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Sumukh Deshpande n Lecturer College of Applied Medical Sciences

BIOSTATISTICS (BST 211). Sumukh Deshpande n Lecturer College of Applied Medical Sciences. Lecture 4. Statistics = Skills for life. Descriptive Statistics of Grouped Data. Continuous Data → Grouped. Number b is NOT included. Continuous Data: Grouped in INTERVALS

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Sumukh Deshpande n Lecturer College of Applied Medical Sciences

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  1. BIOSTATISTICS (BST 211) Sumukh DeshpandenLecturerCollege of Applied Medical Sciences Lecture 4 Statistics = Skills for life.

  2. Descriptive Statistics of Grouped Data

  3. Continuous Data → Grouped Number b is NOT included • Continuous Data: • Grouped in INTERVALS • Usually 5 to 15 intervals • Intervals: • Also called CLASSES • [a – b[ • [b – c[ Also (b-a) = (c-b)

  4. Worked Example Time (in sec) taken for a group of patients to walk a flight of stairs Group the data in a suitable number of classes and calculate the central values and spread of the data Compare the values of grouped to the mean, median and SD before grouping? What do you notice?

  5. Solution 1 Find min, Max and Range Decide how many classes you want (5 to 15) Establish a frequency table and count f for each class Add on a column for mid-points Carry out statistical analysis using appropriate formulae All of that is easily done in MS Excel

  6. Solution 2 We want 5 classes Class width w = range/c Always check your total freq, class width and formulae before reporting results

  7. Median of Grouped Data Median = L + (n/2 - cf ) × w/fm L: is the lower limit of the median class n: is the number of ALL observations, n= Sf cf: is the sum of frequencies of all classes before the median class w: is the width of the median class fm: is the frequency of the median class

  8. Median of This Data Set 8 + 4 = 12 …and 12 +4 =16 This is the median class Since n = 30, the median is near the 15th observation Now, apply the formula! n = 30 L = 36 w = 9 cf = 12 Median = 42.75 fm = 4 Median = L + (n/2 - cf ) × w/fm

  9. Mode of Grouped Data Mode(s) = midpoint(s) of the class(es) of highest frequency Mode = 58.5

  10. Summary of Grouped Data Stats 30 observations grouped into 5 classes with w = 9

  11. What if it was Ungrouped Data? The data is ranked and processed as discrete entries

  12. Comparison of Grouped and Ungrouped Data Stats What happens if you chose 10 classes instead of 5? How about 15 classes? 20?30? Use the Excel sheet to check your prediction

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