Secondary school mathematics class 9 rs aggarwal Solutions for Chapter 18 mean median and mode of ungrouped data

Find the mean of:

(i) the first eight natural numbers

(ii) the first ten odd numbers

(iii) the first seven multiples of 5

(iv) all the factors of 20

(v) all prime numbers between 50 and 80.

The number of children in 10 families of a locality are 2, 4, 3, 4, 2, 0, 3, 5, 1 and 6. Find the mean number of children per family.

The following are the numbers 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.

The daily minimum temperature recorded (in oF) at a place during six days of a week was as under:

Find the mean temperature.

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.

The mean weight of 6 boys in a group is 48kg. The individual weights of five of them are 51kg, 45kg,

49kg, 46kg and 44kg. Find the weight of the sixth boy.

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.

The mean of 24 numbers is 35. If 3 is added to each number, what will be the new mean?

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

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

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

numbers?

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

set of 20 numbers.

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.

The average height of 30 boys was calculated to be 150cm. It was detected later that one value of 165cm

was wrongly copied as 135cm for the computation of the mean. Find the correct mean.

The mean weight of a class of 34 students is 46.5kg. If the weight of the teacher is included, the mean

rises by 500g. Find the weight of the teacher.

The mean weight of a class of 36 students is 41kg. If one of the students leaves the class then the mean is

decreased by 200g. Find the weight of the student who left.

The average weight of a class of 39 students is 40kg. When a new student is admitted to the class, the

average decreases by 200g. Find the weight of the new student.

The average weight of 10 oarsmen in a boat is increased by 1.5kg when one of the crew who weighs

58kg is replaced by a new man. Find the weight of the new man.

The mean of 8 numbers is 35. If a number is excluded then the mean is reduced by 3. Find the excluded

number.

The mean of 150 items was found to be 60. Later on, it was discovered that the values of two items were

misread are 52 and 8 instead of 152 and 88 respectively. Find the correct mean.

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.

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.

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

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.

Arun scored 36 marks in English, 44 marks in Hindi, 74 marks in mathematics and x marks in science.

If he has secured an average of 50 marks, find the value of x.

A ship sails out to an island at the rate of 15 km/hr and sails back to the starting point at 10 km/hr. Find

the average sailing speed for the whole journey.

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

of the girls is 40kg. Find the average weight of the boys.

The aggregate monthly expenditure of a family was ₹ 18720 during the first 3 months, ₹ 20340 during the next 4 months and ₹ 21708 during the last 5 months of a year. If the total savings during the year be ₹35340 find the average monthly income of the family.

The average weekly payment to 75 workers in a factory is ₹ 5680. The mean weekly payment to 25 of

them is ₹ 5400 and that of 30 others is ₹ 5700. Find the mean weekly payment of the remaining workers.

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.

The average monthly salary of 20 workers in an office is ₹ 45900. If the manager’s salary is added, the

average salary becomes ₹ 49200 per month. What’s manager’s monthly salary?

Obtain the mean of the following distribution:

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

Find the mean weight of the workers.

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

Calculate the mean diameter of the heads of the screws.

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

Calculate the mean age of the students.

Find the mean of the following frequency distribution:

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

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

If the mean of the following data is 8, find the value of p.

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

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

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

Find the missing frequencies in the following frequency distribution whose mean is 50.

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

The mean of the following distribution is 50.

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

Find the median of:

(i) 2, 10, 9, 9, 5, 2, 3, 7, 11

(ii) 15, 6, 16, 8, 22, 21, 9, 18, 25

(iii) 20, 13, 18, 25, 6, 15, 21, 9, 16, 8, 22

(iv) 7, 4, 2, 5, 1, 4, 0, 10, 3, 8, 5, 9, 2

Find the median of:

(i) 17, 19, 32, 10, 22, 21, 9, 35

(ii) 72, 63, 29, 51, 35, 60, 55, 91, 85, 82

(iii) 10, 75, 3, 15, 9, 47, 12, 48, 4, 81, 17, 27

The marks of 15 students in an examination are

25, 19, 17, 24, 23, 29, 31, 4, 19, 20, 22, 26, 17, 25, 21.

Find the median score.

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

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

Find the median height.

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.

The ages (in years) of 10 teachers in a school are

32, 44, 53, 47, 37, 54, 34, 36, 40, 50.

Find the median age.

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.

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.

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.

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?

Find the mode of the following items.

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

Determine the mode of the following values of a variable.

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

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.

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.

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.

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.

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.