1. To find the mean, divide the sum of the products of the class marks and frequencies by the total sum of the frequencies. 2. To find the median, locate the median class and use its lower boundary plus the class width times the median position. 3. To find the mode, identify the class with the highest frequency.

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