#### Chapters

Chapter 2 - Banking (Recurring Deposit Account)

Chapter 3 - Shares and Dividend

Chapter 4 - Linear Inequations (In one variable)

Chapter 5 - Quadratic Equations

Chapter 6 - Solving (simple) Problems (Based on Quadratic Equations)

Chapter 7 - Ratio and Proportion (Including Properties and Uses)

Chapter 8 - Remainder and Factor Theorems

Chapter 9 - Matrices

Chapter 10 - Arithmetic Progression

Chapter 11 - Geometric Progression

Chapter 12 - Reflection

Chapter 13 - Section and Mid-Point Formula

Chapter 14 - Equation of a Line

Chapter 15 - Similarity (With Applications to Maps and Models)

Chapter 16 - Loci (Locus and Its Constructions)

Chapter 17 - Circles

Chapter 18 - Tangents and Intersecting Chords

Chapter 19 - Constructions (Circles)

Chapter 20 - Cylinder, Cone and Sphere

Chapter 21 - Trigonometrical Identities

Chapter 22 - Height and Distances

Chapter 23 - Graphical Representation

Chapter 24 - Measure of Central Tendency(Mean, Median, Quartiles and Mode)

Chapter 25 - Probability

## Chapter 24 - Measure of Central Tendency(Mean, Median, Quartiles and Mode)

#### Page 0

Draw histogram for the following distributions:

Class Interval |
0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |

Frequancy |
12 | 20 | 26 | 18 | 10 | 6 |

Draw histogram for the following distributions:

Class Interval |
10-16 | 16-22 | 22-28 | 28-34 | 34-40 |

Frequency |
15 | 23 | 30 | 20 | 16 |

Drraw histrogram for the following distributions:

Class interval |
30-39 | 40-49 | 50-59 | 60-69 | 70-79 |

Frequency |
24 | 16 | 09 | 15 | 20 |

Draw histogram ffor the following distributtions:

Class Marks |
16 | 24 | 32 | 40 | 48 | 56 | 64 |

Frequency |
8 | 12 | 15 | 18 | 25 | 19 | 10 |

Draw a cumulative frequency curve (ogive) for each of the following distributions:

Class Interval | 10 – 15 | 15 – 20 | 20 – 25 | 25 – 30 | 30 – 35 | 35 – 40 |

Frequency | 10 | 15 | 17 | 12 | 10 | 8 |

Draw a cumulative frequency curve (ogive) for each of the following distributions:

Class Interval | 10 – 19 | 20 – 29 | 30 – 39 | 40 – 49 | 50 – 59 |

Frequency | 23 | 16 | 15 | 20 | 12 |

Draw an ogive for each of the following distributions:

Marks obtained | Less than 10 | Less than 20 | Less than 30 | Less than 40 | Less than 50 |

No of students | 8 | 25 | 38 | 50 | 67 |

Draw an ogive for each of the following distributions:

Age in years (less than) |
10 | 20 | 30 | 40 | 50 | 60 | 70 |

Cumulative frequency |
0 | 17 | 32 | 37 | 53 | 58 | 65 |

Construct a frequency distribution table for the numbers given below, using the class intervals

21 – 30, 31 – 40 ………… etc.

75, 65, 57, 26, 33,44, 58, 67, 75, 78, 43, 41, 31, 21, 32, 40, 62, 54, 69, 48, 47, 51, 38, 39, 43, 61, 63, 68, 53, 56, 49, 59, 37, 40, 68, 23, 28, 36 and 47.

Use the table obtained to draw: (1) a histrogram (2) an ogive

Use the information given in the adjoining histogram to construct a frequency table.

Use this table to construct an ogive.

Class mark |
12.5 | 17.5 | 22.5 | 27.5 | 32.5 | 32.5 | 42.5 |

Frequency |
12 | 17 | 22 | 27 | 30 | 21 | 16 |

(a) From the distribution, given above, construct a frequency table.

(b) Use the table obtained in part (a) to draw: (i) a histogram, (ii) an ogive

Use graph paper for this question.

