Tabular presentation PRESENTATION OF DATA

Data summarization Is the organization of data in a way for easy understanding. It is the first step of data interpretation (analysis). Consists of the following steps: 1) Data entering. 2) Ordered array. 3) Summarization

Data entering Generally, computers are used for data entry. Nowadays, many software are developed for data entering, presentation and data analysis. Examples of statistical software: MS Excel. Epi-Info. SPSS. Stata.

Ordered array It is the first step in the process of data organization after data entering. An ordered array is a listing of values from the smallest value to the largest value. It enables one to determine quickly the largest and smallest measurements. It also enables to determine roughly proportion of people lying below and above certain value.

FREQUENCY DISTRIBUTION TABLES It determines the number of observations falling into each class In qualitative data we are counting the number of observations in each category. These counts are called frequencies. And they are also presented as relative percentages of the total numbers. In quantitative data frequencies can be counted by grouping data into equal intervals and counting frequency of event in each interval.

GROUPING DATA To group a set of observations, we select a set of contagious, non overlapping intervals, such that each value in the set of observation can be placed in one interval only, and no single observation should be missed.The interval is called: CLASS INTEVAL.

NUMBER OF CLASS INTERVALS The number of class intervals should not be too few because of the loss of important information, and not too many because of the loss of the needed summarization

NUMBER OF CLASS INTERVALS When there is a priori classification of that particular observation we can follow that classification. But when there is no such classification we can follow the Sturge's Rule

NUMBER OF CLASS INTERVALS Sturge's Rule: k= 1+3.322 log n k= number of class intervals n= number of observations in the set The result should not be regarded as final, modification is possible

WIDTH OF CLASS INTERVAL The width of the class intervals should be the same, if possible. R W=-------- K W= Width of the class interval R= Range (largest value – smallest value) K= Number of class intervals

RELATIVE FREQUENCY DISTRIBYTION It determines the proportion of observation in the particular class interval relative to the total observations in the set.

CUMULATIVE FREQUENCY DISTRIBUTION This is calculated by adding the number of observation in each class interval to the number of observations in the class interval above, starting from the second class interval onward.

CUMULATIVE RELATIVE FREQUENCY DISTRIBUTION This is calculated by adding the relative frequency in each class interval to the relative frequency in the class interval above, starting also from the second class interval onward.

CUMULATIVE DISTRIBUTION Cumulative frequency and cumulative relative frequency distributions are used to facilitate obtaining information regarding the frequency or relative frequency within two or more contagious class intervals.

The following are 7 1 7 7 10 the number of 12 12 10 3 2 hours of 45 patients 4 3 8 7 5 slept following the administration of a 8 5 1 3 11 certain hypnotic 3 1 7 13 5 drug: 10 17 17 3 4 11 4 4 4 3 5 8 7 7 5 13 8 1 8 8

Construct a table showing: Frequency Relative frequency Cumulative frequency Cumulative relative frequency distribution.

Number of class intervals: K=1+3.322 log n =1+3.322 log45 =1+3.322 X 1.653 =6.4 =6 Width of class interval: R 17-1 W=------= ------- = 2.7 = 3 K 6

CLASS FREQUENCY RELATIVE CUMULATIVE CUM.REL. INTERVAL FREQUENCY FREQUENCY FREQUENCY (hour) % % 1-3 11 24.4 11 24.4 4-6 10 22.2 21 46.6 7-9 13 28.9 34 75.5 10-12 7 15.6 41 91.1 13-15 2 4.4 43 95.5 16-18 2 4.4 45 99.9 Total 45 99.9

The following are the weight (in ounces) of malignant tumours removed from the abdomen of 57 subjects:

1 11 31 41 51 68 22 21 12 16 36 28 2 12 32 42 52 63 23 22 32 24 19 25 3 13 33 43 53 42 24 23 49 69 46 45 4 14 34 44 54 27 25 24 38 47 30 12 5 15 35 45 55 30 44 25 42 23 43 57 6 16 36 46 56 36 65 26 27 22 49 51 7 17 37 47 57 28 43 27 31 43 12 23 8 18 38 48 32 25 28 50 27 42 9 19 39 49 79 74 29 38 49 28 10 20 30 40 50 27 51 21 28 31

