![[GOALS]
After completing this chapter, YOU
should be able to:
• Organize DATA using a frequency distribution
• Represent data in frequency distributions graphically using
histograms, frequency polygons and ogives
• Represent data using bar graphs, Pareto charts, time series
graphs, and pie chart
• Draw and interpret a stem and leaf plot
STAB 2004 Biometry & Experimental Design](https://image.slidesharecdn.com/notesstab2004chapter2-250323155913-f950d690/85/Chapter-2-Frequency-Distribution-Illustrations-Graphs-3-320.jpg)
Chapter 2 Frequency Distribution Illustrations/Graphs
- 2. Contents • Organizing data – FREQUENCY DISTRIBUTIONS • Graphical forms – HISTOGRAM, – FREQUENCY POLYGONS and – OGIVES • Other types of Graphs – BAR GRAPH – PARETO CHARTS – TIME SERIES GRAPH – PIE GRAPH – STEM AND LEAF PLOT STAB 2004 Biometry & Experimental Design
- 3. [GOALS] After completing this chapter, YOU should be able to: • Organize DATA using a frequency distribution • Represent data in frequency distributions graphically using histograms, frequency polygons and ogives • Represent data using bar graphs, Pareto charts, time series graphs, and pie chart • Draw and interpret a stem and leaf plot STAB 2004 Biometry & Experimental Design
- 4. Data Presentation/Illustration • The first step in DATA analysis – Once DATA has been collected, DATA should always be illustrated • Suitable DATA illustrations are based on data types – May just be in table form – Or can be converted into some kind of illustrations/figures – Commonly known as graphs? SUMMARY OF A LARGE DATA SETS STAB 2004 Biometry & Experimental Design
- 5. Raw DATA 183 163 152 157 157 165 173 180 164 160 166 157 168 167 156 155 178 169 171 175 169 168 165 166 164 163 161 157 181 163 157 169 177 174 183 181 182 171 184 179 Height (cm) for 40 students STAB 2004 Biometry & Experimental Design
- 6. Organizing DATA • Data in original form are called RAW DATA • Researchers organize data frequency distribution – The organization of raw data in table form using classes and frequencies • Frequency distribution consists of: – Classes (quantitative/qualitative category) – Corresponding frequencies STAB 2004 Biometry & Experimental Design
- 7. Organizing DATA Types of FREQUENCY DISTRIBUTION – Categorical frequency distribution • For data that can be placed in specific categories such as nominal or ordinal level data – Grouped frequency distribution • When range of data is large, data must be grouped into classes that are more than one unit in width – Ungrouped frequency distribution • When the range of data values is relatively small, single data value is used for each class STAB 2004 Biometry & Experimental Design
- 8. HISTOGRAM • Most common form of DATA presentation • Suitable for large sets of DATA • For continuous data – Compare with bar chart/bar graph • The first step is to construct a FREQUENCY TABLE STAB 2004 Biometry & Experimental Design
- 9. Frequency Table STEP Determine the classes • Find the highest value (H) and the lowest value (L) • Find the range (R) where R = (H – L) • Select the number of classes (C) desired – Usually the number of classes are between 5 to 20 • Find the class width by dividing the range by the number of classes STAB 2004 Biometry & Experimental Design
- 10. Frequency Table • Estimate – No. of classes, C = 1 + 3.3 log n – Class width CW = (H – L ) / C • Example: – For our raw data number of students (n = 40) – The highest value is 184, whilst the lowest 152 – Therefore, C = 1 + 3.3 (log 40) = 6.3 (~ 6) CW = (184 – 152) / 6.3 = 5.1 (~ 5.0) STAB 2004 Biometry & Experimental Design
- 11. Frequency Table STAB 2004 Biometry & Experimental Design
- 12. For Grouped Frequency Distribution For the data 149.5 – 154.5 is called the class limit 149.5 lower class limit 154.5 upper class limit class boundaries are numbers used to separate the classes so that no gaps existed in the frequency distribution THE RULE OF THUMB Class limits should have the same decimal place value as the data but the class boundaries should have one additional place value and end in a 5 STAB 2004 Biometry & Experimental Design
- 13. HISTOGRAM 152 157 162 172 177 182 167 STAB 2004 Biometry & Experimental Design
- 14. HISTOGRAM Interpretation: • DATA distribution (DATA range) • Centre of DATA • Area under each bar is the frequency or relative frequency STAB 2004 Biometry & Experimental Design
- 15. POLYGON 152 157 162 172 177 182 167 STAB 2004 Biometry & Experimental Design
