#### 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

#### Selina Selina ICSE Concise Mathematics Class 10

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

#### Selina solutions for Class 10 Maths Chapter 24 Exercise Exercise 24(A) [Page 356]

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 |

Find the Arithmetic mean.

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.

If the mean of the following distribution is 3, find the value of p.

x | 1 | 2 | 3 | 5 | p + 4 |

f | 9 | 6 | 9 | 3 | 6 |

In th following table, Σf = 200 and mean = 73. find the missing frequencies f_{1}, and f_{2}.

x | 0 | 50 | 100 | 150 | 200 | 250 |

f | 46 | f_{1} |
f_{2} |
25 | 10 | 5 |

Find the arithmetic mean (correct to the nearest whole-number) by using step-deviation method.

x |
5 |
10 |
15 |
20 |
25 |
30 |
35 |
40 |
45 |
50 |

f |
20 |
43 |
75 |
67 |
72 |
45 |
39 |
9 |
8 |
6 |

Find the mean (correct to one place of decimal) by using short-cut method.

x |
40 |
41 |
43 |
45 |
46 |
49 |
50 |

f |
14 |
28 |
38 |
50 |
40 |
20 |
10 |

#### Selina solutions for Class 10 Maths Chapter 24 Exercise Exercise 24(B) [Pages 362 - 363]

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

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 |

Calculate the mean of the distribution, given below, using the short cut method :

Mark |
11-20 |
21-30 | 31-40 | 41-50 | 51-60 | 61-70 | 71--80 |

no.of students | 2 | 6 | 10 | 12 | 9 | 7 | 4 |

#### Selina solutions for Class 10 Maths Chapter 24 Exercise Exercise 24(C) [Pages 372 - 373]

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.

#### Selina solutions for Class 10 Maths Chapter 24 Exercise Exercise 24(D) [Page 374]

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 |

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?

#### Selina solutions for Class 10 Maths Chapter 24 Exercise Exercise 24(E) [Pages 375 - 377]

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 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.

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?

Income of 100 students of their parents is given as follows

Income (in thousand Rs.) |
No. of students (f) |

0 - 8 | 8 |

8 - 16 | 35 |

16 - 24 | 35 |

24 - 32 | 14 |

32 - 40 | 8 |

Draw an ogive for the given distribution on a graph sheet.

Use a suitable scale for your ogive. Use your ogive to estimate:

(i) the median income.

(ii) Calculate the income below which freeship will be awarded to students if their parents income is in the bottom 15%

(iii) Mean income.

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:

(i) the median

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

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

(iv) the lower quartile

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 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 = rS 1000 on one axis and 2 cm = 50 employee on the other axis. From the graph detemine:

(1) the median 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 quartile.

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 |

The mean of following numbers is 68. Find the value of ‘x’.

45, 52, 60, x, 69, 70, 26, 81 and 94

Hence estimate the median.

The marks of 10 students of a class in an examination arranged in ascending order is as follows:

13, 35, 43, x, x + 4, 55, 61, 71, 80

If the median marks is 48, find the value of x. Hence find the mode of the given data.

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

Wages (in Rs.) |
400-450 | 450-500 | 500-550 | 550-600 | 600-650 | 650-700 | 700-750 |

No. of Workers |
2 | 6 | 12 | 18 | 24 | 13 | 5 |

Use a graph paper to draw an ogive for the above distribution. (Use a scale of 2 cm = Rs.

50 on x-axis and 2 cm = 10 workers on y-axis). Use your ogive to estimate:

1) the median wage of the workers

2) the lower quartile wage of workers

3) the numbers of workers who earn more than Rs. 625 daily

The histogram below represents the scores obtained by 25 students in a mathematics mental test. Use the data to :

1) Frame a frequency distribution table

2) To calculate mean

3) To determine the Modal class

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

#### Selina Selina ICSE Concise Mathematics Class 10

## Selina solutions for Class 10 Mathematics chapter 24 - Measure of Central Tendency(Mean, Median, Quartiles and Mode)

Selina solutions for Class 10 Maths chapter 24 (Measure of Central Tendency(Mean, Median, Quartiles and Mode)) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Selina ICSE Concise Mathematics for Class 10 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Selina textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 10 Mathematics chapter 24 Measure of Central Tendency(Mean, Median, Quartiles and Mode) are Median of Grouped Data, Histograms, Ogives (Cumulative Frequency Graphs), Basic Concepts of Statistics, Graphical Representation of Histograms, Graphical Representation of Ogives, Finding the Mode from the Histogram, Finding the Mode from the Upper Quartile, Finding the Mode from the Lower Quartile, Median from the Ogive, Calculation of Inter Quartile Range, Measures of Central Tendency - Mean, Median, Mode for Raw and Arrayed Data.

Using Selina Class 10 solutions Measure of Central Tendency(Mean, Median, Quartiles and Mode) exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Selina Solutions are important questions that can be asked in the final exam. Maximum students of CISCE Class 10 prefer Selina Textbook Solutions to score more in exam.

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