DBSE | Class 9Th | Maths | Statistics | Means | Exercise 01 (Part 02)

DBSE | Class 9Th | Maths | Statistics | Means | Exercise 01 (Part 02)

Exercise 01:

1. For a particular year, following is the distribution of ages (in years) of primary school teachers in a district :

(i) Write the lower limit of the first class interval.

(ii) Find the class interval whose frequency is 6?

(iii) Find the class mark of the class 45 – 50.

(iv) Is the above given data continuous group data? Why or why not?

(v) Try to represent the given data graphically.

(vi) Discuss and share various ways of data representation.

2. Record the blood groups of your class and represent the data in the form of a frequency

distribution table.

a) Try to represent the given data graphically.

b) Discuss and share various ways of data representation.

c) Which is the most common, and which is the rarest, blood group among these students?

d) Which blood group is a universal donor?

e) Which blood group is the universal recipient?

f) What is your opinion about blood donation? Share and discuss with family and friends.

3. Record the weight of students of your class and represent the data in the form of a

frequency distribution table.

a) What can you conclude about their weight from the table?

b) How does the collected data help us?

4. A company manufactures car batteries of a particular type. The lives (in years) of 50 such

batteries were recorded as follows:

3.1, 2.6, 3.0, 3.7, 3.2, 2.2, 4.1, 3.5, 4.5, 3.5, 2.3, 3.2, 3.4, 3.8, 3.2, 4.6, 4.1, 3.7, 2.5, 4.4, 3.4, 3.3, 2.9, 3.0, 4.3, 2.8, 3.5, 3.2, 3.9, 3.2, 3.2, 3.1, 4.7, 3.7, 3.4, 4.6, 3.8, 3.2, 2.6, 3.5, 4.2, 2.9, 3.6, 2.9, 3.0, 3.5, 3.8, 4.0, 4.5, 4.0

a) Construct a grouped frequency distribution table for this data.

b) What do you infer from the data?

1. The monthly income (in rupees) of 25 families is given below:

85000, 10000, 55000, 35000, 20000, 15000, 65000, 15000, 18000, 90000, 35000, 25000, 25000, 30000, 80000, 35000, 100000, 22000, 38000, 52000, 13000, 17000, 24000, 36000, 20000.

Compute:

1. How many families earn more than the average family income?

2. Which type of family income occurs the most frequently?

3. Find the family income from which half of the families get less than or equal to and

the other half get greater than or equal to that income? Now Explore the per capita

income of Delhi, India and the World.

Group discussion:

1. What is your source of data?

2. What do you infer from the collected data?

3. Is per capita income the only representation of Income of a population.

4. What is the limitation of this method?

5. Suggest some other ways which can represent income of a population.

2. The given data shows the runs scored by two cricket players in 10 innings.

Player 1: 50, 35, 10, 45, 60, 25, 50, 55, 50, 20

Player 2: 18, 15, 11, 150, 0, 25, 15, 11, 130, 25

If you were to choose one player out of two purely based on the performance described

above, who would you choose and why?

3. The given data shows the points scored by a kabbadi player in 16 innings.

5,10,8,8,10,12,4,9,8,7,4,6,5,9,6,3

Find the mean, median, mode and range of the given data.

4. The given table shows the result when 3 coins were tossed simultaneously 20 times.

The number of tails appearing was recorded.

5. Discuss following questions in your group:

i) In which situations can we use the mean as a good estimate?

ii) In which situations can we use the median as a good estimate?

iii) In which situations can we use the mode as a good estimate?

★ The marks scored by 60 students of grade 9 students in a semester end exam in Mathematics (out of 50) is given below:

43, 26, 33, 38, 27, 42, 33, 22, 12, 24, 30, 14, 50, 36, 16, 31, 48, 11, 30, 22, 33, 49, 37, 33, 48, 50, 43, 23, 3, 41, 31, 41, 11, 44, 42, 22, 20, 10, 30, 40, 2, 45, 40, 36, 39, 27, 37, 39, 22, 18, 16, 9, 10, 44, 33, 29, 49, 50, 50, 44

How do you check the performance of a class in a Mathematics Test? 

Sol. 

Group frequency distribution table:

Observe the method suggested by the teacher to find the mean of the group data.

Step 1:

Step 2:

Now find the mean

                  Σ fi × xi

Means =  _________  

                     Σ fi 

                     1920

                =  _________

                        60

Means = 32 Ans.

★ College students were required to participate in at least 5 hours of community service each week.

The following table shows the distribution of the number of hours 100 students worked each

week (on average) for community work.

1. Find the number of hours each student participated in community service during a week.

2. Find the mean of the given data.

3. Why does the college provide community service experience to the students? Share your

opinion.

Practice work:

1. The number of students present (out of 50) in the class in month of April is given below:

40, 38, 50, 50, 47, 48, 45, 49, 50, 35, 48, 49, 50, 47, 45, 40, 50, 50, 48, 46, 48, 42, 45, 45, 50

i) Find the average (arithmetic mean) number of students present in the class in a day?

ii) Share and discuss the possible methods to find the mean of the given data.

iii) Discuss which method is more convenient in finding the mean in the given data.

2. Find the arithmetic mean of the following frequency distribution table:

3. Find the arithmetic mean of the following frequency distribution table: