GSEB Solutions Class 11 Statistics Chapter 2 Presentation of Data Ex 2.2

   

Gujarat Board Statistics Class 11 GSEB Solutions Chapter 2 Presentation of Data Ex 2.2 Textbook Exercise Questions and Answers.

Gujarat Board Textbook Solutions Class 11 Statistics Chapter 2 Presentation of Data Ex 2.2

Question 1.
There were 1400 students studying in a commerce college. Among them, 855 were boys and of them, 225 boys were in the second year. In the second year, the number of boys and the number of girls are equal. Among the 550 students of the first year, the proportion of number of boys and girls is 3:2. In the third year, number of boys is three times the number of girls. Represent the above information in a table.
Answer:
In the given data, there are two attributes :

  1. Year of study and
  2. Sex of students.

Classifying the data on the basis of these two attributes, we prepare a table as follows :
Table showing the number of students studying in a commerce college according to their year of study and sex

Year of study Sex No. of students
Boys Girls
First year 330 220 550
Second year 225 225 450
Third year 300 100 400
Total 855 545 1400

[Explanation :
No. of students in first year = 550.
The proporation of boys-girls was = 3: 2.
∴ No. of boys = \(\frac{3}{5}\) × 550 = 330
No. of girls = \(\frac{2}{5}\) × 550 = 220
No. of students in third year = 1400 – (550 + 450)
= 1400 – 1000 = 400

No. of boys is thrice the No. of girls, i.e., the proportion was 3:1.
∴ No. of boys = \(\frac{3}{4}\) × 400 = 300
No. of girls = \(\frac{1}{4}\) × 400 = 100]
[Note : The figures shown in bold are obtained by simple calculation.]

GSEB Solutions Class 11 Statistics Chapter 2 Presentation of Data Ex 2.2

Question 2.
1600 employees are working in an office. Among these employees the number of men exceeded the number of women by 15% of the total number of employees. The number of unmarried employees are 800 less than the number of married employees. The number of unmarried women is 195. Represent the above data in a suitable table.
Answer:
In the given data, there are two attributes:

  1. Sex of employees and
  2. Marital status.

According to these two attributes data is classified and table is prepared as follows :
Table showing the number of employees working in an office according to their sex and marital status

Marital status Sex Total employees
Male Female
Married 715 485 1200
Unmarried 205 195 400
Total 920 680 1600

[Explanation:
Suppose, the number of males = x.
∴ No. of females = 1600-x
No. of males = No. of females + 1600 x \(\frac{15}{100}\)
∴ x = 1600 – x + 240
∴ 2x = 1840
∴ x = 920
∴ No. of females = 1600 – 920 = 680

Suppose the number of married employees = x
∴ No. of unmarried employees = 1600 – x
Now, No. of unmarried employees = No. of married employees – 800.
∴ 1600 – x = x – 800
∴ 2x = 1600 + 800 = 2400
∴ x = 1200
∴ No. of unmarried employees = 1600 – 1200
= 400]
[Note: The figures shown in bold are obtained by simple calculation.]

Question 3.
Prepare a blank table by considering the following characteristics for the candidates who appear for the different jobs at a bank:
(1) Designation: Manager, clerk, cashier, peon.
(2) Marital status: Married, unmarried.
(3) Gender: Male, female.
Answer:
Table showing the candidates called for the recruitment in a bank according to their post, marital status and gender
GSEB Solutions Class 11 Statistics Chapter 2 Presentation of Data Ex 2.2 1

Question 4.
Out of total 1850 women working in a factory, 549 were residing in labour area. Out of total married women of labour area, 250 had experience and 93 were inexperienced. The number of experienced and inexperienced women from other area were 87 and 400 respectively. The total number of inexperienced women was 1336 and out of them, 136 were from labour area. Out of total women, 1020 were unmarried. Among them, the number of experienced women from labour area and from other area were 163 and 14 respectively. Present these data in tabular form.
Answer:
In the given data, there are three attributes:

  1. Area of-residence
  2. Marital status and
  3. Experience of service.

According to these three attributes, the data is classified and table is prepared as follows :
Table showing the women working in a factory according to their area of residence, marital status and the experience of service
GSEB Solutions Class 11 Statistics Chapter 2 Presentation of Data Ex 2.2 2
[Note: The figures shown in bold are obtained by simple calculation.]

GSEB Solutions Class 11 Statistics Chapter 2 Presentation of Data Ex 2.2

Question 5.
There were 1250 skilled and 400 unskilled workers in a private company in the year 2011. There were 220 female workers and of them, 140 were unskilled. In the year 2012, the number of skilled workers was 1475 and of them, 1300 were males. Out of 250 unskilled workers, 200 were males. In 2013, there were 1700 skilled and 50 unskilled workers. Out of total workers, 250 were females of them 240 were skilled. In the year 2014, there were 2000 workers and of them 2 % were unskilled. Out of total workers, 300 were females and of them, 10 were unskilled. Present the above data in the form of table.
Answer:
In the given data, there are three attributes:

  1. Year : 2011, 2012, 2013, 2014;
  2. Training: Skill, Unskilled;
  3. Sex: Male, Female.

According to these three attributes, the data is classified and table is prepared as follow:

Table showing the number of workers during the years 2011 to 2014, according to their training and sex
GSEB Solutions Class 11 Statistics Chapter 2 Presentation of Data Ex 2.2 3
[Explanation : 2011 : Total number of workers = 1250 Skilled + 400 Unskilled = 1650
No. of female workers = 220
∴ No. of male workers = 1650-220 = 1430
No. of unskilled workers = 400; No. of unskilled female workers= 140
∴No. of unskilled male workers = 400 – 140 = 260

Now, No. of skilled female workers = 220 – 140 = 80
∴ No. of skilled male workers = 1430 – 260 = 1170

2012 : Total number of workers = 1475 skilled + 250 unskilled = 1725
No. of skilled workers 1475;
No. of skilled male workers = 1300

∴ No. of skilled female workers = 1475- 1300 = 175
No. of unskilled workers = 250,
No. of unskilled male workers = 200
∴ No. of unskilled female workers = 250 – 200 = 50
In this manner, calculate for 2013 and 2014.]

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