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### How to Identify Skew and Symmetry in a Statistical Histogram

Sometimes the mean versus median debate can get quite interesting. Especially when you look at the skewness and symmetry of your statistical data in a histogram. [more…]

### How to Interpret Standard Deviation in a Statistical Data Set

Standard deviation can be difficult to interpret as a single number on its own. Basically, a small standard deviation means that the values in a statistical data set are close to the mean of the data set [more…]

### Why Standard Deviation Is an Important Statistic

The standard deviation is a commonly used statistic, but it doesn’t often get the attention it deserves. Although the mean and median are out there in common sight in the everyday media, you rarely see [more…]

### Applying the Empirical Rule (68-95-99.7) to a Statistical Data Set

The *Empirical Rule* (68-95-99.7) says that if the population of a statistical data set has a normal distribution (where the data are in the shape of a bell curve) with population mean [more…]

### How to Calculate Percentiles in Statistics

If all you are interested in is where you stand compared to the rest of the herd, you need a statistic that reports *relative standing*, and that statistic is called a percentile. The [more…]

### What Percentile Tells You about a Statistical Value

Percentiles report the relative standing of a particular value within a statistical data set. If that’s what you’re most interested in, the actual mean and standard deviation of the data set are not important [more…]

### How to Gather a Five-Number Summary from a Statistical Sample

If your data create a histogram that is not bell-shaped, you can use a set of statistics that is based on percentiles to describe the big picture of the data. Called the five-number summary, this method [more…]

### How the Central Limit Theorem Is Used in Statistics

The normal distribution is used to help measure the accuracy of many statistics, including the sample mean, using an important result called the *Central Limit Theorem.* [more…]

### How Treatment Groups, Control Groups, Placebos, and Blind Experiments Are Used in Statistics

Statistical studies often involve several kinds of experiments: treatment groups, control groups, placebos, and blind and double-blind tests. An *experiment* [more…]

### How to Interpret the Margin of Error in Statistics

You’ve probably heard or seen results like this: “This statistical survey had a margin of error of plus or minus 3 percentage points.” What does this mean? Most surveys are based on information collected [more…]

### What a Boxplot Can Tell You about a Statistical Data Set

A boxplot can give you information regarding the shape, variability, and center (or median) of a statistical data set. It is particularly useful for displaying skewed data. [more…]

### What a Time Chart Can Tell You about a Statistical Data Set

A *time chart* (also called a *line graph*) is a statistical display used to examine trends in data over time (also known as time series data). Time charts show time on the [more…]

### How a Time Chart Can Misrepresent Statistical Data

When you create a statistical time chart, you have to evaluate the units of the numbers being plotted. For example, it's misleading to chart the *number* [more…]

### Simplifying Excess Statistical Data in a Time Chart

If a time chart includes too much statistical data, the result can be so complex that it makes it impossible to interpret the data. By reducing the amount of data, it is easier to see patterns emerge from [more…]

### How to Define a Random Statistical Variable

In statistics, a *random variable* is a characteristic, measurement, or count that changes randomly according to a certain set or pattern. Random variables are usually denoted with capital letters such as [more…]

### Statistics: Discrete and Continuous Random Variables

In statistics, numerical random variables represent counts and measurements. They come in two different flavors: discrete and continuous, depending on the type of outcomes that are possible: [more…]

### How to Find Right-Tail Values and Confidence Intervals Using the *t*-Table

You can use a *t*-table to find right-tail probabilities and *p*-values for hypothesis tests and to find *t**-values (critical values) for a confidence interval involving [more…]

### How to Identify the Notation for the Mean and Variance of a Discrete Random Variable

Two of the most important terms in statistics are mean and variance, and so you need to be able to identify their notations when working with discrete random variables. [more…]

### How to Identify a Random Binomial Variable

The most well-known and loved discrete random variable in statistics is the binomial. *Binomial* means *two names*and is associated with situations involving two outcomes; for example yes/no, or success/failure [more…]

### How to Find the Mean, Variance, and Standard Deviation of a Binomial Distribution

Because the binomial distribution is so commonly used, statisticians went ahead and did all the grunt work to figure out nice, easy formulas for finding its mean, variance, and standard deviation. The [more…]

### Understanding the Statistical Properties of the Normal Distribution

When you understand the properties of the normal distribution, you'll find it easier to interpret statistical data. A continuous random variable *X* has a normal distribution if its values fall into a smooth [more…]

### Using the *Z*-Distribution to Find the Standard Deviation in a Statistical Sample

One very special member of the normal distribution family is called the standard normal distribution, or *Z*-distribution. In statistics, the *Z-distribution* [more…]

### How to Change an *X*-Value to a *Z*-Value

If you have a statistical sample with a normal distribution, you can plug an *x*-value for this distribution into a special equation to find its *z*-value. The [more…]

### How to Find Probabilities for *Z* with the *Z*-Table

You can use the *Z*-table to find a full set of "less-than" probabilities for a wide range of *z*-values. To use the *Z-*table to find probabilities for a statistical sample with a standard normal [more…]

### How to Find Statistical Probabilities in a Normal Distribution

If your statistical sample has a normal distribution (*X*), then you can use the *Z*-table to find the probability that something will occur within a defined set of parameters. For example, you could look [more…]