# Interpretation Of Mean And Standard Deviation In Descriptive Statistics Pdf

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*When analysing data, such as the marks achieved by students for a piece of coursework, it is possible to use both descriptive and inferential statistics in your analysis of their marks. Typically, in most research conducted on groups of people, you will use both descriptive and inferential statistics to analyse your results and draw conclusions.*

- SPSS Tutorials: Descriptive Stats for Many Numeric Variables (Descriptives)
- Descriptive and Inferential Statistics
- Understanding Descriptive Statistics

*Sign in. Statistics is a branch of mathematics that deals with collecting, interpreting, organization and interpretation of data.*

The results of your statistical analyses help you to understand the outcome of your study, e. Statistics are tools of science, not an end unto themselves. Statistics should be used to substantiate your findings and help you to say objectively when you have significant results. Therefore, when reporting the statistical outcomes relevant to your study, subordinate them to the actual biological results.

## SPSS Tutorials: Descriptive Stats for Many Numeric Variables (Descriptives)

The results of your statistical analyses help you to understand the outcome of your study, e. Statistics are tools of science, not an end unto themselves.

Statistics should be used to substantiate your findings and help you to say objectively when you have significant results. Therefore, when reporting the statistical outcomes relevant to your study, subordinate them to the actual biological results. Reporting Descriptive Summary Statistics. Means : Always report the mean average value along with a measure of variablility standard deviation s or standard error of the mean.

Two common ways to express the mean and variability are shown below:. This style necessitates specifically saying in the Methods what measure of variability is reported with the mean.

If the summary statistics are presented in graphical form a Figure , you can simply report the result in the text without verbalizing the summary values:. Frequencies: Frequency data should be summarized in the text with appropriate measures such as percents, proportions, or ratios.

Reporting Results of Inferential Hypothesis Tests. In this example, the key result is shown in blue and the statistical result , which substantiates the finding, is in red. This wastes precious words economy!! Summarizing Statistical Test Outcomes in Figures. If the results shown in a figure have been tested with an inferential test, it is appropriate to summarize the outcome of the test in the graph so that your reader can quickly grasp the significance of the findings. It is imperative that you include information in your Materials and Methods, or in the figure legend, to explain how to interpret whatever system of coding you use.

Several common methods for summarizing statistical outcomes are shown below. Comparison of the means of 2 or more groups is usually depicted in a bar graph of the means and associated error bars. For two groups , the larger mean may have asterisks centered over the error bar to indicate the relative level of the p-value. In all cases, the p-value should be reported as well in the figure legend. The asterisk may also be used with tabular results as shown below.

Note how the author has used a footnote to define the p-values that correspond to the number of asterisks. Courtesy of Shelley Ball. For three or more groups there are two systems typically used: lines or letters. The system you use depends on how complicated it is to summarize the result. The first example below shows a comparison of three means. The line spanning two adjacent bars indicates that they are not significantly different based on a multiple comparisons test , and because the line does not include the pH 2 mean, it indicates that the pH 2 mean is significantly different from both the pH 5.

Note that information about how to interpret the coding system line or letters is included in the figure legend. When lines cannot easily be drawn to summarize the result, the most common alternative is to use capital letters placed over the error bars. Letters shared in common between or among the groups would indicate no significant difference. Example: Summarizing Correlation and Regression Analyses.

For relationship data X,Y plots on which a correlation or regression analysis has been performed, it is customary to report the salient test statistics e. If a regression is done, the best-fit line should be plotted and the equation of the line also provided in the body of the graph. Top of Page Reporting Descriptive Summary Statistics Means : Always report the mean average value along with a measure of variablility standard deviation s or standard error of the mean.

If the summary statistics are presented in graphical form a Figure , you can simply report the result in the text without verbalizing the summary values: "Mean total length of brown trout in Sebago Lake increased by 3. Summarizing Statistical Test Outcomes in Figures If the results shown in a figure have been tested with an inferential test, it is appropriate to summarize the outcome of the test in the graph so that your reader can quickly grasp the significance of the findings.

Examples: Comparing groups t-tests, ANOVA, etc Comparison of the means of 2 or more groups is usually depicted in a bar graph of the means and associated error bars. In all cases, the p-value should be reported as well in the figure legend The asterisk may also be used with tabular results as shown below.

Example: Summarizing Correlation and Regression Analyses For relationship data X,Y plots on which a correlation or regression analysis has been performed, it is customary to report the salient test statistics e.

## Descriptive and Inferential Statistics

In statistics, the range is a measure of the total spread of values in a quantitative dataset. Unlike other more popular measures of dispersion, the range actually measures total dispersion between the smallest and largest values rather than relative dispersion around a measure of central tendency. The range is interpreted as t he overall dispersion of values in a dataset or, more literally, as the difference between the largest and the smallest value in a dataset. The range is measured in the same units as the variable of reference and, thus, has a direct interpretation as such. This can be useful when comparing similar variables but of little use when comparing variables measured in different units. However, because the information the range provides is rather limited, it is seldom used in statistical analyses.

Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample and the measures. Together with simple graphics analysis, they form the basis of virtually every quantitative analysis of data. Descriptive statistics are typically distinguished from inferential statistics. With descriptive statistics you are simply describing what is or what the data shows. With inferential statistics, you are trying to reach conclusions that extend beyond the immediate data alone. For instance, we use inferential statistics to try to infer from the sample data what the population might think.

A boxplot provides a graphical summary of the distribution of a sample. The boxplot shows the shape, central tendency, and variability of the data. Use a boxplot to examine the spread of the data and to identify any potential outliers. Boxplots are best when the sample size is greater than Examine the shape of your data to determine whether your data appear to be skewed.

mean and median are very different, most likely there are outliers in the data or the distribution is The standard deviation is one of the most popular measures of dispersion. of descriptive statistics, errors in interpretations are very likely.

## Understanding Descriptive Statistics

The inadequate use of basic statistics is the main responsible for scientific article misinterpretation. The purpose of this review article was to review some basic statistical topics to alert authors and readers about the importance of basic statistics proper reporting. Medical research is not free from the risk of false positive and false negative results due to the choice of statistical tests and presence of small sample sizes.

Use N to know how many observations are in your sample. Minitab does not include missing values in this count. You should collect a medium to large sample of data. Samples that have at least 20 observations are often adequate to represent the distribution of your data.

*Our tutorials reference a dataset called "sample" in many examples. If you'd like to download the sample dataset to work through the examples, choose one of the files below:.*

#### Step 1: Describe the size of your sample

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Ordinal. Median,. Percentile. Interval of. Variation. Spearman,. Kendall. Interval. Mean, Variance,. Range. Standard. Deviation. Pearson. Ratio. Geometric mean.

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