This is a topic in Mathematics in the Modern World under Statistics.

1. Measures of Central
Tendency for Grouped Data

2. Mean of Grouped Data
2 Methods of Mean for Grouped Data

Class Mark or Midpoint Method

Coded Deviation Method
Class mark or Midpoint Method
In this method, the class mark of each interval has to be known
and then it will be multiplied to the corresponding frequency of every
class interval. The formula for the mean using this method is:
=

4. Step 1: Get the
midpoint/
classmark
Step 2: Multiply
the frequency
Step 3: Get the
sum of the
products
CI
f x fx
80 – 84 5 82 410
75 – 79 3 77 231
70 – 74 9 72 648
65 – 69 7 67 469
60 – 64 10 62 620
55 – 59 9 57 513
50 – 54 7 52 364
Total n = 50 = 3255

5. =
=
Thus, the mean of the data is 65.1.

7. Step 1: Get the
midpoint/
classmark
Step 2: Multiply
the frequency
Step 3: Get the
sum of the
products
CI f x fx
48 – 52 4 50 200
53 – 57 7 55 385
58 – 62 7 60 420
63 - 67 8 65 520
68 – 72 6 70 420
73 – 77 6 75 450
78 – 82 2 80 160
Total N = 40 = 2555

10. Steps:
1. Solve the midpoint of the class interval
2. Find the highest frequency. It is the
reference point starting at 0, going up are
positive and going down are negative
3. Multiply the frequency and the unit-
deviation
4. Add the product of step 3
5. Find the reference midpoint and the class
interval
6. Use the formula to solve for the mean
Class
Interval
Frequency
( f )
Midpoin
t
( x )
d' fd'
90 – 94 7 92 2 14
85 – 89 13 87 1 13
80 – 84 16 82 0 0
75 – 79 8 77 -1 -8
70 – 74 6 72 -2 -12
Total n = 50 ∑fd' = 7

11. Find the Median
Time (in
seconds)
Frequency
51 – 55 2
56 – 60 7
61 – 65 8
66 – 70 4
Total 21

12. Solution:
Time (in
seconds)
Class
boundaries
f <CF
51 – 55 50.5 – 55.5 2 2
56 – 60 55.5 – 60.5 7 9
61 – 65 60.5 – 65.5 8 17
66 – 70 65.5 – 70.5 4 21
Total 21

13. Find the Mode
Time (in
seconds)
Frequency
51 – 55 2
56 – 60 7
61 – 65 8
66 – 70 4
Total 21

14. Solution:
= LBMoC + i
= 60.5 + 5
= 60.5 + 5
= 60.5 +
= 64.5
 d1 = frequency of the modal
class minus below
8 – 4
= 4
 d2 =frequency of the modal
class minus above
8 –
7 = 1
Time (in seconds) Class boundaries f
51 – 55 50.5 – 55.5 2
56 – 60 55.5 – 60.5 7
61 – 65 60.5 – 65.5 8
66 – 70 65.5 – 70.5 4
Total 21

15. Find the mean, median and mode.
CI f x fx CB <CF
90 – 99 3
80 – 89 7
70 – 79 8
60 – 69 5
50 – 59 2
Total 25

16. Median of Grouped Data

17. Find the mean using the two methods…
CI f x fx d' Fd
90 – 99 3 94.5 283.5 2 6
80 – 89 7 84.5 591.5 1 7
70 – 79 8 74.5 596 0 0
60 – 69 5 64.5 322.5 -1 -5
50 – 59 2 54.5 109 -2 -4
Total 1902.5 4

18. The formula for the median for grouped data: