1. Data summary Qualitative or categorical variables: Those variables yield observations on which individuals can be categorized according to some characteristics. Examples: Gender –Marital status – Education level. Note: There is no meaning for some calculations on qualitative variables such (mean- median- variance) but proportions are useful in this case.

2. Data summary Quantitative variables: Those variables yield observations that can be measured or counted and it can be divided to: Discrete: Only take values from some discrete set of possible values (whole are integer) and it can be countable. Examples: The number of girls in the class – the number of children in one family – the number of time you visit a doctor.

3. Data summary Continues: Values from continues range of possible values, although the recorded measurements are rounded. Examples: Weight, height, hemoglobin levels, blood pressure. Note: for continues variables we need instruments to measure the data.

4. Why we are obligate to summarize data? We are obligating to summary data because: 1.We want to show data in summarized form. 2. To ease the communication with it in order to use proper statistical tests.

5. Summary of categorical data We can obtain frequencies of categorical data and summarize them in a table or graphs.

6. Frequency table Considerable information can be obtained from large masses of statistical data by grouping the data into classes and determining the number of observations that fall in each of the classes. Such an arranged is called a frequency distribution or frequency table. Frequency table be the most convenient way to summarize or display data. There are two types of frequency distributions will be considered to: –Categorical or qualitative frequency distributions. –Grouped frequency distributions.

7. Categorical or qualitative frequency tables Example : Gaza strip divided to 5 governates, suppose in our class student distributed to these places as: KhanYounis, Rafah, Middle, Middle,North,Gaza, Rafah,Middle, North, KhanYounis, Rafah, Gaza, Middle,Middle,Rafah, North, KhanYounis, Gaza, Gaza, Rafah. The above data can’t be easy to understand or to deal with it, so we should summarize our data in a categorical table as :

8. Categorical or qualitative frequency tables

9. Relative frequency [R.F] = Example: R.F (for North ) =

10. Grouped frequency Distribution Suppose we have 40 similar car batteries recorded to the nearest tenth of year as : (Walpole R., Myers R., Myers S., Ye(2012), Probability and Statistics for Engineers and Scientists, pp. 21).

11. Grouped frequency Distribution 2.24.13.54.53.23.732.6 3.41.63.13.33.83.14.73.7 2.54.33.43.62.93.33.93.1 3.33.13.74.43.24.11.93.4 4.73.83.22.63.934.23.5

12. How to construct a frequency table? 1. We should calculate the range as: Range = Maximum value – Minimum value 2. We should decide the number of intervals. Note: The number of intervals should be between 5 and 15. 3. Determine the size of interval. 4. Start tabulate from first class interval with smallest value or less.

13. How to construct a frequency table? Minimum value = 1.6 Maximum value = 4.7 Range= 4.7-1.6=3.1 Number of classes = 7 “optional” Size of class interval =

14. How to construct a frequency table? Class intervalfrequencyR.F % 1.5 – 1.925 2.0 – 2.412.5 2.5 – 2.9410 3.0 – 3.41537.5 3.5 – 3.91025 4.0 – 4.4512.5 4.5 – 4.937.5 Total40100

15. How to construct a frequency table? R.F (3.0-3.4) =

16. Any questions?