The table given below shows the monthly wages of some factory workers

(i) Using the table, calculate the cumulative frequencies of workers

(ii) Draw a cumulative frequency curve.

Use 2 cm = ₹ 500, starting the origin at ₹ 6500 on x-axis, and 2 cm = 10 workers on the y – axis.

Wages (in Rs) | 6500-7000 | 7000-7500 | 7500-8000 | 8000-8500 | 8500-9000 | 9000-9500 | 9500-10000 |

No of workers | 10 | 18 | 22 | 25 | 17 | 10 | 8 |

The following table shows the distribution of the heights of a group of factory workers:

Ht. (cm) |
150 - 155 |
155 – 160 |
160 - 165 |
165 – 170 |
170 – 175 |
175 - 180 |
180 – 185 |

No of workers: |
6 | 12 | 18 | 20 | 13 | 8 | 6 |

(i) Determine the cumulative frequencies.

(ii) Draw the ‘less than’ cumulative frequency curve on graph paper. Use 2 cm = 5 cm height on one axis and 2 cm = 10 workers on the other.

Construct a frequency distribution table for each of the following distributions

Marks (less than) | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |

Cumulative frequency | 0 | 7 | 28 | 54 | 71 | 84 | 105 | 147 | 180 | 196 | 200 |

Construct a frequency distribution table for each of the following distributions

Marks (less than) | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |

Cumulative frequency | 100 | 87 | 65 | 55 | 42 | 36 | 31 | 21 | 18 | 7 | 0 |

#### Page 0

Find the mean of the following set of numbers:

6, 9, 11, 12 and 7

Find the mean of the following set of numbers:

11, 14, 23, 26, 10, 12, 18 and 6

Marks obtained (in mathematics) by 9 student are given below

60, 67, 52, 76, 50, 51, 74, 45 and 56

find the arithmetic mean

Marks obtained (in mathematics) by 9 student are given below:

60, 67, 52, 76, 50, 51, 74, 45 and 56

if marks of each student be increased by 4; what will be the new value of arithmetic mean.

Find the mean of the natural numbers from 3 to 12.

Find the mean of 7, 11, 6, 5, and 6

If each number given in (a) is diminished by 2, find the new value of mean.

If the mean of 6, 4, 7, ‘a’ and 10 is 8. Find the value of ‘a’

The mean of the number 6, ‘y’, 7, ‘x’ and 14 is 8. Express ‘y’ in terms of ‘x’.

The age of 40 students are given in the following table :

Age (in yrs) | 12 | 13 | 14 | 15 | 16 | 17 | 18 |

Frequency | 2 | 4 | 6 | 9 | 8 | 7 | 4 |

If 69.5 is the mean of 72, 70, ‘x’, 62, 50, 71, 90, 64, 58 and 82, find the value of ‘x’.

The following table gives the hights of plants in centimeter. If the mean height if plants is 60.95 cm; find the value of `f`.

Height (cm) | 50 | 55 | 58 | 60 | 65 | 70 | 71 |

no of plants | 2 | 4 | 10 | f | 5 | 4 | 3 |

From the data given below . calculate the mean wage, correct to the nnearst rupee.

category |
A |
B |
C |
D |
E |
F |

Wages (Rs,day)(x) |
50 | 60 | 70 | 80 | 90 | 100 |

no.of workers |
2 | 4 | 8 | 12 | 10 | 6 |

(1) If the number of workers in each category is doubled, , what would be the new mean wage?

(2) If the wages per day in each category are incresed by 60% what is the new mean wages?

(3) If the number of workers in each caategory is doubled is and the wages per day worker are reduced by 40%, what would be the new mean wage?

The content of 100 match boxes were checked to detemine the number of matches they contained .

no of matches |
35 | 36 | 37 | 38 | 39 | 40 | 41 |

no of boxes |
6 | 10 | 18 | 25 | 21 | 12 | 8 |

(1) Calculate, correct to one decimal place, the means number of matches per box .

