lesson-data-presentation-tools-1.pptx
- 3. DESCRIPTIVE STATISTICS - enable us to understand data through summary values and graphical presentations. - can be illustrated in an understandable fashion by presenting them graphically using statistical and data presentation tools. A. TABULAR PRESENTATION OF DATA Tables display numbers or words arranged in a grid. Tabular method can be used to represent data sets with two variables. A tabular presentation is illustrated in Table 1.
- 4. Table 1 Profile of the Respondents in Terms of Age and Gender Age Bracket Male Female F % F % 21-25 9 8.18 4 3.63 26-30 8 7.27 14 12.72 31-35 7 6.36 6 5.45 36-40 6 5.45 7 6.36 41-45 9 8.18 22 20 46-50 5 4.54 8 7.27 51-Above 2 1.81 3 2.72 Total 46 41.79% 64 58.15% Frequency Table Purpose. Frequency or one-way tables represent the simplest method for analyzing categorical (nominal) data.
- 5. For example, in a survey of spectator interest in different sports, we could summarize the respondents’ interest in watching basketball in a frequency table as follows. “Watching Basketball” Response Frequency Cumulative f Percentage Cumulative Percent Always Oftentimes Sometimes Seldom Never 39 16 26 19 0 39 55 81 100 0 39.00 16.00 26.00 19.00 0 39.00 55.00 81.00 100 0 The table above shows the number, proportion, and cumulative proportion of respondents who characterized their interest in watching basketball as (5) Always interested, (4) Oftentimes interested, (3) Sometimes interested, (2) Seldom interested, or (1) Never interested.
- 6. Applications. In practically every research project, a first “look” at the data usually includes frequency of males and females who participated in the survey, the number of respondents. In medical research, one may tabulate the number of patients displaying specific symptoms; one may tabulate the frequency of different causes.
- 7. Frequency Distribution The easiest method of organizing data is a frequency distribution, which converts raw data into a meaningful pattern for statistical analysis. The following are the steps of constructing a frequency distribution: 1. Specify the number of class intervals. A class is a group (category) of interest. No totally accepted rule tells us how many intervals are to be used. 2. When all intervals are to be the same width, the following rule may be used to find the required class interval width: W = (L-S)/N Where: W = class width L = the largest data S = the smallest data N = number of classes
- 8. Example: Suppose the ages of a sample of 10 students are: 20.0, 18.1, 18.5, 21.3, 19.4, 25.3, 22.0, 23.1, 23.9, and 23.5 We select N=4 and W=(25.3-18.1)/4 = 1.8 which is rounded-up to 2. The frequency table is as follows: Class Interval……..Class Frequency..…….Relative Frequency 18-20……………4……………..40% 21-22……………2……………..20% 23-24……………3……………..30% 25-26…………….1……………..10 % Note: The sum of all the relative frequency must always be equal to 1.00 or 100%. In the above example, we see that 40% of all students are younger than 24 years old, but older than 22 years old.
- 9. Illustration: Consider the following set of data, which are the scores recorded for 30 participants. We wish to summarize this data by creating a frequency distribution of the scores. Data Set- Scores Recorded for 30 Participants 50 45 49 50 43 49 50 49 45 49 47 47 44 51 51 44 47 46 50 44 51 49 43 43 49 45 46 45 51 46
- 10. To create a frequency distribution from this data we proceed as follows: 1. Identify the highest and lowest values in the data set. HS = 51 and LS = 43 2. Create a column with the title of the variable we are using, in this case score. Enter the highest score at the top, and include all values within the range from the highest score to the lowest score. 3. Create a tally column to keep track of the scores as you enter them into the frequency distribution. 4. Create a frequency column, with the frequency of each value, as shown in the tally column, recorded. 5. At the bottom of the frequency column record the total frequency for the distribution proceeded by N=30 6. Enter the name of the frequency distribution at the top of the table. Scores Recorded for 30 Participants Scores Recorded Tally Frequency Frequency Distribution 51 50 49 48 47 46 45 44 43 //// //// ////// /// /// //// /// /// 4 4 6 0 3 3 4 3 3 N= 30
- 11. Cumulative Frequency Distribution A cumulative frequency distribution can be created from a frequency distribution by adding an additional column called “Cumulative Frequency” Frequency Distribution Scores Recorded for 30 Participants Scores Recorded Tally Frequency Cumulative Frequency Cumulative 51 50 49 48 47 46 45 44 43 //// //// ////// /// /// //// /// /// 4 4 6 0 3 3 4 3 3 N= 30 6 3 13 10 16 16 22 26 30
- 12. Grouped Frequency Distribution -in some cases it is necessary to group the values of the data to summarize the data properly. Creating a Grouped Frequency Distribution 1. Find the largest and smallest value. Data Set – Scores in the Major Examine (Statistics) 57 39 52 52 43 50 53 42 58 55 58 50 53 50 49 45 49 51 44 54 49 57 55 59 45 50 45 51 54 58 53 49 52 51 41 52 40 44 49 45 43 47 47 43 51 55 55 46 54 41 2. Compute the Range = HS – LS = 20 3. Select the number of classes desired. This is usually 5 to and 20. 4. Find the class width by dividing the range the range by the number of classes and rounding up. 5. Pick a suitable starting point less than or equal to the minimum value. 6. To find the upper limit of the first class, subtract one from the lower limit of the second class. 7. Find the boundaries by subtracting 0.5 units from the lower limits and adding 0.5units from the upper limits. 8. Tally the data. 9. Find the frequencies. 10. Find the cumulative frequencies. Depending on what you’re trying to accomplish.
