Chapter 11 - Statistics
Practice set 11.1
1. The following table shows the number of saplings planted by 30 students. Fill in the boxes and find the average number of saplings planted by each student.
|
No. of saplings (Scores) xi |
No. of students (frequency) fi | fi × xi |
|---|---|---|
1 | 4 | 4 |
2 | 6 | ___ |
3 | 12 | ___ |
4 | 8 | ___ |
N = ___ | Σfi × xi = ___ |
Mean (x̄) = \(\large \frac {?}{N}\)
= \(\large \frac {?}{?}\)
= __
∴ The average number of trees planted is _____.
Solution:
|
No. of saplings (Scores) xi |
No. of students (frequency) fi | fi × xi |
|---|---|---|
1 | 4 | 4 |
2 | 6 | 12 |
3 | 12 | 36 |
4 | 8 | 32 |
N = 30 | Σfi × xi = 84 |
Mean (x̄) = \(\large \frac {Σfi × xi}{N}\)
= \(\large \frac {84}{30}\)
= 2.8
∴ The average number of trees planted is 2.8
2. The following table shows the electricity (in units) used by 25 families of Eklara village in the month of May. Complete the table and answer the following questions.
|
Electricity used (Units) xi |
No.of families (frequency) fi | fi × xi |
|---|---|---|
30 | 7 | ___ |
45 | 2 | ___ |
60 | 8 | ___ |
75 | 5 | ___ |
90 | 3 | ___ |
N = ___ | Σfi × xi = ___ |
Solution:
|
Electricity used (Units) xi |
No.of families (frequency) fi | fi × xi |
|---|---|---|
30 | 7 | 210 |
45 | 2 | 90 |
60 | 8 | 480 |
75 | 5 | 375 |
90 | 3 | 270 |
N = 25 | Σfi × xi = 1425 |
(1) How many families use 45 units of electricity?
Ans: Two families use 45 units of electricity.
(2) State the score, the frequency of which is 5.
Ans: The score with frequency 5 is 75.
(3) Find N, and Σfixi
Ans: From the above table, N = 25 and Σfixi = 1425
(4) Find the mean of electricity used by each family in the month of May.
Ans:
Mean (x̄) = \(\large \frac {Σfi × xi}{N}\)
= \(\large \frac {1425}{25}\)
= 57
3. The number of members in the 40 families in Bhilar are as follows:
1, 6, 5, 4, 3, 2, 7, 2, 3, 4, 5, 6, 4, 6, 2, 3, 2, 1, 4, 5, 6, 7, 3, 4, 5, 2, 4, 3, 2, 3, 5, 5, 4, 6, 2, 3, 5, 6, 4, 2. Prepare a frequency table and find the mean of members of 40 families.
Solution:
|
No. of members (Scores) xi |
No. of families (frequency) fi | fi × xi |
|---|---|---|
1 | 2 | 2 |
2 | 8 | 16 |
3 | 7 | 21 |
4 | 8 | 32 |
5 | 7 | 35 |
6 | 6 | 36 |
7 | 2 | 14 |
N = 40 | Σfi × xi = 156 |
Mean (x̄) = \(\large \frac {Σfi × xi}{N}\)
= \(\large \frac {156}{40}\)
= 3.9
Ans: Mean of members of 40 families is 3.9
4. The number of Science and Mathematics projects submitted by Model high school, Nandpur in last 20 years at the state level science exhibition is :
2, 3, 4, 1, 2, 3, 1, 5, 4, 2, 3, 1, 3, 5, 4, 3, 2, 2, 3, 2. Prepare a frequency table and find the mean of the data.
|
No. of projects (Scores) xi | (frequency) fi | fi × xi |
|---|---|---|
1 | 3 | 3 |
2 | 6 | 12 |
3 | 6 | 18 |
4 | 3 | 12 |
5 | 2 | 10 |
N = 20 | Σfi × xi = 55 |
Mean (x̄) = \(\large \frac {Σfi × xi}{N}\)
= \(\large \frac {55}{20}\)
= 2.75
Ans: Mean of the data is 2.75
Practice set 11.2
1. Observe the following graph and answer the questions.
1. Observe the following graph and answer the questions.
(1) State the type of the graph.
