STATISTICS What is statistics? Statistics is the art and science of learning from data. Statistics is made up of research studies and the analysis of the information (data) produced by those studies. The first part of the statistical method is design-planning a study, such as how to obtain relevant data. The design often is done by taking a relevant sample from a population of all of the subjects (usually people) of interest. After all of the data has been gathered, there are two kinds of statistical analyses: 1) Descriptive statistics summarize the sample data with numbers and graphs 2)Inferential statistics make decisions and predictions about the entire population, based on the information in the sample data. With random sampling, each subject in the population has the same chance of being in the sample. This is desirable, since then the sample tends to be a good reflection of the population. Randomization is also important to good experimental design. The measurements we make of a characteristic vary from individual to individual. Likewise, results of descriptive and inferential statistics vary, depending on the sample chosen. The calculations for data analysis are easy. Computer software such as Excel are used in this course. The data are organized in a data file

Descriptive Statistics Our first task, using Excel to arrive at our solution, is to design a chart so that the taxpayers attending the forthcoming meeting will know what happened to their tax dollars. The total amount of tax dollars collected is 2 million dollars. Expenditures made were: $440,000 for schools, $1,160,000 for roads, $320,000 for administration, and $80,000 for supplies. We will want to enter this data into Excel and create a pie chart. On a new worksheet, enter in cells A1:A4 Schools, Roads, Admin, and Supplies. Make sure all the data fits in one column (you may widen the column). Enter into cells B1:B4 the expenditure amounts. Highlight cells A1:B4 by dragging. From the Insert tab, in the Charts group, select Pie. Several sub-types are displayed. Select the 1st one in the upper-left corner. From the Design tab, in the Chart layouts group, click on Layout 1. In your Chart, click on Chart Title, and key in Tax Dollar Expenditures. Click Enter. The title is displayed in the chart. By clicking and holding the mouse button, position the chart next to your data. Go to the Office button, and save your chart as pie-chart using Save As.

We are now changing our chart to a horizontal bar chart We are now changing our chart to a horizontal bar chart. Click anyplace inside the chart. The handles will show on the box. Right-click. A text box will appear. Select Change Chart type. Select Bar. Select the 1st Bar type, called Clustered Bar. Click OK. From the Layout tab, in the Labels Group, select Data Labels. At the bottom of the pull down list, choose More Data Label Options. Under Label Options, deselect the checkmark next to Category Name. Click Close. From the Layout tab, in the Axis group, choose Gridlines. Choose Primary Vertical Gridlines. From the pull-down list choose None-Do not display Vertical Gridlines. The data now shows as a horizontal bar chart.

Now we may change our horizontal Bar chart to a vertical Bar chart Now we may change our horizontal Bar chart to a vertical Bar chart. Make sure the handles show on the chart box. Right-click. Select Change Chart Type. Select Column. Choose the 1st chart, Clustered Column. Click OK. The data now shows in the form of a vertical Bar chart.

Example 2 Given the following Frequency Distribution, portray the imports in the form of a Histogram. Imports ($ Millions) Number of suppliers $ 2 up to $5 6 5 up to 8 13 8 up to 11 20 11 up to 14 10 14 up to 17 1 First determine the midpoint of each range in the import column, then use that midpoint for the x- values. 3.5 6 6.5 13 9.5 20 12.5 10 15.5 1 Click and drag to highlight A1:B6.

This is not yet a Histogram, however it is a Vertical Bar Chart. Imports Suppliers 3.5 6 6.5 13 9.5 20 12.5 10 15.5 1 Under the Insert tab, in the Charts group select Column. Select the first chart, Clustered Column. This is not yet a Histogram, however it is a Vertical Bar Chart.

From the Design tab, Chart Layouts group, click on the down arrow From the Design tab, Chart Layouts group, click on the down arrow. Choose Layout 8 (the Histogram). This displays your chart in the form of a Histogram. You may add Axis titles and Gridlines. Unusual is the sudden decrease in the 5th class. This unusual data is called an “outlier” since it is outside of the other data. An outlier may be very large or very small.

Next we will describe data as a Line Chart Next we will describe data as a Line Chart. Line Charts are used to describe single streams of data. For example, measurements taken during a period of time may be easily described by a Line Chart. Month Cholesterol level 1 217 3 246 5 206 7 270 9 225 In the next session, we will observe Measures of Central Tendency, Variability, and Position such as the mean, median, mode, percentile ranks, z-scores, standard deviation which may be calculated easily using Excel.