RS Agarwal Solution | Class 9th | Chapter-18 |  Mean, Median and Mode of Ungrouped Data | Edugrown

Exercise MCQ

Question 1

If the mean of x, x+2, x+4, x+6 and x+8 is 11, the value of x is

Solution 1

Question 2

If the mean of x, x + 3, x + 5, x + 10 is 9, the mean of the last three observations is

Solution 2

Question 3

Solution 3

Question 4

If each observation of the data is decreased by 8 then their mean

(a) remains the same

(b) is decreased by 8

(c) is increased by 5

(d) becomes 8 times the original meanSolution 4

Correct option: (b)

If each observation of the data is decreased by 8 then their mean is also decreased by 8. Question 5

The mean weight of six boys in a group is 48 kg. The individual weights of five them are 51 kg, 45 kg, 48 kg and 44 kg. The weight of 6^th boy is

1. 52 kg
2. 52.8 kg
3. 53 kg
4. 47 kg

Solution 5

Question 6

The mean of the marks scored by 50 students was found to be 39. Later on it was discovered that a score of 43 was misread as 23. The correct mean is

1. 38.6
2. 39.4
3. 39.8
4. 39.2

Solution 6

Question 7

The mean of 100 items was found to be 64. Later on it was discovered that two items were misread as 26 and 9 instead of 36 and 90 respectively. The correct mean is

1. 64.86
2. 65.31
3. 64.91
4. 64.61

Solution 7

Question 8

The mean of 100 observations is 50. If one of the observations 50 is replaced by 150, the resulting mean will be

1. 50.5
2. 51
3. 51.5
4. 52

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

The mean of the following data is 8

X	3	5	7	9	11	13
Y	6	8	15	P	8	4

The value of p is

1. 23
2. 24
3. 25
4. 21

Solution 12

Question 13

The runs scored by 11 members of a cricket team are

15, 34, 56, 27, 43, 29, 31, 13, 50, 20, 0

The median score is

1. 27
2. 29
3. 31
4. 20

Solution 13

Question 14

The weight of 10 students (in kgs) are

55,40,35,52,60,38,36,45,31,44

The median weight is

1. 40 kg
2. 41 kg
3. 42 kg
4. 44 kg

Solution 14

Question 15

The median of the numbers 4,4,5,7,6,7,7,12,3 is

1. 4
2. 5
3. 6
4. 7

Solution 15

Question 16

The median of the numbers 84,78,54,56,68,22,34,45,39,54 is

1. 45
2. 49.5
3. 54
4. 56

Solution 16

Question 17

Mode of the data 15,17,15,19,14,18,15,14,16,15,14,20,19,14,15 is

1. 14
2. 15
3. 16
4. 17

Solution 17

Question 18

The median of the data arranged in ascending order

8, 9, 12, 18, (x +2), (x + 4), 30, 31, 34, 39 is 24. The value of x is.

1. 22
2. 21
3. 20
4. 24

Solution 18

Exercise Ex. 18A

Question 1(iv)

Find the arithmetic mean of:

All the factors of 20Solution 1(iv)

Factors of 20 are: 1,2,4,5,10,20

Question 1(iii)

Find the arithmetic mean of:

The first seven multiple of 5Solution 1(iii)

First seven multiples of 5 are: 5,10,15, 20, 25, 30, 35

Therefore, Mean =20Question 1(ii)

Find the arithmetic mean of:

The first ten odd numbersSolution 1(ii)

First ten odd numbers are:

1,3,5,7,9,11,13,15, 17, and 19

Question 1(i)

Find the arithmetic mean of:

The first eight natural numbersSolution 1(i)

first eight natural numbers are:

1,2,3,4,5,6,7and 8

Question 1(v)

Find the mean of:

all prime numbers between 50 and 80.Solution 1(v)

Prime numbers between 50 and 80 are as follows:

53, 59, 61, 67, 71, 73, 79

Total prime numbers between 50 and 80 = 7

Question 2

The number of children in 10 families of a locality are

2,4,3,4,2,0,3,5,1,6.

Find the mean number of children per family.Solution 2

Question 3

The following are number of books issued in a school library during a week:

105, 216, 322, 167, 273, 405, and 346.

