1. 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.

2. Descriptive Statistics of Grouped Data

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

4. Worked Example
Time (in sec) taken for a group of patients to walk a flight of stairs 57 53 45 22 28 31 19 24 30 54 42 34 63 18 61 62 52 40 36
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. This is the median class
Median of This Data Set
8 + 4 = 12
…and =16
This is the median class
Since n = 30, the median is near the 15th observation
Now, apply the formula!
L = 36
n = 30
cf = 12
w = 9
Median = 42.75
fm = 4
Median = L + (n/2 - cf ) × w/fm

9. Mode of Grouped Data Mode = 58.5
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
Parameter
Value
Mean 42
Median
42.75
Mode
58.5
SD(n-1)
15.15

11. What if it was Ungrouped Data?18 19 22 24 28 30 31 34 36 40 42 45 52 53 54 57 61 62 63
The data is ranked and processed as discrete entries
Parameter
Value
Mean
40.9
Median 41
Mode 54
SD(n-1)
16.28

12. Comparison of Grouped and Ungrouped Data Stats
Parameter
Ungrp
Grp (5)
Mean
40.9 42
Median 41
42.75
Mode 54
58.5
SD(n-1)
16.28
15.15
What happens if you chose 10 classes instead of 5?
How about 15 classes? 20?30?
Use the Excel sheet to check your prediction