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# Statistics Tutorial

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❶Watt [1] Just a few of the many quotes about the use, misuse [2] and fallibility of statistics. Thanks to all authors for creating a page that has been read , times.

Find some software that will help you manipulate a given set of values. Insert the values that are displayed in the image. How that is done will depend on your software. Chances are, it will have a grid like appearance. Basically, you are asking the program to come up with in this instance , the mean 5. Note that the software doesn't have to lay the information out in a straight line to come up with the answer.

Understand what it indicates. These numbers indicate that if this was a room full of children 24 of them , that the average age the mean is 5. The mode of six would indicate that there are more six year old children than any other age in the room. The median is indicated by taking the set of 1,1,1,2,3,4,4,5,5,5,6,6,6,6,6,7,7,7,7,8,8,8,9,9 and counting 12 in from each side. In this instance, it puts you straight in the middle of the sixes and therefore the median is six. Decide what you are going to use the statistics for.

You can use stats to tell about percentage of games won, percentage of games won versus another team, etc.

Go to your newspaper for the information or your team's web page or sports web page. Calculate the win percentage. Divide the number of wins by the total number of games. Calculate the loss percentage.

Divide the number of losses by the total number of games. Minnesota Vikings have a current tally of 1 win and 3 losses out of 4 games. Washington Redskins with 3 wins and 2 losses. This would, seemingly, be comparing apples and oranges, because of the different number of games played. With this information, you can tell that the Redskins are easily outplaying the Vikings at this juncture. Pick a site with statistical information about various cities.

Determine the median income of your county. Mode [3] - the most frequent occurrence of a variable in a set or sampling of variables. The mode of the sample [1, 3, 6, 6, 6, 6, 7, 7, 12, 12, 17] is 6. Median [3] - Relates to, or constitutes the middle value of a distribution. Find the Median of: Standard Deviation [3] - A measure of the spread of the values in a given set.

The higher the standard deviation, the less numbers in the set tend to cluster near the mean. Distribution [3] - Statistical data arranged to show the frequency with which the possible values of a variable occur. Bell-shaped curve [3] - The curve representing a continuous frequency distribution with a shape having the overall curvature of the vertical cross section of a bell; usually applied to the normal distribution.

Probability [3] - The measure of how likely something is going to occur e. Outliers [7] - are the numbers that can feasibly throw off the statistics because they are 'one offs'. By that, they are atypical of the rest of the data. Statistics can help understand a phenomenon by confirming or rejecting a hypothesis. It is vital to how we acquire knowledge to most scientific theories. You don't need to be a scientist though; anyone wanting to learn about how researchers can get help from statistics may want to read this statistics tutorial for the scientific method.

This section of the statistics tutorial is about understanding how data is acquired and used. The results of a science investigation often contain much more data or information than the researcher needs. This data-material, or information, is called raw data. To be able to analyze the data sensibly, the raw data is processed into " output data ". There are many methods to process the data, but basically the scientist organizes and summarizes the raw data into a more sensible chunk of data.

Any type of organized information may be called a " data set ". Then, researchers may apply different statistical methods to analyze and understand the data better and more accurately. Depending on the research, the scientist may also want to use statistics descriptively or for exploratory research. What is great about raw data is that you can go back and check things if you suspect something different is going on than you originally thought. This happens after you have analyzed the meaning of the results.

The raw data can give you ideas for new hypotheses, since you get a better view of what is going on. You can also control the variables which might influence the conclusion e. In statistics, a parameter is any numerical quantity that characterizes a given population or some aspect of it. This part of the statistics tutorial will help you understand distribution, central tendency and how it relates to data sets. Much data from the real world is normal distributed , that is, a frequency curve, or a frequency distribution , which has the most frequent number near the middle.

Many experiments rely on assumptions of a normal distribution. This is a reason why researchers very often measure the central tendency in statistical research, such as the mean arithmetic mean or geometric mean , median or mode. The central tendency may give a fairly good idea about the nature of the data mean, median and mode shows the "middle value" , especially when combined with measurements on how the data is distributed. Scientists normally calculate the standard deviation to measure how the data is distributed.

But there are various methods to measure how data is distributed: To create the graph of the normal distribution for something, you'll normally use the arithmetic mean of a " big enough sample " and you will have to calculate the standard deviation.

However, the sampling distribution will not be normally distributed if the distribution is skewed naturally or has outliers often rare outcomes or measurement errors messing up the data. One example of a distribution which is not normally distributed is the F-distribution , which is skewed to the right.

So, often researchers double check that their results are normally distributed using range, median and mode. How do we know whether a hypothesis is correct or not? Why use statistics to determine this?

Using statistics in research involves a lot more than make use of statistical formulas or getting to know statistical software. Making use of statistics in research basically involves. Statistics in research is not just about formulas and calculation. Many wrong conclusions have been conducted from not understanding basic statistical concepts. Statistics inference helps us to draw conclusions from samples of a population. When conducting experiments , a critical part is to test hypotheses against each other.

Thus, it is an important part of the statistics tutorial for the scientific method. Hypothesis testing is conducted by formulating an alternative hypothesis which is tested against the null hypothesis , the common view.

The hypotheses are tested statistically against each other. The researcher can work out a confidence interval , which defines the limits when you will regard a result as supporting the null hypothesis and when the alternative research hypothesis is supported. This means that not all differences between the experimental group and the control group can be accepted as supporting the alternative hypothesis - the result need to differ significantly statistically for the researcher to accept the alternative hypothesis.

This is done using a significance test another article. Caution though, data dredging , data snooping or fishing for data without later testing your hypothesis in a controlled experiment may lead you to conclude on cause and effect even though there is no relationship to the truth. Depending on the hypothesis, you will have to choose between one-tailed and two tailed tests. Sometimes the control group is replaced with experimental probability - often if the research treats a phenomenon which is ethically problematic , economically too costly or overly time-consuming, then the true experimental design is replaced by a quasi-experimental approach.

Often there is a publication bias when the researcher finds the alternative hypothesis correct, rather than having a "null result", concluding that the null hypothesis provides the best explanation.

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