(2) Determine how many extra matches would have to be added to the the total contents of the total content of the 100 boxes to bring the mean up to exactly 39 matches.

#### Page 0

The following table givens the age of 50 student of a class . find the arithmetic mean of thier agges.

Age- Years |
16-18 |
18-20 |
20-22 |
22-24 |
24-26 |

No.of students |
2 | 7 | 21 | 17 | 3 |

The following table given the weekly wages of workers in a factory.

Weekly Wages |
No.of workers |

50-55 | 5 |

55-60 | 20 |

60-65 | 10 |

65-70 | 10 |

70-75 | 9 |

75-80 | 6 |

80-85 | 12 |

85-90 | 8 |

Calculate the mean by using:

Direct Method

c

c

c Weekly wages (Rs) |
No.of workers |

50-55 | 5 |

55-60 | 20 |

60-65 | 10 |

65-70 | 10 |

70-75 | 9 |

75-80 | 6 |

80-85 | 12 |

85-90 | 8 |

Calculate the mean by ussing:

Short-Cut method

The following are the marks obtained by 70 boys in a class test:

Marks | No. of boys |

30-40 | 10 |

40-50 | 12 |

50-60 | 14 |

60-70 | 12 |

70-80 | 9 |

80-90 | 7 |

90-100 | 6 |

Calculate the mean by :

Short - cut method

The following are the marks obtained by 70 boys in a class test:

Marks | No. of boys |

30-40 | 10 |

40-50 | 12 |

50-60 | 14 |

60-70 | 12 |

70-80 | 9 |

80-90 | 7 |

90-100 | 6 |

Calculate the mean by :

Step - deviation method

Find mean by step- deviation method:

C.i | 63-70 | 70-77 | 77-84 | 84-91 | 91-98 | 98-105 | 105-112 |

Freq | 9 | 13 | 27 | 38 | 32 | 16 | 15 |

The mean of the following distribution is `21 1/7 `. find the value of `f`

C.I | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |

Freq | 8 | 22 | 31 | f | 2 |

Using step- deviation method , calculate the mean marks of the following distribution.

C.I | 50-55 | 55-60 | 60-65 | 65-70 | 70-75 | 75-80 | 80-85 | 85-90 |

Frequency | 5 | 20 | 10 | 10 | 9 | 6 | 12 | 8 |

Using the information given in the adjoining histogram, calculate the mean.

If the mean of the following obseervations is 54, find the value of `p`

Class |
0-20 | 20-40 | 40-60 | 60-80 | 80-100 |

Frequency |
7 | p | 10 | 9 | 13 |

The mean of the folowing is 62.8 and the sum of all the frequencies is 50. find the missing frequency `f_1 and f_2`

Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 |

Freq | 5 | `f_1` | 10 | `f_2` | 7 | 8 |

#### Page 0

A student got the following marks in 9 questions of a question paper.

3, 5, 7, 3, 8, 0, 1, 4 and 6.

Find the median of these marks.

The weights (in kg) of 10 students of a class are given below:

21, 28.5, 20.5, 24, 25.5, 22, 27.5, 28, 21 and 24.

Find the median of their weights.

The marks obtained by 19 students of a class are given below:

27, 36, 22, 31, 25, 26, 33, 24, 37, 32, 29, 28, 36, 35, 27, 26, 32, 35 and 28. Find:

median

The marks obtained by 19 students of a class are given below:

27, 36, 22, 31, 25, 26, 33, 24, 37, 32, 29, 28, 36, 35, 27, 26, 32, 35 and 28. Find:

lower quartile

The marks obtained by 19 students of a class are given below:

27, 36, 22, 31, 25, 26, 33, 24, 37, 32, 29, 28, 36, 35, 27, 26, 32, 35 and 28. Find:

upper quartile

The marks obtained by 19 students of a class are given below:

27, 36, 22, 31, 25, 26, 33, 24, 37, 32, 29, 28, 36, 35, 27, 26, 32, 35 and 28. Find:

interquartile range

From the following data, find:

