3. ⮚ Branch of mathematics deals with the study of collecting, analyzing,
interpreting, organizing and presenting data in a particular manner.
⮚ Areas Where Statistics Is Used
Weather Forecasting
Health Insurance
Manufacturing
Sales Tracking
Medical Studies
Urban Planning
⮚ Statistics : Latin Word Means Political
State
4. Topic : Collection of Data
Primary Data
Collected form the first hand experience
Secondary Data
Common Sources – Books, Personal Sources, Journals, Newspapers, Web series,
Govt. Records etc.
5. Topic : Presentation of Data
Ungrouped Data
(Raw Data)
Grouped Data
10-20, 20-30, 30-40.........} Class Intervals
10
20
▪ Lower Limit Upper Limit
Class Size = Upper limit – lower limit
Class Mark = Mid-point of class interval
In this chapter, we’ll learn to calculate Mean, Median, Mode of Grouped
Data
6. Topic : Mean
Sum of All Observations
Arithmetic Mean =
Total No. Of Observations
Written as
Scores of a cricketers in his 10 matches is as follows :-
25, 45, 50, 70, 30, 30, 50, 50, 90, 0
Mean = 25 + 45 + 50 + 70 + 30 + 30 + 50 +
50 + 90 + 0
10
8. 3
1
26
28
25
A
B
C
D
Topic : Mean
The mean of six numbers is 21. If one number is excluded, then their mean
is 19, the excluded number is
[CBSE 2009]
9. 28
3
1
43
3
7
A
B
C
D
The mean of 9 observations is 36. If the mean of the first 5 observations is
32 and that of the last 5 observations is 39, then the fifth observation
is
Topic : Mean
10. The average monthly income (in )
₹ of certain agricultural workers is S
and that of other workers is T
. The number of agricultural workers are 1
1
times that of other workers. Then the average monthly income (in )
₹ of
all the
workers is
.
Topic : Mean
A
B
C
D
[ICSE
2020]
11. Topic : Method To Find Mean
Direct
Method
Assumed
Mean Method
Step Deviation
Method
12. Topic : Direct Method
Prepare a table having columns
of
Class Interval
Mid-Point (xi)
(Class
Marks)
Frequency (fi) Product of Fixi
13. Candidates of four schools appear in a mathematics test. The data is as
follows:
the average score of the candidates of all the four schools is 66, then find
the number of candidates that appeared from school III.
Topic : Mean
Schools No.of
Candidates
Average Score
I 60 75
II 48 80
III ? 55
IV 40 50
A B
C D
5
1
52 50 53
14. 3
4
5
6
A
B
C
D
The numbers 3, 5, 7 and 9 have their respective frequencies x – 2, x+2, x
– 3, and x + 3. If the mean is 6.5, then the value of x is
Topic : Mean
15. Topic : Assumed Mean Method
(used when class-mark is large)
Prepare a table having columns
of
Class Interval Class Marks (xi) Frequency (fi)
Deviation
(di=xi-a)
fi di
Preferably chose among the
central values of Class-Marks
Column)
This ‘a’ is our assumed
mean
16. ⮚ Try to find the mean of above question data using this
method.
You’ll be amazed, answer is same..Yeahhh....
17. Topic : Step Deviation Method
⮚ Shortcut method for computing mean. (used when values of both xi & fi are
large)
⮚ Prepare a table having columns of
Class
Intervals
Class Marks
(xi)
Frequency
(fi)
Deviation
(di=xi-a)
fi ui
19. Topic : Points To Be Noted
⮚ If 𝑥̅ is mean of a,b,c,d. Each one is increased by some real no. (k ≠ o) then
mean
will also be increased by k i.e. new mean will be
20. ⮚ If 𝑥̅ is mean of p,q,r
,s,t. Each one is multiplied by some real no. (c ≠ o) then new
mean will be c 𝑥
⮚ Similarly mean of a, b, c, d, → 𝑥̅ then mean of
will be
21. Mean of l,u,c,k is 𝑥
then
mean
of
l – a, u
– a, c –
a, k – a
will
be 𝑥̅ - a
where a
is any
real no.
24. Topic : Mode
⮚ 𝑙 – Lower Limit
⮚ h – Class size
⮚ f1 – freq. of modal class
⮚ f2 – freq of class following modal class
⮚ fo – freq of class preceding the modal
class
⮚ Value of observation having the maximum frequency
In case of
grouped
frequency
distribution
Modal Class – Class with maximum frequency
25. Topic : Mode
When the teacher
says – Almost
students scored
65 marks in the
test
27. Topic : Median – Positional Average
⮚ Middle most value of data, when arranged in ascending order or descending
order
Median
▪ 7 Observation arranged in Ascending Order
28. Average of these two will be
median
▪ Ten Observation Arranged in Ascending Order
31. The following frequency distribution gives the daily wages of labourers in
.