Construct a table showing : Frequency Relative frequency Cumulative frequency Cumulative rel ative frequency

Number of class intervals: K=1+3.322 log n =1+3.322 log 57 =1+3.322 X1.76 = 6.8.3 = 7 Width of class interval: R 79-12 67 W=---------= ------------=-----------= 9.6 = 10 K 7 7

Frequency Cum.Freq Class Rel.Freq Cum.Rel interval % Freq% 10-19 5 5 8.77 8.77 20-29 19 24 33.33 42.10 30-39 10 34 17.54 59.64 40-49 13 47 22.81 82.45 50-59 4 51 7.02 89.47 60-69 4 55 7.02 96.49 70-79 2 57 3.51 100.00 TOTAL 57 100.00

Tabular presentation Presentation of data in tables so as to organize the data into a compact, concise and readily comprehensible form. They can display the characteristics of data more efficiently than the raw data.

Types Simple Table : including one variable (quantitative or qualitative ) and the corresponding frequency Cross tabulation: ( Two – dimensional tables), two variables are cross classified Contingency table: demonstrating the relationship between two or more variables

Graphical and Pictorial presentation of data The use of diagrams or pictures to display distribution or characteristics of one or more sets of data in a compact and readily comprehensible form. They can provide a better visual appreciation of characteristics of data than tabular presentation

Graphs It is a pictorial display of quantitative data using a coordinate system , where the X is the horizontal axis and the Y is the vertical axis. X-axis usually includes the independent variable (method of classification) Y-axis includes the dependant variable ( frequency or relative frequency or other indicator)

Stem-and-Leaf Plot Summarizes quantitative data. Each data point is broken down into a “ stem ” and a “ leaf .” First, “stems” are aligned in a column. Then, “leaves” are attached to the stems.

Stem-and-Leaf Plot Stem-and-leaf of Shoes N = 139 Leaf Unit = 1.0 12 0 223334444444 63 0 555555555555566666666677777778888888888888999999999 (33) 1 000000000000011112222233333333444 43 1 555555556667777888 25 2 0000000000023 12 2 5557 8 3 0023 4 3 4 4 00 2 4 2 5 0 1 5 1 6 1 6 1 7 1 7 5

Histogram Graphical display of frequency distribution of quantitative variable . The values of the quantitative variable( as class interval) will be placed on the X-axis ( representing the width of the rectangles), and the corresponding frequency (or relative frequency) will be placed on the Y-axis (representing the height of the rectangles)

Histogram The area is proportional to the height, and the frequencies in different categories can be directly compared by examining the relative height of the respective bar. It is important that the class interval should be equal, otherwise the area should be compared. Only one set of data can be shown in one histogram

Frequency Polygon Another form of graphical presentation of frequency distribution of quantitative variables. It is similar to the histogram , but instead of using rectangles to present data, the midpoint of the top of each rectangle are plotted , and connected together by straight lines.

Frequency Polygon More than one set of data can be demonstrated on the same graph, to facilitate direct comparison. It provides information about underlying characteristics of data . The area under the frequency polygon is equal to the area under the equivalent histogram

Scatter diagram A pair of measurements is plotted as a single point on a graph. The value of one variable of each pair is plotted on the X axis and the value of the other variable is plotted on the Y axis

Scatter diagram The pattern made by the plotted points is indicative of the relationship between these two variables, which might be linear (if they follow straight line) or curvilinear (if the pattern doesn't follow straight line)

Scatter diagram A scatter diagram could suggest: No relationship : when one variable changes with no change in the other variable ,or when the pattern is buzzard Linear relationship : an increase in the 1st variable is associated with an increase (positive) or decrease (negative) in the 2nd variable, and the pattern follows a straight line. Curvilinear (positive or negative) relationship: the pattern of increase or decrease will not follow a straight line .

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