Median

25, 10, 40, 88, 45, 60, 77, 36, 18, 95, 56, 65, 7, 0, 38 and 83

From the following data, find:

Upper quartile

25, 10, 40, 88, 45, 60, 77, 36, 18, 95, 56, 65, 7, 0, 38 and 83

From the following data, find:

Inter-quartile range

25, 10, 40, 88, 45, 60, 77, 36, 18, 95, 56, 65, 7, 0, 38 and 83

The ages of 37 students in a class are given in the following table:

Age (in year) |
11 | 12 | 13 | 14 | 15 | 16 |

Frequency |
2 | 4 | 6 | 10 | 8 | 7 |

The weight of 60 boys are given in the following distribution table

Weight (kg) |
37 | 38 | 39 | 40 | 41 |

No.of boys |
10 | 14 | 18 | 12 | 6 |

Find

(1) median

(2) lower quartile

(3)Upper quartile

(4) Interquatile range

Estimate the median for the given data by drawing an ogive:

Class |
0-10 | 10-20 | 20-30 | 30-40 | 40-50 |

Frequency |
4 | 9 | 15 | 14 | 8 |

By drawing an ogive, estimate the following frequency distribution:

Weight (kg) | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 |

No.of boys | 11 | 25 | 12 | 5 | 2 |

From the following cumulative frequency table , find :

Median

Lower quartile

Upper quaetile

Marks (less than ) |
10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |

Cumulative frequency |
5 | 24 | 37 | 40 | 42 | 48 | 70 | 77 | 79 | 80 |

In a school, 100 pupils have heights as tabulate below:

Height (in cm ) | No. of pupils |

121-130 | 12 |

131-40 | 16 |

141-150 | 30 |

151-160 | 20 |

161-170 | 14 |

171-180 | 8 |

Find the median height by drawing an ogive.

Attempt this question on a graph paper. The table shows the distribution of marks gained by a group of 400 students in an examination.

Marks (Less than ) |
10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |

No.of student | 5 | 10 | 30 | 60 | 105 | 180 | 270 | 355 | 390 | 400 |

Using scaie of 2cm to represent 10 marks and 2 cm to represent 50 student, plot these point and draw a smooth curve though the point

Estimate from the graph :

(1)the midian marks

(2)the quartile marks

Attempt this question on graph paper.

Age (yrs ) |
5-15 | 15-25 | 25-35 | 35-45 | 45-55 | 55-65 | 65-75 |

No.of casualties |
6 | 10 | 15 | 13 | 24 | 8 | 7 |

(1)Construct the 'less than' Cumulative frequency curve for the above data. using 2 cm =10 years on one axis and 2 cm =10 casualties on the other.

(2)From your graph determine :

(a)the median

(b)the lower quartile

#### Page 0

Find the mode of the following data:

7, 9, 8, 7, 7, 6, 8, 10, 7 and 6

Find the mode of the following data:

9, 11, 8, 11, 16, 9, 11, 5, 3, 11, 17 and 8

The following table shows the frequency distribution of heights of 51 boys:

Height (cm) |
120 | 121 | 122 | 123 | 124 |

Frequency |
5 | 8 | 18 | 10 | 9 |

find the mode of heights.

Find the mode of following data, using a histogram:

Class |
0-10 | 10-20 | 20-30 | 30-40 | 40-50 |

Frequency |
5 | 12 | 20 | 9 | 4 |

The folloeing table shows the expenditure of 60 boys on books. find the mode of their expenditure:

Expenditure (Rs) | No.of students |

20-25 | 4 |

25-30 | 7 |

30-35 | 23 |

35-40 | 18 |

40-45 | 6 |

45-50 | 2 |

The mean of 1, 7, 5, 3, 4 and 4 is m. The numbers 3, 2, 4, 2, 3, 3 and p have mean m-1 and median q. Find p and q.

Find the median and mode for the set of numbers:

2, 2, 3, 5, 5, 5, 6, 8 and 9

A boy scored following marks in various class tests during a term; each test being marked out of 20.

