2.1:
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Recall that data are broadly classified into quantitative data and qualitative data.
Quantitative data represent the measurements or counts of numerical values, such as varying heights of students in a class.
Conversely, qualitative data, also known as categorical data, represent non-numerical variables such as the different colors of hair.
For efficient statistical analysis, these unorganized, large data sets are summarized and represented numerically in tabular form or visually in graphical form.
For example, the temperature changes measured during a day can be summarized in the form of a table.
These data can also be represented graphically. Here, the time is given along the horizontal axis, and the temperature is displayed along the vertical axis.
The points in the graph are joined to form the pattern providing a visual understanding of how the daytime temperature changes with time.
The graph also identifies the outliers from the other data values that indicate extreme temperatures observed in the day.
2.1:
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Data are individual items of information obtained from a population or sample. Data may be classified as qualitative (categorical), quantitative continuous, or quantitative discrete. Because it is not practical to measure the entire population in a study, researchers use samples to represent the population. A random sample is a representative group from the population chosen by using a method that gives each individual in the population an equal chance of being included in the sample. Random sampling methods include simple random sampling, stratified sampling, cluster sampling, and systematic sampling. Convenience sampling is a nonrandom method of choosing a sample that often produces biased data.
Once the data is collected, it can be described and presented in many different formats. For example, suppose a person is interested in buying a house in a particular area. Not having much information about the house prices, the buyer might ask the real estate agent to give a sample data set of prices. Reading through all the prices in the sample can be a little overwhelming. A better way might be to look at the median price and the variation in the prices. The median and variation are just two ways that one can use to describe data. The agent might also provide a graph of the data, which could be a more convenient way to understand the house prices.
The area of statistics that details the numerical and graphical ways to describe and display the sample data is called "Descriptive Statistics." A statistical graph is a tool that helps one learn about the shape or distribution of a sample or a population. A graph can be a more effective way of presenting data than a stack of numbers because it is easy to observe data clusters and identify positions where there are only a few data values. Newspapers and the Internet use graphs to show trends and to enable readers to compare facts and figures quickly. Some types of graphs that are used to summarize and organize data are the dot plot, the bar graph, the histogram, the stem-and-leaf plot, the frequency polygon (a type of broken line graph), the pie chart, and the box plot.