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# Selina solutions for Concise Mathematics Class 10 ICSE chapter 24 - Measure of Central Tendency(Mean, Median, Quartiles and Mode) [Latest edition]

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

Exercise 24(A)Exercise 24(B)Exercise 24(C)Exercise 24(D)Exercise 24(E)

### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 24 Measure of Central Tendency(Mean, Median, Quartiles and Mode) Exercise 24(A) [Page 356]

Exercise 24(A) | Q 1.1 | Page 356

Find the mean of the following set of numbers:

6, 9, 11, 12 and 7

Exercise 24(A) | Q 1.2 | Page 356

Find the mean of the following set of numbers:

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

Exercise 24(A) | Q 2.1 | Page 356

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

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

find the arithmetic mean

Exercise 24(A) | Q 2.2 | Page 356

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.

Exercise 24(A) | Q 3 | Page 356

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

Exercise 24(A) | Q 4.1 | Page 356

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

Exercise 24(A) | Q 4.2 | Page 356

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

Exercise 24(A) | Q 5 | Page 356

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

Exercise 24(A) | Q 6 | Page 356

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

Exercise 24(A) | Q 7 | Page 356

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.

Exercise 24(A) | Q 8 | Page 356

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

Exercise 24(A) | Q 9 | Page 356

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
Exercise 24(A) | Q 10 | Page 356

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?

Exercise 24(A) | Q 11 | Page 356

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.

Exercise 24(A) | Q 12 | Page 356

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
Exercise 24(A) | Q 13 | Page 356

In th following table, Σf = 200 and mean = 73. find the missing frequencies f1, and f2.

 x 0 50 100 150 200 250 f 46 f1 f2 25 10 5
Exercise 24(A) | Q 14 | Page 356

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
Exercise 24(A) | Q 15 | Page 356

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 Concise Mathematics Class 10 ICSE Chapter 24 Measure of Central Tendency(Mean, Median, Quartiles and Mode) Exercise 24(B) [Pages 362 - 363]

Exercise 24(B) | Q 1 | Page 362

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
Exercise 24(B) | Q 2.1 | Page 362

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

Exercise 24(B) | Q 2.2 | Page 362
 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

Exercise 24(B) | Q 3.1 | Page 362

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

Exercise 24(B) | Q 3.2 | Page 362

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

Exercise 24(B) | Q 4 | Page 362

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
Exercise 24(B) | Q 5 | Page 362

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
Exercise 24(B) | Q 6 | Page 362

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
Exercise 24(B) | Q 7 | Page 362

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

Exercise 24(B) | Q 8 | Page 362

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
Exercise 24(B) | Q 9 | Page 362

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

Exercise 24(B) | Q 10 | Page 363

Calculate the mean of the distribution given below using the short cut method.

 Marks 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 Concise Mathematics Class 10 ICSE Chapter 24 Measure of Central Tendency(Mean, Median, Quartiles and Mode) Exercise 24(C) [Pages 372 - 373]

Exercise 24(C) | Q 1 | Page 372

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.

Exercise 24(C) | Q 2 | Page 372

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.

Exercise 24(C) | Q 3.1 | Page 372

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

Exercise 24(C) | Q 3.2 | Page 372

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

Exercise 24(C) | Q 3.3 | Page 372

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

Exercise 24(C) | Q 3.4 | Page 372

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

Exercise 24(C) | Q 4.1 | Page 372

From the following data, find:

Median

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

Exercise 24(C) | Q 4.2 | Page 372

From the following data, find:

Upper quartile

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

Exercise 24(C) | Q 4.3 | Page 372

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

Exercise 24(C) | Q 5 | Page 372

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
Exercise 24(C) | Q 6 | Page 372

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

Exercise 24(C) | Q 7 | Page 372

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
Exercise 24(C) | Q 8 | Page 372

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
Exercise 24(C) | Q 9 | Page 373

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
Exercise 24(C) | Q 10 | Page 373

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 Concise Mathematics Class 10 ICSE Chapter 24 Measure of Central Tendency(Mean, Median, Quartiles and Mode) Exercise 24(D) [Page 374]

Exercise 24(D) | Q 1.1 | Page 374

Find the mode of the following data:
7, 9, 8, 7, 7, 6, 8, 10, 7 and 6

Exercise 24(D) | Q 1.2 | Page 374

Find the mode of the following data:

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

Exercise 24(D) | Q 2 | Page 374

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.

Exercise 24(D) | Q 3 | Page 374

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
Exercise 24(D) | Q 4 | Page 374

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
Exercise 24(D) | Q 5 | Page 374

Find the median and mode for the set of numbers:
2, 2, 3, 5, 5, 5, 6, 8 and 9

Exercise 24(D) | Q 6.1 | Page 374

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?

Exercise 24(D) | Q 6.2 | Page 374

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?

Exercise 24(D) | Q 6.3 | Page 374

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?

Exercise 24(D) | Q 6.4 | Page 374

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?

Exercise 24(D) | Q 7 | Page 374

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.

Exercise 24(D) | Q 8 | Page 374

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 Concise Mathematics Class 10 ICSE Chapter 24 Measure of Central Tendency(Mean, Median, Quartiles and Mode) Exercise 24(E) [Pages 375 - 377]

Exercise 24(E) | Q 1 | Page 375

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.

Exercise 24(E) | Q 3 | Page 375

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.

Exercise 24(E) | Q 4 | Page 375

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?

Exercise 24(E) | Q 5 | Page 375

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.

Exercise 24(E) | Q 6 | Page 375

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

Exercise 24(E) | Q 7 | Page 375

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

Exercise 24(E) | Q 8 | Page 376

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.

Exercise 24(E) | Q 9 | Page 376

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
Exercise 24(E) | Q 10 | Page 376

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

Exercise 24(E) | Q 11 | Page 376

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.

Exercise 24(E) | Q 12 | Page 376

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.

Exercise 24(E) | Q 13 | Page 376

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.

Exercise 24(E) | Q 14 | Page 377

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.

Exercise 24(E) | Q 15 | Page 377

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

Exercise 24(E) | Q 20 | Page 377

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.

Exercise 24(E) | Q 21 | Page 377

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

13, 35, 43, 46, 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.

Exercise 24(E) | Q 22 | Page 377

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. ofWorkers 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

Exercise 24(E) | Q 23 | Page 377

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)

Exercise 24(A)Exercise 24(B)Exercise 24(C)Exercise 24(D)Exercise 24(E)

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

Selina solutions for Concise Mathematics Class 10 ICSE 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 Concise Mathematics Class 10 ICSE 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 Concise Mathematics Class 10 ICSE 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, Finding the Median, upper quartile, lower quartile from the Ogive, Calculation of Lower, Upper, Inter, Semi-Inter Quartile Range, Measures of Central Tendency - Mean, Median, Mode for Raw and Arrayed Data, Mean of Grouped Data, Mean of Ungrouped Data, Median of Ungrouped Data, Mode of Ungrouped Data, Mode of Grouped Data, Mean of Continuous Distribution.

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