Find the average number of books issued per day.Solution 3

Sol.3 

Question 4

The daily minimum temperature recorded (in degree F) at a place during a week was as under:

Monday	Tuesday	Wednesday	Thursday	Friday	Saturday
35.5	30.8	27.3	32.1	23.8	29.9

Find the mean temperature.Solution 4

Question 5

If the mean of five observations x, x + 2, x + 4, x + 6, x + 8 is 13, find the value of x and hence find the mean of the last three observations.Solution 5

Total numbers of observations = 5

Thus, last three observations are (9 + 4), (9 + 6) and (9 + 8),

i.e. 13, 15 and 17

Question 6

The mean weight of 6 boys in a group is 48 kg. The individual weights of five of them are 51 kg, 45 kg, 49 kg, 46 kg and 44 kg. Find the weight of the sixth boy.Solution 6

Mean weight of the boys =48 kg

Sum of the weight of6 boys =(48×6)kg =288kg

Sum of the weights of 5 boys=(51+45+49+46+44)kg=235kg

Weight of the sixth boy=(sum of the weights of 6 boys ) – (sum of the weights of 5 boys)

=(288-235)=53kg.

Question 7

The mean of the marks scored by 50 students was found to be 39. Later on it was discovered that a score of 43 was misread as 23. Find the correct mean.Solution 7

Calculated mean marks of 50 students =39

 calculated sum of these marks=(39x 50)=1950

Corrected sum of these marks

=[1950-(wrong number)+(correct number)]

=(1950-23+43) =1970

correct mean =Question 8

The mean of 24 numbers is 35. If 3 is added to each number, what will bethe new mean?Solution 8

Let the given numbers be x₁,X_2……X₂₄

Question 9

The mean of 20 numbers is 43. If 6 is subtracted from each of the numbers , what will be the new mean ?Solution 9

Let the given numbers be x₁, x₂…..x₂₀

Then , the mean of these numbers =

Question 10

The mean of 15 numbers is 27. If each numbers is multiplied by 4, what will be the mean of the new numbers ?Solution 10

Let the given numbers be x₁, x₂…….x₁₅

Then the mean of these numbers=27

Question 11

The mean of 12 numbers is 40. If each number is divided by 8, what will be the mean of the new numbers?Solution 11

Question 12

The mean of 20 number is 18. If 3 is added to each of the first ten numbers , find the mean of the new set of 20 numbers.Solution 12

Question 13

The mean of six numbers is 23 . If one of the numbers is excluded , the mean of the remaining numbers is 20. Find the excluded number.Solution 13

Mean of 6 numbers = 23

Sum of 6 numbers =(23×6 )=138

Again , mean of 5 numbers =20

Sum of 5 numbers=(20x 5 ) =100

 The excluded number= (sum of 6 numbers )-(sum of 5 numbers)

=(138-100) =38

 The excluded number=38.Question 14

The average height of 30 boys was calculated to be 150 cm. It was detected later that one value of 165 cm was wrongly copied as 135 cm for the computation of the mean. Find the correct mean.Solution 14

Mean height of 30 boys = 150 cm

⇒ Total height of 30 boys = 150 × 30 = 4500 cm

Correct sum = 4500 – incorrect value + correct value

= 4500 – 135 + 165

= 4530

Question 15

The mean weight of a class of 34 students is 46.5 kg. If the of the teacher is included, the mean rises by 500 g. Find the weight of the teacherSolution 15

_{Mean weight of 34 students = 46.5 kg}

_{Total weight of 34 students =(34×46.5)kg =1581 kg}

_{Mean weight of 34 students and the teacher =(46.5+0.5)kg=47kg} 

_{Total weight of 34 students and the teacher}

_{=(47×35)kg =1645kg}

 _{Weight of the teacher =(1645-1581)kg= 64kg}Question 16

The mean weight of a class of 36 students is 41 kg. If one of the students leaves the class then the mean is decreased by 200 g. find the weight of the student who left.Solution 16

_{Mean weight of 36 students = 41 kg}

_{Total weight of 36 students = 41x 36 kg = 1476kg}

_{One student leaves the class mean is decreased by 200 g.}

 _{New mean =(41-0.2)kg = 40.8 kg}      

_{Total weight of 35 students = 40.8×35 kg = 1428 kg.}

_{the weight of the student who left =(1476-1428)kg =48 kg.}Question 17

The average weight of a class of 39 students is 40 kg . When a new student is admitted to the class , the average decreases by 200 g . find the weight of the new student.Solution 17