- 16. POLYGON • Join all middle values (midpoints) of each bar • Gives shape of DATA distribution • If the number of classes are added, class width gets smaller, therefore smoother line of polygon will produce a curve • If the curve is symmetry like a bell-shape, the data is NORMALLY distributed STAB 2004 Biometry & Experimental Design
- 17. OGIVE STAB 2004 Biometry & Experimental Design
- 18. OGIVE STAB 2004 Biometry & Experimental Design
- 19. Shapes of DATA distribution • Normal/Bell shape – e.g.: photosynthesis rate in leaves in a day • Uniform – e.g.: daily temperature • Left-skewed – e.g.: Number of bats captured in a day • Right-skewed – e.g.: Number of trees at different size classes STAB 2004 Biometry & Experimental Design
- 20. Shapes of DATA distribution • Bimodal – e.g.: Monthly total rainfall in Malaysia • Polymodal – e.g.: Organismal response across environmental gradient • J-shaped – e.g.: Plant growth rate • Reversed J-shaped – e.g.: Abundance of insect in forest from common to rare species STAB 2004 Biometry & Experimental Design
- 21. Other Illustrations/Graphs • Graphs • Tables • Charts • Plots STAB 2004 Biometry & Experimental Design
- 22. Other Graphs: Bar Graphs • Bar Graphs – Represents data by using vertical or horizontal bars – The heights or lengths of the bars represent the frequencies of the data – Data are qualitative or categorical STAB 2004 Biometry & Experimental Design
- 23. Other Graphs: Pareto Charts • Pareto Charts – Represents a frequency distribution for a categorical variable; – Frequencies are displayed by the heights of vertical bars arranged in order from highest to lowest – Variable displayed on the horizontal axis is qualitative or categorical – When you analyze a Pareto chart, make comparisons by looking at the heights of the bar STAB 2004 Biometry & Experimental Design
- 24. Other Graphs: Pareto Charts • Constructing a Pareto chart 1. Make the bars the same width 2. Arrange the data from largest to smallest according to frequency 3. Make the units that are used for the frequency EQUAL IN SIZE* STAB 2004 Biometry & Experimental Design
- 25. Other Graphs: Time Series Graph • Time Series Graph – Represents data that occur over a specific period of time – Often represented by lines instead of bars – When you analyze a time series graph, look for trend or pattern that occurs over the time period – Two data sets can be compared on the same graph called compound time series graph STAB 2004 Biometry & Experimental Design
- 26. Other Graphs: Pie Graph • Pie Graph – Is a circle that is divided into sections or wedges according to the percentage of frequencies in each category – Since there are 360o in a circles, the frequency for each class must be converted into a proportional part of the circle Degrees = frequency . 360o sum of frequencies STAB 2004 Biometry & Experimental Design
- 27. Other Graphs: Stem and Leaf Plot • Stem and Leaf Plot – Data plot that uses part of the data value as the stem and part of the data value as the leaf to form groups of classes – Method of organizing data and is a combination of sorting and graphing – Has advantage in retaining the actual data while showing them in graphical form STAB 2004 Biometry & Experimental Design
- 28. Other Graphs: Stem and Leaf Plot • Constructing a Stem and Leaf Plot 1. Arrange the data in order 2. Separate the data according to the first digit 3. A display can be made by using the leading digit as the stem and the trailing digit as the leaf 4. When the data values are in the hundreds the stem cam take the first two digit 5. Related distribution ca even be compared by using back-to- back stem and leaf plot Stem and leaf plots are part of the technique called exploratory data analysis STAB 2004 Biometry & Experimental Design
- 29. Misleading Graph • Graphs are visual representation that enables readers to analyze and interpret easily as compared to looking at numbers HOWEVER • Inappropriately drawn graph will lead to false conclusions • Graph can be misrepresented: – Truncating scales/axis misinterpretation of large or slight changes – Exaggerating one dimensional to two dimension – Omitting labels or units – Sources of information are not clear STAB 2004 Biometry & Experimental Design
- 30. Summary First step in data presentation is to illustrate the DATA Use types of frequency distribution to organize DATA Choose suitable illustrations based on type of DATA Differentiate between use and misuse of graphs STAB 2004 Biometry & Experimental Design