1. Graphing of data (2) Histograms – Polygon - Ogive

2. Distribution of frequency chart (Histogram) By dividing each frequency class by the total number of observations, we obtain the proportion of the set in each of the class. This calculation named relative frequency distribution.

3. Distribution of frequency chart (Histogram) Characteristics of Histograms: A) It is useful to quantative variables. B) There are no spaces between bars. C) It’s a proportion not a frequency. D) X-axis should be continuous. E) Y-axis should begin with zero and represent the (R.F). F) Bar width represent the interval for each group. G) Sum of area bars equal 1.

4. Distribution of frequency chart (Histogram) Example: Relative Frequency Distribution of Battery life: Class intervalClass midpointFrequencyRelative Frequency 0-1.50.700 1.5-1.91.720.05 2.0-2.42.210.025 2.5-2.92.740.1 3.0-3.43.2150.375 3.5-3.93.7100.25 4.0-4.44.250.125 4.5-4.54.730.075 Total 401

5. We can represent the histogram as in the below diagram

6. Distribution of frequency chart (Histogram) Each bar of histogram is marked with its lower class boundary at the left and its upper class boundary at the right. Instead of using class boundaries along the horizontal scale, it is often more practical to use class midpoint values centered below their correspondent bars.

7. Distribution of frequency chart (Histogram) Interpreting a histogram: 1.From a histogram we can conclude where the data are centered. 2.Data variation. 3.Shape of distribution. 4.Presence of outliers.

8. Distribution of frequency chart (Histogram) Why it’s not true to use frequency instead of R.F?

9. Distribution of frequency chart (Histogram) Why it’s not true to use frequency instead of R.F? Using a frequency is not true because: 1.Frequency is not a proportion. 2. Sum of bar areas is not equal one.

10. Frequency Polygon What is a Polygon? It is a 2-dimensional shape and they are made of strait lines connected directly above class midpoint values, the heights of the points correspondent to the class frequency, and the line segments are extended to the right and left so that the graph begins and ends on X-axis, that’s mean the shape is closed.

11. Frequency Polygon Frequency polygon may take on a number of different shapes as: 1.Bell-shape or symmetrical distribution. 2.Bimodal distribution (having two beaks) 3.Rectangular distribution in which each class interval is equally represented [uniform] or no mode. 4.A symmetric positively (right) skewed distribution, since its tail is in positive direction. 5.A symmetric negatively (left) skewed distribution, since its tail is in negative direction. 6.Other shapes like (J shape), (U shape).

12. Frequency Polygon Example: life Battery Class midpointFrequency 0.70 1.72 2.21 2.74 3.215 3.710 4.25 4.73 40

13. Frequency Polygon Polygon diagram

14. Cumulative Frequency polygons (Ogive) An Ogive is a line graph is a line graph that depicts cumulative frequencies and Ogive may be use midpoint or class boundaries a long X-axis and Ogives are useful for determining the number of values below or above particular value, also Ogives are useful in comparing between two sets of data.

15. Cumulative Frequency polygons (Ogive) Example: The same Battery data life after calculating cumulative Relative Frequency: Class intervalRelative FrequencyCumulative R.F 0-1.500 1.5-1.90.05 2.0-2.40.0250.075 2.5-2.90.10.175 3.0-3.40.3750.55 3.5-3.90.250.8 4.0-4.40.1250.925 4.5-4.50.0751 Total1

16. Cumulative Frequency polygons (Ogive) Cumulative frequency polygons

17. Cumulative Frequency polygons (Ogive) Cumulative frequency polygons Interpretations from previous diagram: 80% of data or less is equal or less than 3.7.

18. Cumulative Frequency polygons (Ogive) Example 2: The table bellow is a Systolic Blood Pressure for 63 Smokers people and 63 Nonsmokers people and the data has been summarized in the table as:

19. Cumulative Frequency polygons (Ogive) Example 2: Cumulative relative Frequency% Class boundaryNonsmokersSmokes 89.51614 109.55455 129.58382 149.59790 169.510095 189.5100

20. Cumulative Frequency polygons (Ogive) Example 2 diagrams:

21. Cumulative Frequency polygons (Ogive) From the previous diagram we can conclude that: 90% of smoker’s people their Systolic Blood pressure is less than 149.5 and 100% of Nonsmokers their Systolic Blood pressure is less than 149.5.