15, 17, 16, 7, 10, 12, 14, 16, 19, 12 and 16

What are his modal marks?

A boy scored following marks in various class tests during a term; each test being marked out of 20.

15, 17, 16, 7, 10, 12, 14, 16, 19, 12 and 16

What are his median marks?

A boy scored following marks in various class tests during a term; each test being marked out of 20.

15, 17, 16, 7, 10, 12, 14, 16, 19, 12 and 16

What are his total marks?

A boy scored following marks in various class tests during a term; each test being marked out of 20.

15, 17, 16, 7, 10, 12, 14, 16, 19, 12 and 16

What are his mean marks?

Find the mean, median and mode of the following marks obtained by 16 students in a class test marked out of 10 marks.

0, 0, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 6, 6, 7 and 8.

At a shooting competition the score of a competitor were as given below

Score | 0 | 1 | 2 | 3 | 4 | 5 |

No.of shots | 0 | 3 | 6 | 4 | 7 | 5 |

(1)What was his modal score?

(2) What was his median score?

(3) What was his total score ?

(4) What was his mean score?

#### Page 0

The following distribution represents the height of 160 students of a school.

Height (in cm) |
No. of Students |

140 – 145 | 12 |

145 – 150 | 20 |

150 – 155 | 30 |

155 – 160 | 38 |

160 – 165 | 24 |

165 – 170 | 16 |

170 – 175 | 12 |

175 – 180 | 8 |

Draw an ogive for the given distribution taking 2 cm = 5 cm of height on one axis and 2 cm = 20 students on the other axis. Using the graph, determine:

(1) The median height.

(2) The interquartile range.

(3) The number of students whose height is above 172 cm.

The following table given the weekly of workers in a factory:

Weekly wages (in Rs) |
No.of workers |

50-55 | 5 |

55-60 | 20 |

60-65 | 10 |

65-70 | 10 |

70-75 | 9 |

75-80 | 6 |

80-85 | 12 |

85-90 | 8 |

Calcculate: (1)the mean, (2) the model class, (3) th number of workers getting weekly qages below Rs. 80 and (4) the number of workers getting Rs . 65 or more but less than Rs.85 as weekly wages.

Draw an ogive for the data given beelow and from the graph determine:

(1) the median marks

(2) the number of students who obtained more than 75% marks

Marks |
No.of students |

0-9 | 5 |

10-19 | 9 |

20-29 | 16 |

30-39 | 22 |

40-49 | 26 |

50-59 | 18 |

60-69 | 11 |

70-79 | 6 |

80-89 | 4 |

90-99 | 3 |

The marks of 200 students in a test were recorded as follows:

Marks |
No. of students |

10-19 | 7 |

20-29 | 11 |

30-39 | 20 |

40-49 | 46 |

50-59 | 57 |

60-69 | 37 |

70-79 | 15 |

80-89 | 7 |

Construct the cumulative frequency table. Drew the ogive and use it too find:

(1) the median and

(2) the number of student who score more than 35% marks.

In a malaria epidemic, the number of cases diagnosed were as follows:

Date july | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

num | 5 | 12 | 20 | 27 | 46 | 30 | 31 | 18 | 11 | 5 | 0 | 1 |

on what days do the mode and upper and lower quartiles occur?

The marks of 20 students in a test were as follows:

2, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19 and 20.

Calculate:

(i) the mean (ii) the median (iii) the mode

The marks obtained by 120 students in a mathematics test is given below:

Dr

Marks |
No.of students |

0-10 | 5 |

10-20 | 9 |

20-30 | 16 |

30-40 | 22 |

40-50 | 26 |

50-60 | 18 |

60-70 | 11 |

70-80 | 6 |

80-90 | 4 |

90-100 | 3 |

Draw an ogive for the given distributions on a graph sheet. use a suitable scale for your ogive. use your ogive to estimate:

the median

the number of student who obtained more than 75% in test.

the number of students who did not pass in the test if the pass percentage was 40.

the lower quartile

find the mean for the following frequency distribution:

C.I | 0-50 | 50-100 | 100-150 | 150-200 | 200-250 | 250-300 |

Freq | 4 | 8 | 16 | 13 | 6 | 3 |

Draw a histogram and hence estimate the mode for the following frequency distribution:

Class |
0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |

Freq |
2 | 8 | 10 | 5 | 4 | 3 |

For the following set of data, find the median:

10, 75, 3, 81, 17, 27, 4, 48, 12, 47, 9 and 15.

