## RS Aggarwal Solutions Chapter 14 Statistics Ex 14E in PDF for Free Download

Contents

**Question 1.****The mean mark obtained by 7 students in a group is 226 If the marks obtained by six of them are 340, 180, 260, 56, 275 and 307 respectively, find the marks obtained by the seventh student.****Solution:**

Mean marks of 7 students = 226

∴Total marks of 7 students = 226 x 1 = 1582

Marks obtained by 6 of them are 340, 180, 260, 56, 275 and 307

∴ Sum of marks of these 6 students = 340 + 180 + 260 + 56 + 275 + 307 = 1418

∴ Marks obtained by seventh student = 1582 – 1418 = 164 Ans.

**Question 2.****The mean weight of a class of 34 students is 46.5 kg. If the weight of the teacher is included, the mean rises by 500 g. Find the weight of the teacher.****Solution:**

Mean weight of 34 students = 46.5 kg.

∴ Total weight of 34 students = 46.5 x 34 kg = 1581 kg

By including the weight of teacher, the mean weight of 35 persons = 500 g + 46.5 kg

= 46.5 + 0.5 = 47.0 kg

∴ Total weight = 47.0 x 35 = 1645 kg

∴ Weight of the teacher = (1645 – 1581) kg = 64 kg Ans.

**Question 3.****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:**

Mean weight of 36 students = 41 kg

∴ Total weight of 36 students = 41 x 36 kg = 1476 kg

After leaving one student, number of students = 36 – 1 =35

Their new mean = 41.0 – 200g = (41.0 – 0.2) kg = 40.8 kg.

∴ Total weight of 35 students = 40.8 x 35 = 1428 kg

∴ Weight of leaving student = (1476 – 1428) kg = 48 kg Ans.

**Question 4.****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:**

Average weight of 39 students = 40 kg

∴ Total weight of 39 students = 40 x 39 = 1560 kg

By admitting of a new student, no. of students = 39 + 1 =40

and new mean = 40 kg – 200 g = 40 kg – 0.2 kg = 39.8 kg

∴Weight of 40 students = 39.8 x 40 kg = 1592 kg

∴Weight of new student = 1592 – 1560 kg = 32 kg Ans.

**Question 5.****The average monthly salary of 20 workers in an office is Rs. 7650. If the manager’s salary is added, the average salary becomes Rs. 8200 per month, What is the manager’s salary per month ?****Solution:**

Average salary of 20 workers = Rs. 7650

∴Their total salary = Rs. 7650 x 20 = Rs. 153000

By adding the salary of the manager, their mean salary = Rs. 8200

∴Their total salary = Rs. 8200 x 21 = Rs. 172200

∴Salary of the manager = Rs. 172200 – Rs. 153000 = Rs. 19200 Ans.

**Question 6.****The average monthly wage of a group of 10 persons is Rs. 9000. One member of the group, whose monthly wage is Rs. 8100, leaves the group and is replaced by a new member whose monthly wage is Rs. 7200. Find the new monthly average wage.****Solution:**

Average wage of 10 persons = Rs. 9000

Their total wage = Rs. 9000 x 10 = Rs. 90000

Wage of one person among them = Rs. 8100

and wage of new member = Rs. 7200

∴ New total wage = Rs. (90000 – 8100 + 7200) = Rs. 89100

Their new mean wage = Rs. = Rs. 8910

**Question 7.****The average monthly consumption of petrol for a car for the first 7 months of a year is 330 litres, and for the next 5 months is 270 litres. What is the average consumption per month during the whole year ?****Solution:**

Mean consumption of petrol for 7 months of a year = 330 litres

Mean consumption of petrol for next 5 months = 270 litres

∴Total consumption for first 7 months = 7 x 330 = 2320 l

and total consumption for next 5 months = 5 x 270 = 1350 l

Total consumption for 7 + 5 = 12 months = 2310 + 1350 = 3660 l

Average consumption = = 305 liters per month.

**Question 8.****Find the mean of 25 numbers if the mean of 15 of them is 18 and the mean of the remaining numbers is 13.****Solution:**

Total numbers of numbers = 25

Mean of 15 numbers = 18

∴Total of 15 numbers = 18 x 15 = 270

Mean of remaining 10 numbers = 13

∴Total = 13 x 10 = 130

and total of 25 numbers = 270 + 130 = 400

∴Mean = = 16 Ans.

**Question 9.****The mean weight of 60 students of a class is 52.75 kg. If the mean weight of 25 of them is 51 kg, find the mean weight of the remaining students.****Solution:**

Mean weight of 60 students = 52.75 kg.

Total weight = 52.75 x 60 = 3165 kg

Mean of 25 out of them = 51 kg.

∴Their total weight = 51 x 25 = 1275 kg

∴ Total weight of remaining 60 – 25 = 35 students = 3165 – 1275 = 1890 kg 1890

Mean weight = = 54 kg Ans.

**Question 10.****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 the new man.****Solution:**

Average increase of 10 oarsman = 1.5 kg.

