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

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

Question 1. There were 1400 students enrolled in a commerce college. Of these, 855 were boys, and among the boys, 225 were in their second year. In the second year, the number of boys was equal to the number of girls. Out of 550 first-year students, the ratio of boys to girls was 3:2. In the third year, the number of boys was three times the number of girls. Present this information in a table.

Answer: The provided data presents two key attributes for classification:
1. The academic year of study, and
2. The gender of the students.
Based on these two attributes, the student data is organized into the following table, illustrating the distribution of students in a commerce college by 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:
The total number of students in the first year was 550.
The boy-to-girl proportion for first-year students was 3:2.
Therefore, the number of boys = \( \frac{3}{5} \times 550 = 330 \)
And the number of girls = \( \frac{2}{5} \times 550 = 220 \)
The number of students in the third year = \( 1400 - (550 + 450) \)
= \( 1400 - 1000 = 400 \)
The number of boys in the third year is three times the number of girls, which means the proportion was 3:1.
Thus, the number of boys = \( \frac{3}{4} \times 400 = 300 \)
And the number of girls = \( \frac{1}{4} \times 400 = 100 \)]
[Note: Figures highlighted in bold are derived through straightforward calculations.]
In simple words: This question requires organizing student data from a college, categorized by their academic year and gender, into a clear table after calculating various unknown figures based on given ratios and totals.

🎯 Exam Tip: Pay close attention to proportions and conditional counts (e.g., "of them, 225 boys were in the second year") when filling out the table. Ensure all derived values align with the total student count.

Question 2. An office has 1600 employees. The number of men among these employees exceeded the number of women by 15% of the total employee count. The number of unmarried employees was 800 fewer than the number of married employees. There were 195 unmarried women. Present these data in a suitable table.

Answer: The given information highlights two primary attributes for classification:
1. The gender of the employees, and
2. Their marital status.
By classifying the data according to these two attributes, a table is constructed as follows:
Table illustrating the distribution of employees in an office based on their gender and marital status:

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

[Explanation:
Let's assume the number of male employees is \(x\).
Therefore, the number of female employees = \(1600 - x\).
The number of males = Number of females + \(1600 \times \frac{15}{100}\)
\(x = (1600 - x) + 240\)
\(2x = 1840\)
\(x = 920\)
So, the number of females = \(1600 - 920 = 680\).
Now, let's assume the number of married employees is \(x\).
Thus, the number of unmarried employees = \(1600 - x\).
The number of unmarried employees = Number of married employees - 800.
\(1600 - x = x - 800\)
\(2x = 1600 + 800 = 2400\)
\(x = 1200\)
Therefore, the number of unmarried employees = \(1600 - 1200 = 400\).]
[Note: Figures presented in bold are derived through simple calculations.]
In simple words: This task involves organizing office employee data into a table, classifying them by gender and marital status. It requires using given percentages and differences to determine the total counts for each category.

🎯 Exam Tip: When constructing tables from descriptive text, first identify all categories and sub-categories. Then, carefully deduce unknown values using algebraic equations based on the provided relationships and totals.

Question 3. Prepare a blank table considering the following characteristics for candidates applying for various bank jobs:
(1) Designation: Manager, clerk, cashier, peon.
(2) Marital status: Married, unmarried.
(3) Gender: Male, female.

Answer: To represent the candidates called for recruitment at a bank, considering their post, marital status, and gender, the following blank table structure is prepared:
Table showing candidates for bank recruitment by post, marital status, and gender:

Post	Marital status						Total candidates
	Married			Unmarried
	Male	Female	Total	Male	Female	Total	Male	Female	Total
Manager
Clerk
Cashier
Peon
Total

In simple words: This task requires creating an empty table structure to categorize potential bank employees based on their job designation, whether they are married or unmarried, and their gender.

🎯 Exam Tip: For blank tables, ensure all specified attributes are included as clear row or column headers, and add appropriate "Total" rows and columns for complete data aggregation.

