Introduction
Definition: Comprehension means 'understanding' whatever you read and answering questions related to it. Answering question to a given passage depends actually on the following abilities of a student.
(i) How good you are in understanding the meaning of the entire passage;
(ii) In finding the answer in the passage; (iii) Command you have in English Language. 
Histogram
It.is a graphical representation of frequency distribution in which class-intervals are taken along x - axis and frequency are taken along y - axis.
Frequency Polygon
The curve obtained by joining midpoints of successive tops of the rectangles of a histogram represents frequency polygon.
Bar Graph
It is the most simple and widely used chart (or graph).
In this representation, bars are drawn with some width at each column. The scale showing the heights of the bars is represented along with the axis and in proportion to the frequency. 
Mode
It is defined as the value of variable which has highest frequency. The mode of data 10, 12, 14, 10, 14, 20, 30, 10, 25, 23, 10, 12 is 10, because it occurs most of the time. In the class - interval 1- 5, 5 is called upper limit and 1 is the lower limit.
David throws a die 10 times and the following are outcomes 2, 5, 6, 6, 1, 5, 4,1, 4, 6, 5. The mean of the above observation is:
(a) 3
(b) 4.5
(c) 5
(d) 45
(e) None of these
Answer: (b)
Explanation
\[mean=\frac{sum\,of\,observation}{Total\,number\,of\,observation}\]
\[=\frac{2+5+6+6+1+5+4+1+4+6+5}{10}=4.5\]
If a, b, c, d, and e are five consecutive odd numbers, then their mean is:
(a) b
(b) c
(c) e
(d) a
(e) None of these
Answer: (b)
Explanation
Let the consecutive odd numbers a, b, c, d and e are as follows
\[a=2x+1,b=2x+3,c=2x+5,\text{ }d=2x+7\]and\[~e=2x+9\]
\[\frac{(2x+1)+(2x+3)+(2x+5)+(2x+7)+(2x+9)}{5}=c\]
The median of first five consecutive even numbers p, q, r, s and t is:
(a) \[(q+s)\div 2\]
(b) p
(c)\[~(p+q)\div 2\]
(d) \[(p+q+r)\div 3\]
(e) None of these
Answer: (a)
The mean, median and mode of the following data are respectively: 5, 17, 21, 21, 7,13,1, 3
(a) 10, 10, 21
(b) 11, 21, 2
(c) 11, 10, 21
(d) 11, 10, 5
(e) None of these
Answer: (c)
Stuart performs his project work on the topic that the number of students likes soft drink of different flavours in a school. After collecting the data he wants to know the most flavoured soft drink which is liked by most of the students. Which central tendency makes his wish true?
(a) Mean
(b) Row data
(c) Median
(d) Mode
(e) None of these
Answer: (d)
Mean of Grouped Data
Mean \[=\frac{\sum\limits_{i=\,1}^{n}{{{x}_{i}}{{f}_{i}}}}{\sum\limits_{i=1}^{n}{{{f}_{i}}}}\]where\[=\sum\limits_{i=1}^{n}{{{x}_{i}}{{f}_{i}}={{x}_{i}}{{f}_{i}}+{{x}_{2}}{{f}_{2}}+{{x}_{3}}{{f}_{3}}+{{x}_{4}}{{f}_{4}}+........}\]
And \[\sum\limits_{i=1}^{n}{{{f}_{i}}={{f}_{1}}+{{f}_{2}}+{{f}_{3}}+{{f}_{4}}+}.......\]
The difference between upper and lower limit of a class interval is called class size.
Range
The difference between maximum and minimum value of the observation is called range.
Class Interval
A data can be classified into different intervals for convenience to analyzing it. The interval in which variates lies is called class interval.
Class Mark
C.M. \[=\frac{1}{2}\](lower limit + upper limit) 
Median
Step 1: Arrange the given data either in ascending or descending order
Step 2: Count the number of observation.