∴ Total increased weight =1.5 x 10 = 15kg

Weight of out going oarsman = 58 kg .

∴ Weight of new oarsman = 58 + 15 = 73 kg Ans.

**Question 11.****The mean of 8 numbers is 35. If a number is excluded then the mean is reduced by 3. Find the excluded number.****Solution:**

Mean of 8 numbers = 35

∴Total of 8 numbers = 35 x 8 = 280

After excluding one number, mean of 7 numbers = 35 – 3 = 32

Total of 7 numbers = 32 x 7 = 224

Hence excluded number = 280 – 224 = 56 Ans.

**Question 12.****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:**

Mean of 150 items = 60

Total of 150 items = 60 x 150 = 9000

New total = 9000 + 152 + 88 – 52 – 8 = 9000 + 240 – 60 = 9180

∴New mean = = 61.2 Ans.

**Question 13.****The mean of 31 results is 60. If the mean of the first 16 results is 58 and that of the last 16 results is 62, find the 16th result****Solution:**

Mean of 31 results = 60

∴Total of 31 results = 60 x 31 = 1860

Mean of first 16 results = 58

∴Total of first 16 results = 58 x 16 = 928

and mean of last 16 results = 62

∴Total of last 16 results = 62 x 16 = 992

∴16th result = (928 + 992) – 1860 = 1920 – 1860 = 60 Ans.

**Question 14.****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 6th number.****Solution:**

Mean of 11 numbers = 42

∴Total of 11 numbers = 42 x 11 = 462

Mean of first 6 numbers = 37

∴Total of first 6 numbers = 37 x 6 = 222

Mean of last 6 numbers = 46

∴Total of last 6 numbers = 46 x 6 = 276

∴6th number = (222 + 276) – 462 = 498 – 462 = 36 Ans.

**Question 15.****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 and that of the last 13 students is 55 kg, find the weight of the 13 th student.****Solution:**

Mean weight of 25 students = 52 kg

∴ Total weight of 25 students = 52 x 25 = 1300 kg

Mean weight of first 13 students = 48 kg

∴ Total weight of first 13 students = 48 x 13 kg = 624 kg

Mean of last 13 students = 55 kg

∴Total of last 13 students = 55 x 13 kg = 715 kg

∴Weight of 13th student = (624 + 715) – 1300 = 1339 – 1300 = 39 kg Ans.

**Question 16.****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:**

Mean of 25 observations = 80

Total of 25 observations = 80 x 25 = 2000

Mean of another 55 observations = 60

∴ Total of these 55 observations = 60 x 55 = 3300

Total number of observations = 25 + 55 = 80

and total of 80 numbers = 2000 + 3300 = 5300

Mean of 80 observations = = 66.25 Ans.

**Question 17.****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:**

Marks in English = 36

Marks in Hindi = 44

Marks in Mathematics = 75

Marks in Science = x

∴Total number of marks in 4 subjects = 36 + 44 + 75 + x = 155 + x

Average marks in 4 subjects = 50

∴Total marks = 50 x 4 = 200

∴155 + x = 200

=> x = 200 – 155

=> x = 45

Hence, marks in Science = 45 Ans.

**Question 18.****The mean monthly salary paid to 75 workers in a factory is Rs. 5680. The mean salary of 25 of them is Rs. 5400 and that of 30 others is Rs. 5700. Find the mean salary of the remaining workers.****Solution:**

Mean of monthly salary of 75 workers = Rs. 5680

Total salary of 75 workers = Rs. 5680 x 75 = Rs. 426000

Mean salary of 25 among them = Rs. 5400

Total of 25 workers = Rs. 5400 x 25 = Rs. 135000

Mean salary of 30 among them = Rs. 5700

∴Total of 30 among them = Rs. 5700 x 30 = Rs. 171000

∴ Total salary of 25 + 30 = 55 workers = Rs. 135000 + 171000 = Rs. 306000

∴Total salary of remaining 75 – 55 = 20 workers = Rs. 426000 – 306000 = Rs. 120000

∴ Mean of remaining 20 workers = Rs. = Rs. 6000 Ans.

**Question 19.****A ship sails out to an island at the rate of 15 km/h and sails back to the starting point at 10 km/h. Find the average sailing speed for the whole journey.****Solution:**

Let distance between two places = 60 km

∴Time taken at the speed of 15 km/h = = 4 hours

and time taken at speed of 10 km/h for coming back = = 6 hours

Total the taken = 4 + 6 = 10

hours and distance covered = 60 + 60 = 120 km

∴Average speed = =12 km/hr.

**Question 20.****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:**

No. of total students = 50

No. of boys = 40

∴ No. of girls = 50 – 40 = 10

Average weight of class = 44kg

∴Total weight of 50 students = 44 x 50 = 2200 kg

Average weight of 10 girls = 40 kg

∴Total weight = 40 x 10 = 400 kg

Total weight of 40 boys = 2200 – 400 = 1800 kg

∴Average weight of 40 boys = kg = 45 kg Ans.

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