must divide by six).

The mean is calculated by adding all the values in a group together, then dividing the sum by the total number in the group. In this case, six homes are for sale. The six home values are added together , then that value is divided by six.

The median is determined by ordering the values in the group from least to greatest: 155, 214, 305, 315, 535, 720. The value directly in the middle is the median. For instance, if there are five numbers, the third is the median. Here, we have an even number of values so there is no value directly in the middle. To find the median when there is no middle-most value, find the average of the two middle values. The mean is determined by adding the two values and dividing by two (the number in the group):

The mean is calculated by adding the values from the four days together, then dividing the sum by the total number of values. In this case, four values must be added:

The mode is the number that appears most frequently in a series of numbers. First, organize the numbers in order from least to greatest: 4, 4, 7, 8, 17, 17, 17, 25, 26, 35. The number 17 appears three times, more than any other number.