# Summarizing presenting data

For example: Tabulation of data on the population of the world classified by three or more characteristics like religion, sex and literacy, etc. Presenting data in Graphs Tabulation that help us to organize the collected data in a meaningful fashion; however, this way of presenting statistical data does not always prove to be interesting to a layman.

### Why is it necessary to summarize data

However, calculated range is less informative than interval values and therefore not recommended. Assignment rules are determined by four distinct scales of measurement: nominal, ordinal, interval and ratio 2. Frequency distribution is simply a table in which the data are grouped into classes on the basis of common characteristics and the numbers of cases which fall in each class are recorded. Corresponding author: Sangseok Lee, M. The median is the 50th percentile, the third quartile is the 75th percentile and the maximum is the th percentile i. Mean also called the average ii. Numeric data are presented by arithmetic mean only if data fit to normal distribution. Generally, error bar plot consists of the line crossed with three marks. References 1. While categorical data might be presented by description of categories or numbers assigned to them, numerical data are always presented by numbers 3. The best graphical summary for dichotomous and categorical variables is a bar chart and the best graphical summary for an ordinal variable is a histogram. Three common measures of central tendency are the arithmetic mean mean , median, and mode. Bimodal and multimodal distributions require further analysis of data characteristics that are beyond this article. Scientific hypothesis and type of the study define variables that have to be measured, producing data.

On the other hand, i. For data not normally distributed, median with data range minimum to maximum, interquartile range or percentile range and mode are used. In the example, it is clearly visible that empirical distribution fits to normal.

Variables are dichotomous, ordinal, categorical or continuous. Median also called the second quartile, the middle quartile or the 50th percentile iii.

Dispersion Dispersion refers to estimates of the spread of data around central value. Empirical distribution denotes data distribution from the research sample, while theoretical distribution presents mathematical function.

### Importance of data presentation

Numerical data Original raw data collected during the research are usually not presented in scientific papers, with the exception of the cases when only few measurements occur e. So, we have look another statistical tools that will aid our decision. Corresponding author: Sangseok Lee, M. We use to draw multiple bar charts if the total of different phenomena is meaningless. With more subjects included in the research, numerical data must be summarized by descriptive statistics. Box-whisker plots provide a very useful and informative summary for continuous variables. It consists of vertical rectangles aligned on x-axis, where width of rectangles relates to value ranges for a variable and height is proportional to frequency of values presented. A specific quantile or percentile is a value in the data set that holds a specific percentage of the values at or below it. While categorical data might be presented by description of categories or numbers assigned to them, numerical data are always presented by numbers 3. Both bar charts and histograms can be designed to display frequencies or relative frequencies, with the latter being the more popular display. Numeric data are presented by arithmetic mean only if data fit to normal distribution. For example: Tabulation of data on the population of the world classified by one characteristic like religion is an example of a simple tabulation. The best numerical summaries for continuous variables include the mean and standard deviation or the median and interquartile range, depending on whether or not there are outliers in the distribution.

Statistics and Econometrics 2nd ed.

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