_{Mean weight of 39 students =40 kg}

_{Total weight of 39 students = 40x 39) = 1560 kg}

_{One student joins the class mean is decreased by 200 g.}

 _{New mean =(40-0.2)kg = 39.8 kg}               

_{Total weight of 40 students =(39.8×40)kg=1592 kg.}

_{the weight of new student}

_{= Total weight of 40 students – Total weight of 39 students}

_{= 1592-1560 = 32 kg}Question 18

The average weight of 10 oarsmen in a boat is increased by 1.5 kg when one of the crew who weighs 58 kg is replaced by a new man . find the weight of a new man.Solution 18

The increase in the average of 10 oarsmen = 1.5 kg

_{Total weight increased =(1.5×10) kg=15 kg}

Since the man weighing 58 kg has been replaced,

 _{Weight of the new man =(58+15)kg =73kg.}Question 19

The mean of 8 numbers is 35 . if a number is excluded then the mean is reduced by 3 . find the excluded number.Solution 19

_{Mean of 8 numbers=35}

_{Total sum of 8 numbers = 35×8 = 280}

 _{Since One number is excluded, New mean = 35 – 3 = 32}

_{Total sum of 7 numbers = 32×7 = 224}

_{the excluded number = Sum of 8 numbers – Sum of 7 numbers}

_{= 280 – 224 = 56}Question 20

The mean of 150 items was found to be 60. Later on , it was discovered that the values of two items were misread as 52 and 8 instead of 152 and 88 respectively. Find the correct mean.Solution 20

_{Mean of 150 items = 60}

_{Total Sum of 150 items = 150×60 = 9000}

_{Correct sum of items =[(sum of 150 items)-(sum of wrong items)+(sum of right items)]}

_{= [9000 – (52 + 8) + (152 + 88)]}

_{= [9000-(52+8)+(152+88)]}

_{= 9180}

 _{Correct mean =}Question 21

The mean of 31 results 60. If the mean of the first 16 results is 58 and that of the last 16 numbers is 62, find the 16^th result.Solution 21

_{Mean of 31 results=60}

_{Total sum of 31 results = 31×60 = 1860}

_{Mean of the first 16 results =16×58=928}

_{Total sum of the first 16 results=16×58=928}

_{Mean of the last 16 results=62}

_{Total sum of the last 16 results=16×62=992}

_{The 16th result = 928 + 992 – 1860}

                          _{= 1920 – 1860 = 60}

_{The 16th result  = 60.}Question 22

The mean of 11 numbers is 42. If the mean of the first 6 numbers is 37 and that of the last 6 numbers is 46 . find the 6^th number.Solution 22

_{Mean of 11 numbers = 42}

_{Total sum of 11 numbers = 42×11 = 462}

_{Mean of the first 6 numbers = 37}

_{Total sum of first 6 numbers = 37×6 = 222}

_{Mean of the last 6 numbers = 46}  

_{Total sum of last 6 numbers = 6×46 = 276}

_{The 6th number= 276 + 222 – 462}

                          _{= 498 – 462 = 36}

_{The 6th number = 36}Question 23

The mean weight of 25 students of a class is 52 kg . If the mean weight of the first 13 students of the class is 48 kg that of the last 13 students is 55 kg . find the weight of the 13^th student.Solution 23

_{Mean weight of 25 students = 52kg}

_{Total weight of 25 students = 52×25 kg=1300 kg}

_{Mean of the first 13 students = 48 kg}

_{Total weight of the first 13 students = 48×13 kg = 624kg}

_{Mean of the last 13 students = 55 kg}

_{Total weight of the last 13 students = 55×13 kg = 715 kg}

_{The weight of 13th student}

_{= Total weight of the first 13 students +  Total weight of the last 13 students – Total weight of 25 students}

_{= 624+715-1300 kg}

_{= 39 kg.}

Therefore, the weight of 13th student is 39 kg.Question 24

The mean score of 25 observations is 80 and the mean score of another 55 observations is 60. Determine the mean score of the whole set of observations .Solution 24

_{Mean score of 25 observations = 80}

_{Total score of 25 observations = 80×25 = 2000}

_{Mean score of 55 observations = 60}

_{Total score of 55 observations = 60×55 =3300}

Total no. of observations = 25+55 =80 observations

_{Total score = 2000+3300 = 5300}

_{Mean score =}Question 25

Arun scored 36 marks in English , 44 marks in hindi, 75 marks in mathematics and x marks in science . If he has secured an average of 50 marks , find the value of x.Solution 25

