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

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

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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

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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.

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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

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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

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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?

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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

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