The table shows the daily income (in Rs.) of 50 persons. 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 How many persons earn Rs. 200 or more but less than Rs. 300?
22
Analyzing Daily Income Distribution Data
The problem asks us to find the number of persons whose daily income is Rs. 200 or more but less than Rs. 300, based on the provided cumulative frequency distribution table.
Understanding the Daily Income Table
The table gives us the cumulative number of persons earning less than a certain amount. This is a 'less than' type cumulative frequency distribution.
| Income (Rs) | No. of persons (Cumulative Frequency) |
|---|---|
| Less than 200 | 12 |
| Less than 250 | 26 |
| Less than 300 | 34 |
| Less than 350 | 40 |
| Less than 400 | 50 |
The table shows:
- 12 persons earn less than Rs. 200.
- 34 persons earn less than Rs. 300.
Calculating Persons in the Specific Income Range
We are interested in the number of persons earning Rs. 200 or more but less than Rs. 300. This range can be represented as [200, 300).
The persons earning less than Rs. 300 include everyone who earns less than Rs. 200 plus those who earn Rs. 200 or more but less than Rs. 300.
Therefore, to find the number of persons earning Rs. 200 or more but less than Rs. 300, we can subtract the number of persons earning less than Rs. 200 from the number of persons earning less than Rs. 300.
Number of persons earning in the range [200, 300) = (Number of persons earning < Rs. 300) − (Number of persons earning < Rs. 200)
Using the values from the table:
\text{Number of persons} = 34 - 12
\text{Number of persons} = 22
So, 22 persons earn Rs. 200 or more but less than Rs. 300.
Summary of the Calculation
We used the cumulative frequency data to isolate the frequency for the income bracket of interest (Rs. 200 to Rs. 300). The cumulative frequency 'less than 300' accounts for everyone below 300, while 'less than 200' accounts for everyone below 200. Subtracting the latter from the former gives us precisely the number of people in the 200-300 bracket.
Revision Table: Key Concepts
| Concept | Explanation |
|---|---|
| Daily Income | The amount of money earned per day. |
| Cumulative Frequency | The total frequency of all classes less than the upper class boundary of the current class. In a 'less than' table, it's the count of observations below a certain value. |
| Frequency Distribution | A table that organizes data into classes and shows the number of observations (frequency) in each class. |
| Income Range [200, 300) | Represents income from Rs. 200 up to (but not including) Rs. 300. |
Additional Information on Frequency Distributions
Cumulative frequency distributions are useful for understanding the number of observations below (or above) certain values. To get the simple frequency for a specific class interval from a 'less than' cumulative frequency table, you subtract the cumulative frequency of the lower boundary from the cumulative frequency of the upper boundary.
For example, to find the number of persons earning Rs. 250 or more but less than Rs. 300:
- Persons earning < Rs. 300 = 34
- Persons earning < Rs. 250 = 26
- Persons earning [250, 300) = 34 − 26 = 8
This method allows us to convert cumulative frequency data back into class frequencies for specific intervals.
Similar Questions
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2014-2015
2015-2016
2016-0217
2017-2018
2018-2019
625
690
725
775
815
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A = Total number of cars manufactured by all the companies.
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Study the following table and answer the question:
Percentage of marks obtained by six students in five subjects A, B, C, D & E.
Students
Subject
A
(out of 75)
B
(out of 80)
C
(out of 100)
D
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E
(out of 150)
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68
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72
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84
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Years
Chandigarh
Ahmadabad
Pune
Kolkata
2016
1800
2500
1800
2000
2017
2500
2300
1850
1800
2018
2300
2400
1840
1760
2019
2440
1950
1900
1600
2020
2250
2100
2000
1750
From 2016 to 2020, how many more trees were planted in Ahmedabad as compared to trees planted in Pune?Study the following table and answer the question:
Number of student Appeared (A) and Passed (P) in an annual examination from schools Q, R, S & T in five years (2014 to 2018)
Year
Schools
Q
R
S
T
A
P
A
P
A
P
A
P
2014
320
240
400
340
420
273
250
225
2015
400
320
380
285
350
280
300
228
2016
440
286
360
288
330
264
320
256
2017
350
252
420
294
380
247
350
315
2018
375
320
450
405
400
344
375
300
The total number of students passed from school Q in 2014 and 2018 is what percent less than the total number of students appeared from school R and S in 2017?What is the ratio of the total number of motorcycles of type B produced in 2016 and 2018 to the total number of motorcycles of types D produced in 2013, 2015 and 2016?
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