_{Average marks of 4 subjects = 50}

_{Total marks of 4 subjects = 50×4 = 200}

_{36 + 44 + 75 + x = 200}

 _{155  + x = 200}

 _{x = 200 – 155 = 45}

_{The value of x = 45}Question 26

A ship sails out to an island at the rate of 15 km/h and the sails back to the starting point at 10 km /h . find the average sailing speed for the whole journey .Solution 26

_{Let the distance of mark from the staring point be x km.}

_{Then , time taken by the ship reaching the marks=}

_{Time taken by the ship reaching the starting point from the marks =}

_{Total time taken =}

_{Total distance covered =x+x=2x km.}

Question 27

There are 50 students in a class, of which 40 are boys . The average weight of the class is 44 kg and that of the girls is 40 kg . find the average weight of the boys.Solution 27

_{Total number of students = 50}

_{Total number of girls = 50-40 = 10}

_{Average weight of the class = 44 kg}

_{Total weight of 50 students= 44x 50 kg = 2200kg}

_{Average weight of 10 girls = 40 kg}

_{Total weight of 10 girls = 40×10 kg = 400 kg}

_{Total weight of 40 boys = 2200-400 kg =1800 kg}

_{the average weight of the boys =} Question 28

The aggregate monthly expenditure of a family was Rs.18720 during the first 3 months, Rs.20340 during the next 4 months and Rs.21708 during the last 5 months of a year. If the total saving during the year be Rs.35340. Find the average monthly income of the family.Solution 28

Total earnings of the year

= Rs. (3 × 18720 + 4 × 20340 + 5 ×21708 + 35340)

= Rs. (56160 + 81360 + 108540 + 35340)

= Rs. 281400

Number of months = 12

Question 29

The average weekly payment to 75 workers in a factory is Rs.5680. The mean weekly payment to 25 of them is Rs.5400 and that of 30 others is Rs.5700. Find the mean weekly payment of the remaining workers.Solution 29

Average weekly payment of 75 workers = Rs. 5680

⇒ Total weekly payment of 75 workers = Rs. (75 × 5680) = Rs. 426000

Mean weekly payment of 25 workers = Rs. 5400

⇒ Total weekly payment of 25 workers = Rs. (25 × 5400) = Rs. 135000

Mean weekly payment of 30 workers = Rs. 5700

⇒ Total weekly payment of 30 workers = Rs. (30 × 5700) = Rs. 171000

Number of remaining workers = 75 – 25 – 30 = 20

Therefore, Total weekly payment of remaining 20 workers

= Rs. (426000 – 135000 – 171000)

= Rs. 120000

Question 30

The mean marks (out of 100) of boys and girls in an examination are 70 and 73 respectively. If the mean marks of all the students in that examination is 71, find the ratio of the number of boys to the number of girls.Solution 30

Let the ratio of number of boys to the number of girls be x : 1.

Then,

Sum of marks of boys = 70x

Sum of marks of girls = 73 × 1 = 73

And, sum of marks of boys and girls = 71 × (x + 1)

⇒ 70x + 73 = 71(x + 1)

⇒ 70x + 73 = 71x + 71

⇒ x = 2

Hence, the ratio of number of boys to the number of girls is 2 : 1.Question 31

The average monthly salary of 20 workers in an office is Rs.45900. If the manager’s salary is added, the average salary becomes Rs.49200 per month. What’s manager’s monthly salary?Solution 31

Mean monthly salary of 20 workers = Rs. 45900

⇒ Total monthly salary of 20 workers = Rs. (20 × 45900) = Rs. 918000

Mean monthly salary of 20 workers + manager = Rs. 49200

⇒ Total monthly salary of 20 workers + manager = Rs. (21 × 49200) = Rs. 1033200

Therefore, manager’s monthly salary = Rs. (1033200 – 918000) = Rs. 115200

Exercise Ex. 18C

Question 1(i)

_{Find the median of:}

_{2,10, 9, 9, 5, 2, 3, 7, 11}Solution 1(i)

_{Arranging the data in accending order, we have}

_{2,2,3, 5, 7, 9, 9, 10, 11}

_{Here n = 9, which is odd}

Question 1(ii)

_{Find the median of:}

_{15, 6, 16, 8, 22, 21, 9, 18, 25}Solution 1(ii)

_{Arranging the data in ascending order , we have}

_{6, 8, 9, 15, 16, 18, 21, 22, 25}

_{Here n = 9, which is odd}

Question 1(iii)

_{Find the median of}

_{20, 13, 18, 25, 6, 15, 21, 9, 16, 8, 22}Solution 1(iii)

_{Arranging data in ascending order:}

_{6, 8, 9, 13, 15, 16, 18, 20, 21, 22, 25}

_{Here n = 11 odd}

Question 1(iv)

_{Find the median of:}

_{7, 4, 2, 5, 1, 4, 0, 10, 3, 8, 5, 9, 2}Solution 1(iv)

_{Arranging the data in ascending order , we have}

_{0, 1, 2, 2, 3, 4, 4, 5, 5, 7, 8, 9, 10}

_{Here n = 13, which is odd}

Question 2(iii)

_{Find the median of:}

_{10, 75, 3, 15, 9, 47, 12, 48, 4, 81, 17, 27}Solution 2(iii)

_{Arranging the data in ascending order , we have}

_{3, 4, 9, 10, 12, 15, 17, 27, 47, 48, 75, 81 Here n = 12, which is even}

Question 2(ii)

_{Find the median of:}

_{72, 63, 29, 51, 35, 60, 55, 91, 85, 82}Solution 2(ii)

Arranging the data in ascending order , we have

_{29, 35, 51, 55, 60, 63, 72, 82, 85, 91}

_{Here n = 10, which is even}

Question 2(i)

_{Find the median of:}

_{17, 19, 32, 10, 22, 21, 9, 35}Solution 2(i)

_{Arranging the data in ascending order , we have}

_{9, 10, 17, 19, 21, 22, 32, 35}

_{Here n = 8, which is even}

Question 3

_{The marks of 15 students in an examination are :}

25,19,17,24,23,29,31,40,19,20,22,26,17,35,21

Find the median score.
Solution 3

_{Arranging the data in ascending order , we have}

_{17, 17, 19, 19, 20, 21, 22, 23, 24, 25, 26, 29, 31, 35, 40}

_{Here n = 15, which is odd}

Thus, the median score is 23.

Question 4

The heights (in cm) of 9 students of a class are

148, 144, 152, 155, 160, 147, 150, 149, 145.

Find the median heightSolution 4

Total number of students = n = 9 (odd)

Arranging heights (in cm) in ascending order, we have

144, 145, 147, 148, 149, 150, 152, 155, 160

Question 5

_{The weights (in kg ) of 8 children are:}

_{13.4, 10.6, 12.7, 17.2, 14.3, 15, 16.5, 9.8}

_{Find the median weight.}Solution 5

_{Arranging the weights of 8 children in ascending order, we have}

_{9.8, 10.6, 12.7, 13.4, 14.3, 15, 16.5, 17.2}

_{Here , n= 8 , which is even}

Question 6

_{The ages (in years ) of 10 teachers in a school are:}

_{32, 44, 53, 47, 37, 54, 34, 36, 40, 50}

_{Fid the median age.}Solution 6

_{Arranging the ages of teachers in ascending order , we have}

_{32, 34, 36, 37, 40, 44, 47, 50, 53, 54}

_{Here, n =10, which is even}

Question 7

_{If 10, 13, 15, 18, x+1, x+3, 30, 32, 35, 41 are ten observations in an ascending order with median 24, find the value of x.}Solution 7

  _{The  ten observations in ascending order:}

_{10, 13, 15, 18, x+1, x+3, 30, 32, 35, 41}

_{Here, n =10, which is even}

Question 8

The following observations are arranged in ascending order:

26, 29, 42, 53, x, x + 2, 70, 75, 82, 93.

If the median is 65, find the value of x.Solution 8

Total number of observations = n = 10 (even)

Median = 65

Question 9

The numbers 50, 42, 35, (2x + 10), (2x – 8), 12, 11, 8 have been written in a descending order. If their median is 25, find the value of x.Solution 9

Total number of observations = n = 8 (even)

Median = 25

Question 10

Find the median of the data

46, 41, 77, 58, 35, 64, 87, 92, 33, 55, 90.

In the above data, if 41 and 55 are replaced by 61 and 75 respectively, what will be the new median?Solution 10

Total number of observations = n = 11 (odd)

Arranging data in ascending order, we have

33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92

Now, 41 and 55 are replaced by 61 and 75 respectively. 