- 13. Grouped Frequency Distribution -in some cases it is necessary to group the values of the data to summarize the data properly. Creating a Grouped Frequency Distribution 1. Find the largest and smallest value. 59 and 39. 2. Compute the Range = HS – LS =20 3. Select the number of classes desired. This is usually 5 to and 20. 4. Find the class width by dividing the range the range by the number of classes and rounding up. =2 5. Pick a suitable starting point less than or equal to the minimum value. 6. To find the upper limit of the first class, subtract one from the lower limit of the second class. 7. Find the boundaries by subtracting 0.5 units from the lower limits and adding 0.5units from the upper limits. 8. Tally the data. 9. Find the frequencies. Grouped Frequency Distribution for Scores in the Major Examination (Statistics) Class Interval Tally Interval Midpoint Frequency 57 54 51 48 45 42 39 -59 -56 -53 -50 -47 -44 -41 ////// /////// /////////// ///////// /////// ////// //// 58 55 52 49 46 43 40 6 7 11 9 7 6 4 N= 50
- 14. Cumulative Grouped Frequency Distribution for Scores in the Major Examination (Statistics) Class Interval Tally Interval Midpoint Frequency 57 54 51 48 45 42 39 -59 -56 -53 -50 -47 -44 -41 ////// /////// /////////// ///////// /////// ////// //// 58 55 52 49 46 43 40 N= 50 Cumulative Frequency 10. Find the cumulative frequencies. Depending on what you’re trying to accomplish. 50 44 37 26 17 10 4 6 7 11 9 7 6 4
- 15. B. GRAPHICAL PRESENTATION OF DATA Several types of statistical/data presentation tools exist, including: (a) charts displaying frequencies (bar, pie charts), (b) chart displaying trends (run and line charts), (c) charts displaying distributions (histogram), and (d) charts displaying associations (scatter diagrams). Two types of data. -Attribute Data are countable data or data that can be put into categories: examples like the number of people willing to pay, the number of complaints, percentage who want blue/ percentage who want red. -Variable Data are measurement data, based on some continuous scale (length, time, cost).
- 16. 1. Bar Graph (Histogram) Bar graphs show quantities represented by horizontal or vertical bars. FREQUENCY MARKS
- 17. 2. Pie Chart or Circle Graph Pie chats show proportions in relative to a whole, with each wedge representing a percentage of the total. 43% 19% 14% 14% 5%5% Adventure Country Family Structures of 9-to-14-Year-Old Youth live with mother only live with grand parents live with one parent and a step parent live with both parents Live with father only other
- 18. 3. Line Graph (Polygon Method) Line graphs show sets of data points plotted over a time period and connected by straight lines.
- 19. ACTIVITY: (VIDEO PRESENTATION) Given the following set of data as the actual scores of fifty BSA students in their major examination, prepare a table showing the following: 1. Class Interval 2. Tally 3. Interval Midpoint 4. Frequency 5. Cumulative Frequency Data Set – Scores of 50 BSA Students in Major Examination 40 35 58 33 44 63 66 44 25 33 44 40 46 26 55 34 55 78 45 65 41 35 44 27 37 35 57 48 44 48 25 29 56 33 39 44 37 33 55 40 67 28 56 66 50 59 25 37 45 30