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?
48
Understanding the Income Distribution Data
The question provides data on the income of persons in a community. The data is presented in a cumulative frequency format, specifically as a 'less than' cumulative frequency table. This means each entry in the table shows the total number of persons whose income is below a certain value.
Let's look at the given table:
| Income (Rs.) | No. of persons (Less than) |
|---|---|
| Less than 200 | 12 |
| Less than 250 | 26 |
| Less than 300 | 34 |
| Less than 350 | 40 |
| Less than 400 | 50 |
This table tells us things like:
- 12 persons earn less than Rs. 200.
- 26 persons earn less than Rs. 250.
- 50 persons earn less than Rs. 400. This last entry typically represents the total number of persons surveyed, assuming income doesn't exceed this upper limit in this context. So, the total number of persons is 50.
Calculating Persons Earning Rs. 250 or More
We need to find the percentage of persons who earn Rs. 250 or more. From the table, we know the number of persons earning less than Rs. 250 is 26. The total number of persons is 50.
If 26 persons earn less than Rs. 250 out of a total of 50 persons, the remaining persons must be earning Rs. 250 or more.
Number of persons earning Rs. 250 or more = Total number of persons - Number of persons earning less than Rs. 250
Number of persons earning Rs. 250 or more = $50 - 26$
Number of persons earning Rs. 250 or more = $24$
Calculating the Percentage
Now that we know 24 persons earn Rs. 250 or more out of a total of 50 persons, we can calculate the percentage.
Percentage of persons earning Rs. 250 or more = $\left( \frac{\text{Number of persons earning Rs. 250 or more}}{\text{Total number of persons}} \right) \times 100$
Percentage = $\left( \frac{24}{50} \right) \times 100$
Percentage = $0.48 \times 100$
Percentage = $48$
So, 48% of the persons earn Rs. 250 or more.
Step-by-Step Solution Summary
- Identify the total number of persons from the 'less than' cumulative frequency table. This is the number corresponding to the highest income bracket provided, which is 50 (for 'Less than 400').
- Identify the number of persons earning less than the threshold of interest, which is Rs. 250. From the table, this is 26.
- Calculate the number of persons earning the threshold amount or more by subtracting the number earning less than the threshold from the total number of persons: $50 - 26 = 24$.
- Calculate the percentage by dividing the number of persons earning Rs. 250 or more by the total number of persons and multiplying by 100: $\left( \frac{24}{50} \right) \times 100 = 48\%$.
Revision Table: Key Calculations
| Description | Value | Calculation |
|---|---|---|
| Total number of persons | 50 | From 'Less than 400' entry |
| Persons earning < Rs. 250 | 26 | From table entry |
| Persons earning ≥ Rs. 250 | 24 | $50 - 26$ |
| Percentage earning ≥ Rs. 250 | 48% | $\left( \frac{24}{50} \right) \times 100$ |
Additional Information on Cumulative Frequency
A cumulative frequency table shows the running total of frequencies. A 'less than' cumulative frequency table shows, for each class interval, the total number of observations that are less than the upper boundary of that interval.
In this case, the 'income' values act as the upper boundaries of implied class intervals. For example:
- 'Less than 200' means income range is effectively < 200.
- 'Less than 250' means income range is effectively < 250.
To find the number of persons in a specific income bracket (e.g., between 200 and 250), you would subtract the cumulative frequency of the lower boundary from the cumulative frequency of the upper boundary.
For instance, persons earning between Rs. 200 and Rs. 250 (inclusive of 200, exclusive of 250, based on standard interpretation) would be $26 - 12 = 14$ persons.
Understanding how to convert a cumulative frequency back to simple frequency or to calculate values for ranges is crucial for interpreting such statistical data.
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?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?
The data given in the table shows the number of students studying in 4 different disciplines in 5 institutes.
Study the table and answer the question:
Institutes
Arts
Science
Commerce
Computer Science
A
36
48
59
57
B
45
54
55
48
C
55
36
56
51
D
45
48
55
53
E
48
44
52
55
What is the ratio of number of students studying Science in institutes C and D taken together to the number of students studying Computer Science in institutes A and E taken together?