Arranging new data in ascending order, we have

33, 35, 46, 58, 61, 64, 75, 77, 87, 90, 92

Exercise Ex. 18D

Question 1

_{Find the mode of the following items.}

_{0, 6, 5, 1, 6, 4, 3, 0, 2, 6, 5, 6}Solution 1

_{Arrange the given data in ascending order we have}

_{0, 0, 1, 2, 3, 4, 5, 5, 6, 6, 6, 6}

Let us prepare the following table:

Observations(x)	0	1	2	3	4	5	6
Frequency	2	1	1	1	1	2	4

_{As 6 ocurs the maximum number of times i.e. 4, mode = 6}Question 2

_{Determine the mode of the following values of a variable.}

_{23, 15, 25, 40, 27, 25, 22, 25, 20}Solution 2

_{Arranging the given data in ascending order , we have:}

_{15, 20, 22, 23, 25, 25, 25, 27, 40}

_{The frequency table of the data is :}

Observations(x)	15	20	22	23	25	27	40
Frequency	1	1	1	1	3	1	1

_{As 25 ocurs the maximum number of times i.e. 3, mode = 25}Question 3

_{Calculate the mode of the following sizes of shoes by a shop on a particular day}

_{5, 9, 8, 6, 9, 4, 3, 9, 1, 6, 3, 9, 7, 1, 2, 5, 9}Solution 3

_{Arranging the given data in ascending order , we have:}

_{1, 1, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 9, 9, 9, 9, 9,}

_{The frequency table of the data is :}

Observations(x)	1	2	3	4	5	6	7	8	9
Frequency	2	1	2	1	2	2	1	1	5

_{As 9, occurs the maximum number of times i.e. 5, mode = 9}Question 4

_{A cricket player scored the following runs in 12 one-day matches:}

_{50, 30, 9, 32, 60, 50, 28, 50, 19, 50, 27, 35.}

_{Find his modal score.}Solution 4

_{Arranging the given data in ascending order , we have:}

_{9, 19, 27, 28, 30, 32, 35, 50, 50, 50, 50, 60}

_{The frequency table of the data is :}

Observations(x)	9	19	27	28	30	32	35	50	60
Frequency	1	1	1	1	1	1	1	4	1

_{As 50, ocurs the maximum number of times i.e. 4, mode = 50}

Thus, the modal score of the cricket player is 50.
Question 5

If the mean of the data 3, 21, 25, 17, (x + 3), 19, (x – 4) is 18, find the value of x. Using this value of x, find the mode of the data.Solution 5

Total number of observations = n = 7

Mean = 18

Thus, data is as follows:

3, 21, 25, 17, 24, 19, 17

The most occurring value is 17.

Hence, the mode of the data is 17.Question 6

The numbers 52, 53, 54, 54, (2x + 1), 55, 55, 56, 57 have been arranged in an ascending order and their median is 55. Find the value of x and hence find the mode of the given data.Solution 6

Number of values = n = 9 (odd)

Numbers in ascending order:

52, 53, 54, 54, (2x + 1), 55, 55, 56, 57 

Thus, we have

52, 53, 54, 54, 55, 55, 55, 56, 57

The most occurring number is 55.

Hence, the mode of the data is 55. Question 7

For what value of x is the mode of the data 24, 15, 40, 23, 27, 26, 22, 25, 20, x + 3 found 25? Using this value of x, find the median.Solution 7

Mode of the data = 25

So, we should have the value 25 occurring maximum number of times in the given data.

That means, x + 3 = 25

⇒ x = 22

Thus, we have 24, 15, 40, 23, 27, 26, 22, 25, 20, 25.

Arranging data in ascending order, we have

15, 20, 22, 23, 24, 25, 25, 26, 27, 40

Number of observations = 10 (even)

Question 8

The numbers 42, 43, 44, 44, (2x + 3), 45, 45, 46, 47 have been arranged in an ascending order and their median is 45. Find the value of x. Hence, find the mode of the above data.Solution 8

Total number of observations = n = 9 (odd)

Median = 45

Thus, we have

42, 43, 44, 44, 45, 45, 45, 46, 47

The most occurring value is 45.

Hence, the mode of the data is 45.