Using a graph paper, draw an ogive for the following distribution which shows a record of the width in kilograms of 200 students.

Weight |
Frequency |

40-45 | 5 |

45-50 | 17 |

50-55 | 22 |

55-60 | 45 |

60-65 | 51 |

65-70 | 31 |

70-75 | 20 |

75-80 | 9 |

Use your ogive to estimate the following :

(1) The percentage of student weighning 55 kgor more

(2) The weight above the heavist 30% of the student fail

(3) The number of students who are

(a) underweight

(b) overweight

If 55.70 kg considered as sandard weight.

The daily wages of 80 workers in a building project are given below :

Wages (Rs) |
No.of workers |

30-40 | 6 |

40-50 | 10 |

50-60 | 15 |

60-70 | 19 |

70-80 | 12 |

80-90 | 8 |

90-100 | 6 |

100-110 | 4 |

Using graph paper, draw an ogive for the above distribution. Use your ogive, to estimate :

(1)the mediam wages of workers

(2)the percentage of workers who earn more than Rs 75 a day.

(3)the upper quartile wages of the workers

(4)the lower quartile wages of the workers

(5)Inter quartile range

The distribution, given below, shows the marks obtained by 25 students in an aptitude test. find the mean, median and mode of the distribution.

Marks obtained |
5 | 6 | 7 | 8 | 9 | 10 |

No.of students |
3 | 9 | 6 | 4 | 2 | 1 |

The mean of the following distribution in 52 and the frequency of class interval 30-40 'f' find f

C.I |
10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |

freq |
5 | 3 | f | 7 | 2 | 6 | 13 |

The monthly income of a group of 320 employee in a company is given below

Monthly income (thousands) | No.of employee |

6-7 | 20 |

7-8 | 45 |

8-9 | 65 |

9-10 | 95 |

10-11 | 60 |

11-12 | 30 |

12-13 | 5 |

Draw an ogive of the distribution on a graph paper taking 2 cm =50 employee on the other axis from the graph detemine:

(1)the midean wage.

(2)number of employee whose income is below Rs 8500

(3)If salary of a senior employee is above Rs11,500 find the number of senior employee in the company.

(4)the upper quartle .

A mathematics aptitude test of 50 students was recored as follows:

Marks | No. of students |

50-60 | 4 |

60-70 | 8 |

70-80 | 14 |

80-90 | 19 |

90-100 | 5 |

Draw a histrogram for the above data using a graph paper and locate the mode.

Marks obtained by 200 students in an examination are given below:

Marks |
No.of students |

0-10 | 5 |

10-20 | 11 |

20-30 | 10 |

30-40 | 20 |

40-50 | 28 |

50-60 | 37 |

60-70 | 40 |

70-80 | 29 |

80-90 | 14 |

90-100 | 6 |

Draw an ogive for the given distribution taking 2 cm = 10 marks on one axis and 2 cm = 20 students on the other axis. Using the graph, determine

1) The median marks.

2) The number of students who failed if minimum marks required to pass is 40.

3) If scoring 85 and more marks are considered as grade one, find the number of students who secured grade one in the examination.

Marks obtained by 40 students in a short assessment is given below, where a and b are two missing data.

Marks | 5 | 6 | 7 | 8 | 9 |

Number of Students | 6 | a | 16 | 13 | b |

If the mean of the distribution is 7.2, find a and b.

Find the mode and the median of the following frequency distributions.

x | 10 | 11 | 12 | 13 | 14 | 15 |

f | 1 | 4 | 7 | 5 | 9 | 3 |