Question 4. Out of 1850 women working in a factory, 549 resided in the labor area. Among the married women from the labor area, 250 were experienced, and 93 were inexperienced. The counts of experienced and inexperienced women from other areas were 87 and 400, respectively. The total number of inexperienced women was 1336, with 136 of them from the labor area. Of the total women, 1020 were unmarried. Among them, the number of experienced women from the labor area and other area was 163 and 14, respectively. Present these data in a tabular format.

Answer: The provided data involves three classification attributes:
1. Area of residence (labor area or other area),
2. Marital status (married or unmarried), and
3. Work experience (experienced or inexperienced).
Based on these three attributes, the data is organized into the following table:
Table displaying women factory workers by their area of residence, marital status, and work experience:

Area of residence	Marital status						Total women
	Married			Unmarried
	Experienced	Not experienced	Total	Experienced	Not experienced	Total	Experienced	Not experienced	Total
Labour	250	93	343	163	43	206	413	136	549
Other	87	400	487	14	800	814	101	1200	1301
Total	337	493	830	177	843	1020	514	1336	1850

[Note: Figures presented in bold are derived through simple calculations.]
In simple words: This problem requires constructing a detailed table to classify women working in a factory based on where they live, their marital status, and whether they are experienced in their job, using multiple given numerical clues.

🎯 Exam Tip: When dealing with multiple attributes, identify primary and secondary classification criteria. Use a systematic approach, starting with known totals and gradually filling in sub-categories by deduction and calculation.

Question 5. In 2011, a private company employed 1250 skilled and 400 unskilled workers, including 220 female workers, of whom 140 were unskilled. In 2012, there were 1475 skilled workers, with 1300 being males, and 250 unskilled workers, with 200 being males. By 2013, the company had 1700 skilled and 50 unskilled workers, and out of the total workers, 250 were females, 240 of whom were skilled. In 2014, there were 2000 workers, with 2% being unskilled. Out of the total 2000 workers, 300 were females, and 10 of them were unskilled. Present this data in a tabular form.

Answer: The provided data can be categorized using three main attributes:
1. The year (2011, 2012, 2013, 2014),
2. The type of training (skilled, unskilled), and
3. The gender of the workers (male, female).
According to these three attributes, the data is classified and presented in the following table:
Table illustrating the number of workers by year, training, and gender from 2011 to 2014:

Year	Skilled			Unskilled			Total workers
	Male	Female	Total	Male	Female	Total	Male	Female	Total
2011	1170	80	1250	260	140	400	1430	220	1650
2012	1300	175	1475	200	50	250	1500	225	1725
2013	1460	240	1700	40	10	50	1500	250	1750
2014	1670	290	1960	30	10	40	1700	300	2000

[Explanation:
**2011:**
Total number of workers = 1250 Skilled + 400 Unskilled = 1650
Number of female workers = 220
Thus, number of male workers = \(1650 - 220 = 1430\)
Number of unskilled workers = 400; Number of unskilled female workers = 140
So, number of unskilled male workers = \(400 - 140 = 260\)
Now, number of skilled female workers = \(220 - 140 = 80\)
So, number of skilled male workers = \(1430 - 260 = 1170\)
**2012:**
Total number of workers = 1475 skilled + 250 unskilled = 1725
Number of skilled workers = 1475;
Number of skilled male workers = 1300
Thus, number of skilled female workers = \(1475 - 1300 = 175\)
Number of unskilled workers = 250,
Number of unskilled male workers = 200
So, number of unskilled female workers = \(250 - 200 = 50\)
Calculations for 2013 and 2014 are performed similarly.]
In simple words: This problem requires compiling a table that tracks the number of skilled and unskilled male and female workers in a company over four years, using various given totals, percentages, and subtractions to fill in all the details.

🎯 Exam Tip: For problems involving time-series data with multiple classifications, break down the information year by year. Carefully use given totals and percentages to calculate missing values for each attribute (skill level, gender) before compiling the final table.