Exercise Ex. 18B

Question 1

Obtain the mean of the following distribution:

Variable (xi)	4	6	8	10	12
Frequency (fi)	4	8	14	11	3

Solution 1

Question 2

_{The following table shows the weights of 12 workers in a factory :}

Weight (in Kg)	60	63	66	69	72
No of workers	4	3	2	2	1

_{Find the mean weight of the workers.}Solution 2

For calculating the mean , we prepare the following frequency table :

Weight (in kg)(Xi)	No of workers(fi)	fiXi
6063666972	43221	24018913213872
		771

Question 3

The measurements (in mm) of the diameters of the heads of 50 screws are given below:

Diameter (in mm) (xi)	34	37	40	43	46
Number of screws (fi)	5	10	17	12	6

Calculate the mean diameter of the heads of the screws.Solution 3

Question 4

_{The following data give the number of boys of a particular age in a class of 40 students.}

Age (in years)	15	16	17	18	19	20
Frequency (f)	3	8	9	11	6	3

_{Calculate the mean age of the students}Solution 4

For calculating the mean , we prepare the following frequency table :

Age (in years)(Xi)	Frequency(fi)	fiXi
151617181920	3891163	4512815319811460
		698

Question 5

_{Find the mean of the following frequency distribution :}

Variable (xi)	10	30	50	70	89
Frequency(fi)	7	8	10	15	10

Solution 5

For calculating  the mean , we prepare  the following frequency table :

Variable(Xi)	Frequency(fi)	fiXi
1030507089	78101510	702405001050890

Question 6

Find the mean of daily wages of 40 workers in a factory as per data given below:

Daily wages (in Rs.) (xi)	250	300	350	400	450
Number of workers (fi)	8	11	6	10	5

Solution 6

Question 7

If the mean of the following data is 20.2, find the value of p.

Variable (xi)	10	15	20	25	30
Frequency (fi)	6	8	p	10	6

Solution 7

Question 8

_{If the mean of the following frequency distribution is 8, find the value of p.}

X	3	5	7	9	11	13
F	6	8	15	p	8	4

Solution 8

We prepare  the following frequency table :

(Xi)	(fi)	fiXi
35791113	6815P84	18401059P8852

 303 + 9p = 8(41+p)

 303 + 9p= 328 + 8p

 9p – 8p = 328 -303

 P=25

 the value of P=25Question 9

_{Find the missing frequency p for the following frequency distribution whose mean is 28.25.}

X	15	20	25	30	35	40
F	8	7	p	14	15	6

Solution 9

We prepare the following frequency distribution table:

(Xi)	(fi)	fiXi
152025303540	87P14156	12014025p420525240

 1445 + 25p = (28.25)(50+p)

 1445 + 25p = 1412.50 + 28.25p

 -28.25p + 25p = -1445 + 1412.50

 -3.25p = -32.5

 the value of p=10Question 10

_{Find the value of p for the following frequency distribution whose mean is 16.6.}

X	8	12	15	p	20	25	30
F	12	16	20	24	16	8	4

Solution 10

We prepare the following frequency distribution table:

(Xi)	(fi)	fiXi
81215P202530	121620241684	9619230024p320200120

 1228 + 24p = 1660

 24p = 1660-1228

 24p = 432

 the value of p =18Question 11

Find the missing frequencies in the following frequency distribution whose mean is 34.

x	10	20	30	40	50	60	Total
f	4	f1	8	f2	3	4	35

Solution 11

Question 12

_{Find the missing frequencies in the following frequency distribution, whose mean is 50.}

x	10	30	50	70	90	Total
f	17	f1	32	f2	19	120

Solution 12

Let f₁  and f₂ be the missing frequencies. 

We prepare the following frequency distribution table.

(Xi)	(fi)	fixi
1030507090	17f132f219	17030f1160070f21710
Total	120	3480 + 30f1 + 70f2

Here, 

Thus,  …….(1)

Also,

Substituting the value of f₁ in equation 1, we have,

f₂=52 – 28 = 24

Thus, the missing frequencies are f₁ =28 and f₂=24 respectively.Question 13

Find the value of p, when the mean of the following distribution is 20.

x	15	17	19	20 + p	23
f	2	3	4	5p	6

Solution 13

Question 14

The mean of the following distribution is 50.

x	10	30	50	70	90
f	17	5a + 3	32	7a – 11	19

Find the value of a and hence the frequencies of 30 and 70.Solution 14