₹ Find the median of the following distribution
Topic : Median
Wages (inRs) No. of labourers
200-300 3
300-400 5
400-500 20
500-600 10
600-700 6
32. 4
5
6
7
A
B
C
D
The mean of 1
, 3, 4, 5, 7, 4 is m. The numbers 3, 2, 2, 4, 3, 3, p have
mean m – 1 and median q. Then, p + q =
Topic : Median
33. 7
2
7
3
76
75
A
B
C
D
The given numbers are arranged in the descending order : 108, 94, 88,
82, 82, x + 7, x- 7, 60, 58, 42, 39. If the median is 73, then the value of x
is
Topic : Median
34. Cumulative Frequency
Less Than Type More Than Type
⮚ Frequency of all preceeding
class –intervals are added
⮚ Frequencies of all succeeding
classes are added
35. Topic : Points To Be Noted
⮚ If in some problems, median class happens to be first class – interval then cf of
proceeding class be taken as zero.
⮚ Median can be calculated graphically which mean can’t be
⮚ Relation between the three central tendencies.
Mode = 3 Median – 2 Mean
38. Topic : Graphical Representation of
Cumulative Frequency Distribution
⮚ Plotted between cumulative frequencies and upper or lower limits of
class intervals
⮚ Known as cumulative frequency curve or ogives
Two Types of Ogives
Less Than Ogives More than Ogives
39. Topic : Methods For Finding Median Using Curves
Method – I
Value of abscissa corresponding to 𝑁/2 value as ordinate on the curve. (either less
than or More than)
Method – II
X-coordinate of the point of intersection of the two ogives (less than or more than)
will give the value of median.
![3
1
26
28
25
A
B
C
D
Topic : Mean
The mean of six numbers is 21. If one number is excluded, then their mean
is 19, the excluded number is
[CBSE 2009]](https://izqule7twkl7vq3ljkxejyz-s-a2157.bj.tsgdht.cn/pptstatisticsoneshot-250628071758-843a9399/85/PPTpresentation_Statistics_One-Shot-pptx-8-320.jpg)
![The average monthly income (in )
₹ of certain agricultural workers is S
and that of other workers is T
. The number of agricultural workers are 1
1
times that of other workers. Then the average monthly income (in )
₹ of
all the
workers is
.
Topic : Mean
A
B
C
D
[ICSE
2020]](https://izqule7twkl7vq3ljkxejyz-s-a2157.bj.tsgdht.cn/pptstatisticsoneshot-250628071758-843a9399/85/PPTpresentation_Statistics_One-Shot-pptx-10-320.jpg)
![1
7
1
8
1
3
A
B
C
D
Homework
The mean and median of a distribution are 14 and 15 respectively.
The value of mode is:
[ICSE 2020]
16](https://izqule7twkl7vq3ljkxejyz-s-a2157.bj.tsgdht.cn/pptstatisticsoneshot-250628071758-843a9399/85/PPTpresentation_Statistics_One-Shot-pptx-41-320.jpg)
![Find the mode of the following
distribution:
Homework
[CBSE
2020]
Classes: 0-20 20-40 40-60 60-80 80-100
Frequency: 10 8 12 16 4](https://izqule7twkl7vq3ljkxejyz-s-a2157.bj.tsgdht.cn/pptstatisticsoneshot-250628071758-843a9399/85/PPTpresentation_Statistics_One-Shot-pptx-42-320.jpg)
![From the following distribution, find the
median:
Homework
[CBSE
2018]
Classes: 500-600 600-700 700-800 800-900
Frequency: 36 32 32 20](https://izqule7twkl7vq3ljkxejyz-s-a2157.bj.tsgdht.cn/pptstatisticsoneshot-250628071758-843a9399/85/PPTpresentation_Statistics_One-Shot-pptx-43-320.jpg)
![The table below shows the salaries of 280
persons.
Homework
[ICSE
2018]
Salary (In thousand )
₹ No. of Persons
5-10
10-15
15-20
20-25
25-30
30-35
35-40
40-45
45-50
49
133
63
15
6
7
4
2
1](https://izqule7twkl7vq3ljkxejyz-s-a2157.bj.tsgdht.cn/pptstatisticsoneshot-250628071758-843a9399/85/PPTpresentation_Statistics_One-Shot-pptx-44-320.jpg)