Step 3: If the number of observation is odd, then \[median={{\left( \frac{n+1}{2} \right)}^{th}}observation\]
Step 4: If the number of observation is even, then
\[\frac{median={{\left( \frac{n}{2} \right)}^{th}}observation+{{\left( \frac{n}{2}+1 \right)}^{th}}observation}{2}\]
Find the median of 4, 5, 3, 3, 2, 1, 5
Solution:
Arrange the data in ascending order, we get 1, 2, 3, 3, 4, 5, 5 Here the number of observation is 7 which is odd number that is Median \[={{\left( \frac{n+1}{2} \right)}^{th}}\] observation
\[={{\left( \frac{7+1}{2} \right)}^{th}}\] observation i.e. the fourth observation. Therefore, median is 3
Find the median of first six prime number
Solution:
First six prime numbers are 2, 3, 5, 7, 11, 13
\[\frac{median={{\left( \frac{6}{2} \right)}^{th}}observation+{{\left( \frac{6}{2}+1 \right)}^{th}}observation}{2}\]
\[=\frac{third\,observation+fourth\,obsercation}{2}=\frac{5+7}{2}=6\] 
Mean
Mean is defined as the ratio of sum of observation to total number of observation.
or, 
Find the mean of first five even numbers
Solution:
First five even numbers are 2, 4, 6, 8, 10
Introduction
Modern society is information oriented. Every person wants numeric information of different fields of the society like the marks obtained in a particular subject by the students, five year plans etc. Statistics is a branch of Mathematics which deals with the process, analyzing and interpreting the data. Data is defined as the particular information in numeric form.
Primary Data
Primary data means the data that have been collected by collector for some purpose. It means when an authorized organization or an investigator or an enumerator collects the data for the use to himself or with the help or an institution or an expert then the data collected is called primary data.
Secondary Data
Secondary data is data that have been collected by others and used by someone eIse. It means that after performing statistical operations of primary data the result become useful to others is called the secondary data.
Raw Data
Raw data (or ungrouped data) is the data which is not arranged in any particular fashion or pattern. It is the original form of the data. e.g. The height of 5 students in a class is 123 cm, 120 cm, 129 cm, 135 cm, 121 cm.
Grouped Data
Grouped data is the data which is arranged in classes or group to bring out salient mature of the group. Firstly it may arrange in ascending or descending order and then divide into groups.
Variable
A measurable characteristic is called a variable or variate eg. Age, height, income
Attribute
A non - measurable characteristic is called an attribute.
Frequency
The number of times a particular observation occurs in a data is called frequency. In other words, it is number of times an observation occurs, e.g in a data 1, 2, 3,4,5, 2, 1, 3, 2, 4, 6, 5, 2, 3, 2, 1, 2, 5. The frequency of 2 in the above data is 6 because it occurs 6 times in the observation.
The run scored by 11 member of a cricket team are: 34, 0, 25, 34, 67, 73, 67,1, 0,71
Represent the given data by using tally marks.
Solution:
| Scores | Tally mark | more...
 Circumference and area of a Circle
The boundary of the circle is called circumference.
Circumference of a circle \[=2\pi r.\]
Find the circumference of a circle whose diameter is 4.2 cm.
(a) 11.1 cm
(b) 112.2cm
(c) 13.3cm
(d) 13.2cm
(e) None of these
Answer: (d)
Explanation
Diametre of circle = 4.2 cm
\[\therefore \]Radius of circle = 2.1 cm
Circumference \[=2\pi r=2\times \frac{22}{7}\times 2.1=2\times 22\times 0.3=13.2cm\]
Thus the circumference of this circle = 13.2 cm.
Find the radius of circle whose circumference is 88 m.
(a) 14m
(b) 15m
(c) 120m
(d) 25m
(e) None of these
Answer: (a)
Explanation
Circumference (c) = 88 m
\[C=27\pi r=88\Rightarrow 2\times \frac{22}{7}\times r=88\]
Or \[r\frac{7\times 88}{2\times 22}=7\times 2=14\,m\]
Thus the radius of this circle = 14 m
 Find the area of a rhombus shaped field, whose each of the sides is 14 cm and the altitude is 1.6 dm.
(a) \[224c{{m}^{2}}\]
(b) \[214c{{m}^{3}}\]
(c) \[224{{m}^{2}}\]
(d) \[224c{{m}^{6}}\]
(e) None of these
Answer: (a)
Explanation
Base of rhombus = 14 cm
Altitude = 1.6 dm = 16 cm
Area of rhombus = Base \[\times \] Altitude
\[=14\times 16=224c{{m}^{2}}\]
How many tiles \[20cm\times 20cm\] each will be required to pave a footpath 1 m wide carried round the outside of a plot \[28\text{ }m\times 18m\]?
(a) 2,400
(b) 5, 2000
(c) 9,900
(d) 5, 250
(e) None of these
Answer: (a)
Explanation
Area of the outer rectangle
\[=(2,800+2\times 100)\times (1,800+\text{2}\times 100)=3,000\times 2,000\text{ }c{{m}^{2}}\]
Area of the inner rectangle \[=2,800\times 1,800\,c{{m}^{2}}\]
Area of the Footpath
\[=3,000\times 2,000-2,800\times 1,800\text{ }9,60,000\text{ }c{{m}^{2}}\]
Required number of tiles
\[=\frac{area\,of\,footpath}{area\,of\,a\,tile}=\frac{9,60,000}{20\times 20}=2,400\]
 The base of a parallelogram is twice its height. If the area of parallelogram is \[512\text{ }c{{m}^{2}}\] then find the base.
(a) \[33c{{m}^{2}}\]
(b) \[32c{{m}^{2}}\]
(c) \[40c{{m}^{2}}\]
(d) \[199c{{m}^{2}}\]
(e) None of these
Answer: (b)
A rhombus of side equal to 65 cm has an area of 2,016 cm2. Find its diagonals.
(a) 30
(b) 148
(c) 32
(d) 55
(e) None of these
Answer: (c) more...  Triangles
We know that the triangle is a closed region which is bounded by three line segments.
 Find the area of a triangle whose sides are 9 cm, 12 cm and 15 cm.
(a) 51cm3
(b) 52cm3
(c) 53cm4
(d) 54cm2
(e) None of these
Answer: (d)
Explanation
Here, a = 9 cm, b = 12 cm and c = 15 cm
\[\therefore S=\frac{a+b+c}{2}=\frac{9+12+15}{2}=\frac{36}{2}=18\]
Area\[=\sqrt{s(s-a)(s-b)(s-c)}\]\[=\sqrt{s(s-a)(s-b)(s-c)}\]
\[=\sqrt{18\text{ }\times 9\times 6\text{ }\times 3}=54\text{ }c{{m}^{2}}\]
A field in the form of a right triangle with hypotenuse 10 m and one side 8 m. Find the are a of the field.
(a)\[22{{m}^{2}}\]
(b)\[23{{m}^{2}}\]
(c)\[24{{m}^{2}}\]
(d) \[25{{m}^{2}}\]
(e) None of these
Answer: (c)
Given\[AC=10\text{ }m,\text{ }AB=8\text{ }m\]
By Pythagoras theorem, \[B{{C}^{2}}=A{{C}^{2}}-A{{B}^{2}}=100-64=36\Rightarrow BC=6\text{ }cm\]
Area of  \[=\frac{1}{2}\times BC\times AB=\frac{1}{2}\times 6\times 8=24{{m}^{2}}\]
The base of a triangular field is three times of its altitude. If the cost of .catering the field at Rs. 96 per hectare is Rs. 3600 then find the measure of the base and height.
(a) (1500m, 500m)
(b) (900 m, 300 m)
(c) (500m, 1500m)
(d) (400 m, 1200 m)
(e) None of these
Answer: (c)
The cost of cutting grass from a triangular field at Rs. 45 per 100 m2 is Rs.900. Find its height if twice the base of the triangle is 5 times the height.
(a) 30m
(b) 40m
(c) 50m
(d) 10m
(e) None of these
Answer: (b)
The area of an equilateral triangle is more...  Standard Units of Area
The inter relationship among various units of measurement of area are listed below.
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