 FREQUENCY DISTRIBUTION TABLES  FREQUENCY DISTRIBUTION GRAPHS

 Frequency Distribution: Lists each category (label) of data and the number of occurrences.  Sum of all = population or sample size  Relative Frequency: The proportion of occurrences for each category calculated as: Sum of all = 1.

 Bar Graph: Vertical or Horizontal. X-axis contains the categories or labels. For Frequency Distributions the y-axis is the number of occurrances. For Relative Frequency Distributions the y-axis is the proportion (values between 0 and 1). Bars do not need to be touching.

SPECIESZOO AZOO B Elephant63 Giraffe127 Impala1324 Zebra12 Ostrich61 Guinea Hens2512

 CAN TREAT DISCRETE DATA LIKE QUALITATIVE (IF ONLY SEVERAL VALUES) OR AS WE WILL BE TREATING CONTINUOUS DATA (IF MANY VALUES)  SEPARATE CONTINUOUS DATA INTO CLASSES (INTERVALS) AND THEN DO DISTRIBUTION TABLES OR GRAPHS

Frequency Distribution Table: Similar to that for qualitative data, but each class is for a value or an interval (range) of values. Histograms: Vertical bar graphs, where the x-axis is the number line and each bar is for a class. All bars must touch side to side. Uses Lower Class limit on x-axis.

 Cumulative Frequency Distributions: Each class listed as before (lowest to largest), but the frequencies are the total for that frequency and all the lower classes.  Relative Cumulative Frequency Distribution: Each Cumulative Frequency divided by total of all frequencies. The last class will have a cumulative value of 1.0

 Use number of siblings  Do as Frequency Table  Do as Relative Frequency  Do as Cumulative Frequency  Do as Relative Cumulative Frequency

 Class: An interval of numbers along the number line.  Lower Class Limit (LCL): The beginning number of the class.  Upper Class Limit (UCL): The last number of the class.

 Class Width: the difference between lower class limits (or upper class limits), found by taking using data set’s maximum and minimum and calculating rounding up to a convenient value  Midpoint of Each Class: The point in the middle of the class, found by averaging the class lower class limit and the next class lower class limit.

1. Organize data in ascending order:

2. Determine the number of classes (5 – 20): For this we will use Find the maximum and minimum: For this max = 4.91 and min = 1.03

4. Calculate the Class Width: Round UP to a convenient value. We will use 0.70.

5. Determine First Lower Class Limit: For this we will use 1.00 (something convenient and lower than the Minimum). 6. Determine the next 5 Lower Class Limits by adding class width to the first and each subsequent to get the next: =1.70; =2.40 … 3.10, 3.80, 4.50.

7. Determine the first Upper Class Limit by Subtracting 1 from the last place of the second Lower Class Limit: = Find the other 5 Upper Class Limits by adding the class width to each previous Upper Class Limits: =2.39, =3.09, …, 3.79, 4.49, 5.19

9. Now construct the Table ……: CLASS LOWER CLASS LIMITUPPER CLASS LIMIT FREQUENCY ? ? ? ? ? ?

And count the frequencies in each class …:

And complete the Table: CLASS LOWER CLASS LIMITUPPER CLASS LIMIT FREQUENCY

10. Draw the histogram:

 Stem Leaf Plot: Used for recording and showing dispersion of data. Stem can be the integer portion of a number and the leaves the decimal portion. Or the stem could be the tens digit and the leaves the ones digit.  5-3,5,6,7,7,8,9  6-2,3,3,4,6,6,7,8  7-1,1,3,6,9

 Dot Plot: Also used to show dispersion of data. Draw a number line and label the horizontal scale with the numbers from the data from lowest to highest. Then place a dot above the numbers each time the number occurs. * * * * * * * * * * |___|___|___|___|___|___|___|___|___|___|

 Polygon Plot: Line graph using the midpoints for the x-axis and frequencies for the y-axis. Both ends of the line must come back to the 0 on the y-axis.

 Given a Polygon Plot, construct a Frequency Distribution Table. › 1. Find the Class Width: Difference in Midpoints › 2. Find first two LCL’s: Midpoint +/- ½*Class Width › 3. Find First Upper Class Limit: 2 nd LCL – 1 › Find remainder of LCL’s & UCL’s › Find each class’s frequency

 Ogive (pronounced oh jive) Plot: Line Graph used for displaying Cumulative Frequency Distributions. The x-axis is the Upper Class Limit and the y-axis is the Cumulative Frequency. The first point is a class width less than the first Upper Class Limit so that the line starts with a frequency of 0.

 Ogive Plot:

 Time Series Plots: Can be vertical or horizontal bar graphs, or line graphs. X- axis is time intervals or ages (years, months, days) and y-axis is frequency.

 Vertical Scale Manipulation: Not starting the y-axis at 0. Also using a break in the scale. Can make differences look bigger than they really are.  Exaggeration of Bars or Symbols: Used in pictographs.  Horizontal Scale Manipulation: Not all classes or time interval are the same width.

 “Get your facts first, then you can distort then as you please” Mark Twain  “There are lies, damn lies, and STATISTICS” Mark Twain  “Definition of Statistics: The science of producing unreliable facts from reliable figures.” Evan Esar