Presentation on theme: "Chapter 2 Presenting Data in Charts and Tables"— Presentation transcript:
1 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.
2 Computer software can be used to create charts and graphs: SPSSMINITABMs. ExcelMs. VisioOthers
3 How to present categorical data? Tabulating dataSummary tableGraphing dataBar chartsPie charts
4 Bar chartBar chart and pie chart are often used for quantitative data(categorical data)Height of bar chart shows the frequency for each categoryBar graphs compare the values of different items in specific categories or t discrete point in time.
6 Pie chartThe size of pie slice shows the percentage for each categoryIt is suitable for illustrating percentage distributions of qualitative dataIt displays the contribution of each value to a totalIt should not contain too many sectors-maximum 5 or 6
9 How to present numerical data? Ordered arrayStem-and-LeafFrequency DistributionHistogramPolygonCumulative DistributionsOgive
10 The ordered arrayThe sequence of data in rank order:Shows range (min to max)Provides some signals about variability within the rangeOutliers can be identifiedIt is useful for small data setExample:Data in raw form:Data in ordered array:(min to max)
11 Tabulating Numerical Data: Frequency DistributionA frequency distribution is a list or a table….It contains class groups andThe corresponding frequencies with which data fall within each group or categoryWhy use a Frequency Distribution?To summarize numerical dataTo condense the raw data into a more useful formTo visualize interpretation of data quickly
12 Organizing data set into a table of frequency distribution: Determine the number of classesThe number of classes can be determined by using the formula: 2k>n-k is the number of classes-n is the number of data pointsExample:Prices of laptops sold last month at PSC:299, 336, 450, 480, 520, 570, 650, 680, 720765, 800, 850, 900, 920, 990, 1050, 1300, 1500
13 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
14 -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 classinterval can be at least = The classinterval used in this data set is 250Determine class boundaries:Tally the laptop selling prices into the classes:Classes:260 up to 510510 up to 760760 up to 10101010 up to 12601260 up to 1510
15 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 to510 up to760 up to1010 up to1260 up to
16 Step-and-leafA 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.
18 HistogramA graph of the data in a frequency distributionIt uses adjoining columns to represent the number of observations(frequency) for each class interval in the distributionThe area of each column is proportional to the number of observations in that interval
21 PolygonA frequency polygon, like a histogram, is the graph of a frequency distributionIn 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.
26 ExercisesThe price-earnings ratios for 24 stocks in the retail store are:Organize this data set into step-and-leaf displayHow many values are less than 10.0?What are the smallest and largest values
27 Exercises2. The following stem-and-leaf chart shows the number of units produced per day in a factory.8 14 16 259 18
28 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?
29 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 ofDays absent Employees0 up to 4 54 up to8 up to 12 612 up to 16 816 up to 20 2
30 What is the midpoint of the first class? Construct a histogramConstruct a frequency polygonInterpret the rate of employee absenteeism using the two charts