Based on the data in the table, answer the five questions that follow: The following table shows the population (in lakhs) of the cities P, Q and R over the seven years from 2014 to 2020. Based on the data in the table, answer the five questions that follow: Year‐wise Population of CitiesYear Population of City (in Lakhs) P Q R 2014 40 20 50 2015 45 30 40 2016 60 50 60 2017 50 55 70 2018 70 60 80 2019 65 70 90 2020 80 75 100
What is the approximate average population of City-P for all the given years?
59 Lakhs
Calculating the Approximate Average Population of City P
The question asks for the approximate average population of City-P over the seven years from 2014 to 2020, based on the data presented in the table.
| Year | Population of City (in Lakhs) | ||
|---|---|---|---|
| P | Q | R | |
| 2014 | 40 | 20 | 50 |
| 2015 | 45 | 30 | 40 |
| 2016 | 60 | 50 | 60 |
| 2017 | 50 | 55 | 70 |
| 2018 | 70 | 60 | 80 |
| 2019 | 65 | 70 | 90 |
| 2020 | 80 | 75 | 100 |
Understanding Average Population
The average of a set of numbers is calculated by summing all the numbers in the set and then dividing the sum by the total count of numbers in the set.
In this case, we need to find the average population of City P. The set of numbers is the population of City P for each of the given years, and the count is the total number of years (2014 to 2020).
Step-by-Step Calculation of Average Population of City P
Let's find the population of City P for each year from the table:
- 2014: 40 Lakhs
- 2015: 45 Lakhs
- 2016: 60 Lakhs
- 2017: 50 Lakhs
- 2018: 70 Lakhs
- 2019: 65 Lakhs
- 2020: 80 Lakhs
Step 1: Sum the population of City P for all years.
Sum = $40 + 45 + 60 + 50 + 70 + 65 + 80$ Lakhs
Sum = $410$ Lakhs
Step 2: Count the number of years.
The years are from 2014 to 2020, which is $2020 - 2014 + 1 = 7$ years.
Number of years = $7$ years
Step 3: Calculate the average population of City P.
Average Population = $\frac{\text{Sum of Populations}}{\text{Number of Years}}$
Average Population = $\frac{410}{7}$ Lakhs
Step 4: Perform the division to find the approximate value.
$\frac{410}{7} \approx 58.5714$ Lakhs
Comparing with the Options
Now, let's compare our calculated average ($\approx 58.57$ Lakhs) with the given options:
- Option 1: 65 Lakhs
- Option 2: 59 Lakhs
- Option 3: 52 Lakhs
- Option 4: 54 Lakhs
The value 59 Lakhs is the closest approximation to 58.5714 Lakhs.
Conclusion
The approximate average population of City-P for all the given years is 59 Lakhs.
Revision Table: Average Calculation
Understanding the formula for calculating the average is crucial for solving problems like this.
| Concept | Formula | Application in this problem |
|---|---|---|
| Average | $\text{Average} = \frac{\text{Sum of values}}{\text{Number of values}}$ | $\text{Average Population of P} = \frac{\text{Sum of P's population over 7 years}}{\text{7 years}}$ |
| Summation | Adding up all the individual data points. | Summing $40, 45, 60, 50, 70, 65, 80$. |
| Count | The total number of data points. | There are 7 years, so the count is 7. |
Additional Information: Data Interpretation Skills
Problems based on tables and data require careful interpretation and calculation. Here are some related concepts:
- Data Extraction: Ability to correctly read and pull specific data points from the table. In this case, extracting population figures for City P for each year.
- Approximation: Sometimes, exact values are not required, and rounding to the nearest option or performing approximate calculations is sufficient.
- Other Measures: Besides average, other common measures used in data analysis include median, mode, range, and percentage change.
- Median: The middle value in a dataset when arranged in ascending or descending order.
- Mode: The value that appears most frequently in a dataset.
- Range: The difference between the highest and lowest values in a dataset.
Practicing different types of data interpretation questions from tables, charts, and graphs helps improve analytical skills for competitive exams.
Important Questions from Tabulation
The table shows District-wise data of a number of primary school teachers posted in schools of a city.
Study the table and answer the question:
District
Male teachers
Female teachers
East
1650
2375
North
1075
2651
West
1280
1520
South
1170
1085
Central
690
859
What is the difference between the total number of male teachers in the districts East, North, West taken together and the total number of female teachers in the districts East and South?Table shows income (in Rs. ) received by 4 employees of a company during the month of December 2020 and all their income sources.
Source
Amit
Suresh
Nitin
Varun
Salary
35000
38500
29000
42000
Arrears
6000
6300
5000
7500
Bonus
1000
1100
1000
1240
Overtime
1800
1950
1400
1500
What is the ratio of salary of Varun to his income other than salary?Study the table and answer the question:
Income (Rs.)
No. of persons
Less than 200
12
Less than 250
26
Less than 300
34
Less than 350
40
Less than 400
50
What is the percentage of persons earning Rs. 250 or more?The following table shows the annual profit of a company (in Rs. lakh).
2014-2015
2015-2016
2016-0217
2017-2018
2018-2019
625
690
725
775
815
The period which has the maximum percentage increase in profit over the previous year is:
The table given below shows the number of persons participating in a survey from 6 different states.
States Persons S1 100 S2 200 S3 400 S4 500 S5 600 S6 800 What is the ratio of number of person participating in a survey from state S3 to the number of person participating in a survey from state S4?
