Chapter 2 Presenting Data in Charts and Tables Why use charts and graphs? Visually present information that can’t easily be read from a data table. Many details can be shown in a small area. Readers can see immediately major similarities and differences without having to compare and interpret figures.

Computer software can be used to create charts and graphs: SPSS MINITAB Ms. Excel Ms. Visio Others

How to present categorical data? Tabulating data Summary table Graphing data Bar charts Pie charts

Bar chart Bar chart and pie chart are often used for quantitative data(categorical data) Height of bar chart shows the frequency for each category Bar graphs compare the values of different items in specific categories or t discrete point in time.

Bar chart example:

Pie chart The size of pie slice shows the percentage for each category It is suitable for illustrating percentage distributions of qualitative data It displays the contribution of each value to a total It should not contain too many sectors-maximum 5 or 6

Pie char example:

Table example:

How to present numerical data? Ordered array Stem-and-Leaf Frequency Distribution Histogram Polygon Cumulative Distributions Ogive

The ordered array The sequence of data in rank order: Shows range (min to max) Provides some signals about variability within the range Outliers can be identified It is useful for small data set Example: Data in raw form: 23 12 32 567 45 34 32 12 Data in ordered array:12 12 23 32 32 34 45 567 (min to max)

Tabulating Numerical Data: Frequency Distribution A frequency distribution is a list or a table…. It contains class groups and The corresponding frequencies with which data fall within each group or category Why use a Frequency Distribution? To summarize numerical data To condense the raw data into a more useful form To visualize interpretation of data quickly

Organizing data set into a table of frequency distribution: Determine the number of classes The number of classes can be determined by using the formula: 2k>n -k is the number of classes -n is the number of data points Example: Prices of laptops sold last month at PSC: 299, 336, 450, 480, 520, 570, 650, 680, 720 765, 800, 850, 900, 920, 990, 1050, 1300, 1500

In this example, the number of data points is n=18. If we try k=4 which means we would use 4 classes, then 24=16 that is less than 18. So the recommended number of classes is 5. Determine the class interval or width -The class interval should be the same for all classes -Class boundaries never overlap

-The class interval can be expressed in a formula: Where i is the class interval, H is the highest value in the data set, L is the lowest value in the data set, and k is the number of classes. In the example above, H is 1500 and L is 299. So the class interval can be at least =240.2. The class interval used in this data set is 250 Determine class boundaries: 260 510 760 1010 1260 1510 Tally the laptop selling prices into the classes: Classes: 260 up to 510 510 up to 760 760 up to 1010 1010 up to 1260 1260 up to 1510

Compute class midpoints: 385 635 885 1135 1385 (midpoint=(Lower bound+ Upper bound)/2) Count the number of items in each class. The number of items observed in each class is called the class frequency: Laptop selling Frequency Cumulative Freq. price9($) 260 up to 510 4 4 510 up to 760 5 9 760 up to 1010 6 15 1010 up to 1260 1 16 1260 up to 1510 2 18

Step-and-leaf A statistical technique to present a set of data. Each numerical value is divided in two parts—stem(leading digits), and leaf(trailing digit) The steps are located along the y-axis, and the leaf along the x-axis.

Stem Leaf 29 9 33 6 45 0 48 0 52 0 57 0 65 0 68 0 72 0 76 0 80 0 85 0 90 0 92 0 99 0 105 0 130 0 150 0

Histogram A graph of the data in a frequency distribution It uses adjoining columns to represent the number of observations(frequency) for each class interval in the distribution The area of each column is proportional to the number of observations in that interval

Example of histogram:

How can you construct the histogram in SPSS?

Polygon A frequency polygon, like a histogram, is the graph of a frequency distribution In a frequency polygon, we mark the number observations within an interval with a single point placed at the midpoint of the interval, and then connect each set of points with a straight line.

Polygon example:

How can you construct the polygon in SPSS?

Ogive—a graph of cumulative frequency Ogive example:

How can you construct the Ogive in SPSS?

Exercises The price-earnings ratios for 24 stocks in the retail store are: 8.2 9.7 9.4 8.7 11.3 12.8 9.2 11.8 10.8 10.3 9.5 12.6 8.8 8.6 10.6 12.8 11.6 9.1 10.4 12.1 11.5 9.9 11.1 12.5 Organize this data set into step-and-leaf display How many values are less than 10.0? What are the smallest and largest values

Exercises 2. The following stem-and-leaf chart shows the number of units produced per day in a factory. 8 1 4 1 6 2 01333559 9 0236778 16 59 18 00156 23 10 36 25

How many days were studied? How many values are in the first class? What are the smallest and the largest values? How many values are less than 70? How many values are between 50 and 70?

3. The following frequency distribution represents the number of days during a year that employees at GDNT were absent from work due to illness. Number of Number of Days absent Employees 0 up to 4 5 4 up to 8 10 8 up to 12 6 12 up to 16 8 16 up to 20 2

What is the midpoint of the first class? Construct a histogram Construct a frequency polygon Interpret the rate of employee absenteeism using the two charts