Lesson on Mean, Median and Mode for grouped data

4. Ungrouped data
1 st term grades of iii-reverence in math
for the sy 2008-2009
Grade s Fre que nc y (f)
68 1
73 1
74 4
75 3
76 1
77 1
78 6
79 7
80 6
81 7
82 2
86 3
89 2

5. Grouped data
1 st term grades of iii-reverence in math
for the sy 2008-2009
Grade s Fre que nc y (f) Clas s mark fx Cumulative
x fre que nc y
cf
65-69 1 67 67 1
70-74 5 72 360 6
75-79 18 77 1386 24
80-84 15 82 1230 39
85-89 5 87 435 44

6. Presentation of data
Fo r g ro upe d data :
histogram

7. Presentation of data
Fo r g ro upe d data :
Frequency polygon

8. Presentation of data
Fo r g ro upe d data :
ogive

9. Presentation of data
Fo r ung ro upe d data :
Line graph

10. Presentation of data
Fo r ung ro upe d data :
bar graph

11. Presentation of data
Fo r ung ro upe d data :
Pie chart

12. Presentation of data
Fo r ung ro upe d data :
pictograph

13. Grouped data
To s o lve fo r the me an
Divide the sum of the product of all the class
m arks and frequency by the sum of all the
frequency.

14. Grouped data
In s ymbo ls :
x=
∑ fx
∑f
x ∑ fx
whe re is the me an , is the s um o f all the
pro duc tf o f the fre que nc y and the c las s mark and is the s um
∑
o f all the fre que nc y .

15. Grouped data
1 st term grades of iii-reverence in math
for the sy 2008-2009
Grade s Fre que nc y (f) Clas s mark fx Cumulative
x fre que nc y
cf
65-69 1 67 67 1
70-74 5 72 360 6
75-79 18 77 1386 24
80-84 15 82 1230 39
85-89 5 87 435 44

16. Grouped data
To s o lve fo r the me dian
1. Locate the m edian class (the interval that
contains the m iddle point of the
observation). This is found through the
cum ulative frequency colum n.

17. Grouped data
1 st term grades of iii-reverence in math
for the sy 2008-2009
Grade s Fre que nc y (f) Clas s mark fx Cumulative
x fre que nc y
cf
65-69 1 67 67 1
70-74 5 72 360 6
75-79 18 77 1386 24
80-84 15 82 1230 39
85-89 5 87 435 44

18. Grouped data
1 st term grades of iii-reverence in math
for the sy 2008-2009
Grade s Fre que nc y (f) Clas s mark fx Cumulative
x fre que nc y
cf
65-69 1 67 67 1
70-74 5 72 360 6
75-79 18 77 1386 24
80-84 15 82 1230 39
85-89 5 87 435 44

19. Grouped data
To s o lve fo r the me dian
2. Identify the low class boundary of the
er
m edian class, the cum ulative frequency of
the interval before the m edian class and
the class w idth.

20. Grouped data
1 st term grades of iii-reverence in math
for the sy 2008-2009
Grade s Fre que nc y (f) Clas s mark fx Cumulative
x fre que nc y
cf
65-69 1 67 67 1
70-74 5 72 360 6
75-79 18 77 1386 24
80-84 15 82 1230 39
85-89 5 87 435 44

21. Grouped data
In s ymbo ls :
∑ f 
w
 2 − cf b 

median = Lm +  
fm
L
w whe re is m lo we r limit o f the me dian c las s , is
the
∑ the fre que nc y , is the
f
the c las s width , is the s um o f all
cf b
c umulative fre que nc y o f the inte rval be fo re the me dian c las s
fm
and is the fre que nc y o f the me dian c las s .

22. Grouped data
1 st term grades of iii-reverence in math
for the sy 2008-2009
Grade s Fre que nc y (f) Clas s mark fx Cumulative
x fre que nc y
cf
65-69 1 67 67 1
70-74 5 72 360 6
75-79 18 77 1386 24
80-84 15 82 1230 39
85-89 5 87 435 44

23. Grouped data
To s o lve fo r the mo de
Sim identify the m
ply idpoint of the interval
w the largest num of class
ith ber
frequency.

24. Grouped data
1 st term grades of iii-reverence in math
for the sy 2008-2009
Grade s Fre que nc y (f) Clas s mark fx Cumulative
x fre que nc y
cf
65-69 1 67 67 1
70-74 5 72 360 6
75-79 18 77 1386 24
80-84 15 82 1230 39
85-89 5 87 435 44

25. Grouped data
1 st term grades of iii-reverence in math
for the sy 2008-2009
Grade s Fre que nc y (f) Clas s mark fx Cumulative
x fre que nc y
cf
65-69 1 67 67 1
70-74 5 72 360 6
75-79 18 77 1386 24
80-84 15 82 1230 39
85-89 5 87 435 44

26. Exam 2
ple
the no. of hours spent by the students in doing their hom orks
ew
Time (h ) Fre que nc y o f Clas s mark fx Cumulative
s tude nts x fre que nc y
(f) cf
0-2 2 1 2 2
3-5 13 4 52 15
6-8 20 7 140 35
9-11 11 10 110 46
12-14 4 13 52 50

27. synthesis
1. Recite the form for solving the m
ula ean,
m edian and m ode.
2. Howcan w use this lesson in real life?
e
3. discuss w ay/s on howyou can easily
m orize the form for solving the
em ula
m ean, m edian and m ode?

28. assignment
Solve for the m ean, median and mode:(1/2
sheet cw ip)
Clas s Fre que nc y (f) Clas s mark fx Cumulative
inte rvals x fre que nc y
cf
15-24 2 19.5 39 2
25-34 3 29.5 88.5 5
35-44 4 39.5 158 9
45-54 6 49.5 297 15
55-64 5 59.5 297.5 20