Ans: The given graph is a subdivided bar graph.
(2) How much is the savings of Vaishali in the month of April?
Ans: Vaishali’s savings in the month of April is Rs 600.
(3) How much is the total savings of Saroj in the months of March and April?
Ans: Total savings of Saroj in the months of March and April is Rs 800.
(4) How much more is the total savings of Savita than the total savings of Megha?
Ans:
Savita’s total saving = Rs 1000
Megha’s total saving = Rs 500
∴ Difference in their savings
= 1000 – 500
= Rs 500
Savita’s saving is Rs 500 more than Megha.
(5) Whose savings in the month of April is the least?
Ans: Megha’s savings in the month of April is the least.
2. The number of boys and girls, in std 5 to std 8 in a Z.P. school is given in the table. Draw a subdivided bar graph to show the data.
(Scale : On Y axis, 1 cm= 10 students)
Solution:
| Standard | 5th | 6th | 7th | 8th |
|---|---|---|---|---|
Boys | 34 | 26 | 21 | 25 |
Girls | 17 | 14 | 14 | 20 |
Total | 51 | 40 | 35 | 45 |
3. In the following table, the number of trees planted in the year 2016 and 2017 in four towns is given. Show the data with the help of a subdivided bar graph.
Solution:
| Year/Town | Karjat | Wadgaon | Shivapur | Khandala |
|---|---|---|---|---|
2016 | 150 | 250 | 200 | 100 |
2017 | 200 | 300 | 250 | 150 |
Total | 350 | 550 | 450 | 250 |
4. In the following table, data of the transport means used by students in 8th standard for commutation between home and school is given. Draw a subdivided bar diagram to show the data.
(Scale : On Y axis : 1 cm = 500 students)
Solution:
Practice set 11.3
1. Show the following information by a percentage bar graph.
Solution:
| Division of Standard 8 | A | B | C | D |
|---|---|---|---|---|
Number of students securing grade A | 45 | 33 | 10 | 15 |
Total number of students | 60 | 55 | 40 | 75 |
Percentage of students securing grade A | 75% | 60% | 25% | 20% |
Percentage of students not securing grade A | 25% | 40% | 75% | 80% |
2. Observe the following graph and answer the questions.
(1) State the type of the bar graph.
Ans: The given graph is a percentage bar graph.
(2) How much percent is the Tur production to total production in Ajita’s farm?
Ans: Percent of tur production to the total production in Ajita’s farm is 60%.
(3) Compare the production of Gram in the farms of Yash and Ravi and state whose percentage of production is more and by how much?
Ans:
Production of Gram in the farm of Yash = 50%
Production of Gram in the farm of Ravi = 30%
∴ Difference in the production
= 50% – 30%
= 20%
Yash’s production of Gram is more and by 20%
(4) Whose percentage production of Tur is the least?
Ans: Sudha’s percentage production of Tur is the least.
(5) State production percentages of Tur and gram in Sudha’s farm.
Ans: Production percentages of Tur and Gram in Sudha’s farm are 40% and 60% respectively.
3. The following data is collected in a survey of some students of 10th standard from some schools. Draw the percentage bar graph of the data.
Solution:
| School | 1st | 2nd | 3rd | 4th |
|---|---|---|---|---|
Inclination towards science stream | 90 | 60 | 25 | 16 |
Inclination towards science stream | 60 | 20 | 25 | 24 |
Total number of students | 150 | 80 | 50 | 40 |
Percentage of students having inclination towards science stream | 60% | 75% | 50% | 40% |
Percentage of students having inclination towards commerce stream | 40% | 25% | 50% | 60% |
