Question 6:
100 surnames were randomly picked up from a local telephone directory and the frequency
distribution of the number of letters in the English alphabets in the surnames was obtained as
follows:
Number of letters
14
Number of surnames
6
47
30
7 1
Question 5:
Find the following table gives the distribution of the life time of 400 neon lamps:
Life time (in hours)
Number of lamps
1500 2000
14
2000 2500
2500 3000
3000 3500
3500 4000
4000 4500
4500 5000
56
60
86
74
62
48
Find the median life time of a
Question 1:
The following frequency distribution gives the monthly consumption of electricity of 68
consumers of a locality. Find the median, mean and mode of the data and compare them.
Monthly consumption (in units)
Number of consumers
65 85
4
85 105
5
1
Question 3:
A life insurance agent found the following data for distribution of ages of 100 policy holders.
Calculate the median age, if policies are given only to persons having age 18 years onwards but
less than 60 year.
Age (in years)
Number of policy
Question 2:
If the median of the distribution is given below is 28.5, find the values of x and y.
Class interval Frequency
0 10
5
10 20
x
20 30
20
30 40
15
40 50
y
50 60
5
Total
60
Answer:
The cumulative frequency for the given data is calculated as follo
Question 4:
The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data
obtained is represented in the following table:
Length (in mm)
Number or leaves fi
118 126
3
127 135
5
136 144
9
145 153
12
154 162
5
163 171
4
17
Question 3:
The following data gives the distribution of total monthly household expenditure of 200 families
of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly
expenditure.
Expenditure (in Rs)
Number of families
Question 5:
The given distribution shows the number of runs scored by some top batsmen of the world in
one-day international cricket matches.
Runs scored
Number of batsmen
3000 4000
4
4000 5000
18
5000 6000
9
6000 7000
7
7000 8000
6
8000 9000
3
9000 10000
Question 4:
The following distribution gives the state-wise teacher-student ratio in higher secondary schools
of India. Find the mode and mean of this data. Interpret the two measures.
Number of students per teacher
Number of states/U.T
15 20
3
20 25
8
25
Question 2. The following data gives the information on the observed lifetimes (in
hours) of 225 electrical components
Lifetimes (in
0
20
40
60
80
100
hours)
20
40
60
80
100
120
Frequency
10
35
52
61
38
29
Determine the modal lifetimes of the compone
Question 9:
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy
rate.
Literacy rate (in %)
Number of cities
45 55
55 65
3
65 75
10
75 85
11
85 95
8
3
Answer:
To find the class marks, the following relation is u
Question 1:
The following table shows the ages of the patients admitted in a hospital during a year:
age (in years)
5 15
Number of patients
6
15 25
11
25 35
35 45
21
45 55
23
55 65
14
5
Find the mode and the mean of the data given above. Compare and inter
Question 8:
A class teacher has the following absentee record of 40 students of a class for the whole
term. Find the mean number of days a student was absent.
Number of
0
6
10
14
6
10
14
20
11
10
7
4
20
28
38
28
38
40
4
3
1
com.ncerthel
p
students
An
Question 5:
In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes
contained varying number of mangoes. The following was the distribution of mangoes according
to the number of boxes.
Number of mangoes
50 52
Number of bo
Question 7:
To find out the concentration of SO2 in the air (in parts per million, i.e., ppm), the data was
collected for 30 localities in a certain city and is presented below:
concentration of SO2 (in ppm)
Frequency
0.00 0.04
4
0.04 0.08
9
0.08 0.12
9
0
Question 6 The table below shows the daily expenditure on food of 25 households in a locality.
Daily expenditure (in
Rs)
100
150
200
250
300
150
200
250
300
350
4
5
12
2
2
Number of households
Find the mean daily expenditure on food by a suitable met
Question 1:
A survey was conducted by a group of students as a part of their environment awareness
program, in which they collected the following data regarding the number of plants in 20
houses in a locality. Find the mean number of plants per house.
Num
Question 3
The following distribution shows the daily pocket allowance of children of a locality.
The mean pocket allowance is Rs.18. Find the missing frequency f.
Daily pocket allowance
(in Rs)
Number of workers
11
13
15
17
19
13
15
17
19
21
7
6
9
13
Question 5. (1 + tan - sec) (1 + cot + cosec) = ?
Solution
Step 1
We need to find following product
S = (1 + tan - sec) (1 + cot + cosec)
Step 2
On multiplying each terms
S = 1 (1 + tan - sec) + cot (1 + tan - sec) + cosec (1 + tan - sec)
S = (1 + tan -
Solution
Step 1
Since sin(90-) = cos and cos(90-) = sin , expression can be rewritten as
following
=
cos210 + sin210
sin210 + cos210
+ cos(10 + ) - cos(10 + )
Step 2
=1+0=1
Question 2. If sec + tan = p, find value of tan in terms of p.
Solution
Step 1
We
Question 4:
Thirty women were examined in a hospital by a doctor and the number of heart beats per
minute were recorded and summarized as follows. Fine the mean heart beats per minute
for these women, choosing a suitable method.
Number of heart beats
per
Some problem on Units
A beg containing = 1200 gram
= 1.2 kg
Total grain = 9000 kg
Total begs = 9000/1.2
= 7500
1 Quart = (1/4) Gallon
1 Quart = * 6.5
1 Quart = 1.625 quart
1 mile = 1.60934 km
20 mile = 20* 1.60934 km
20 miles = 32.1868 km
1 meter = 39.370
Assignment 7
Forming a Quadratic Equation Whose Roots are Given
A quadratic equation whose roots are given maybe obtained by reversing the
operation of solving quadratic equations by factoring.
Example 1:
Form a quadratic equation whose roots are 2 and -3
Assignment 9
Solving Quadratic Equations by the Quadratic Formula
The third way of solving quadratic equations is by the use of a formula obtained
2
ax + bx+ c=0
by solving the general quadratic equation
a, b and c; a
0.
The method of solving
ax 2+ bx+ c=
Assignment 10
Solving Quadratic Equations by the Method of Completing the Square
Examine the following perfect square trinomials.
1. x2 + 8x + 16 = (x + 4)2
2. x2 - 10x + 25 = (x - 5)2
3. x2 + 5x + 25/4 = (x + 5/2)2
Observe that the last term in each perf
Assignment 8
Discriminant and Roots
In the quadratic formula, the quantity inside the radical sign, b 2 4ac determines
the nature of the roots of the quadratic equation. The quantity b 2 4ac is called the
discriminant of the quadratic equation
2
ax + bx+
Assignment 3
Examples:
x2 + 4x + 3 = 0
x2 + 4x = -3
x2 + 4x + 4 = -3 + 4
(x + 2)2 = 1
1.
x + 2 =
Transpose 3 to the right.
Add 4 to both sides.
The expression at the left side is
factored as the square of a binomial.
1
Extract the square roots of sides, u
Assignment 5
Equations Containing Radicals
Certain equations involving radicals lead to quadratic equations
Example 1:
5 x +6=x+ 2
5x + 6 = ( x + 2 )2
square both sides
5x + 6 = x2 + 4x + 4
expand the right side
x2 - x 2 = 0
transpose all terms to the le