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All questions of Histograms for UGC NET Exam

A histogram is to be drawn for following frequency distribution
Q. The adjusted frequency for classinterval 15-25 will be :
  • a)
    2
  • b)
    5
  • c)
    3
  • d)
    None of the above
Correct answer is option 'B'. Can you explain this answer?

JKL Classes answered
Formula Used:
Adjusted frequency = (Frequency of the classinterval x Minimum ClassWidth)/Class width of the required interval
Calculation:
For classinterval
15 - 25,
Classwidth = upper limit of the class- lower limit of the class
=> Classwidth = 2 5 - 1 5 = 1 0
Frequency of that interval = 10
Minimum classwidth here is for the interval 5 - 10= 5
Adjusted frequency = (10* 5)/10= 5
Therefore, the adjusted frequency for the class interval 15 - 25 is 5.

Study the following graph and answerthe question given below.
Q. What percentage (approx.) of the employees working in the range of Rs. 30,000 - Rs. 40,000?
  • a)
    51%
  • b)
    49%
  • c)
    55%
  • d)
     None of the above
Correct answer is option 'A'. Can you explain this answer?

Given:
The number of employees whose income is in the range of Rs. 20,000 - Rs. 25,000 = 25
The number of employees whose income is in the range of Rs. 25,000 - Rs. 30,000 = 45
The number of employees whose income is in the range of Rs. 30,000 - Rs. 35,000 = 66
The number of employees whose income is in the range of Rs. 35,000 - Rs. 40,000 = 44
number of employees whose income is in the range of Rs. 40,000 - Rs. 45,000 = 35
Calculation:
According to the question, The total number of employee = 25 + 45 + 66 + 44 + 35 = 215
The number of employees whose income is in the range of Rs. 30,000-Rs. 40,000 = 66 + 44 = 110
The required percentage = 110 x 100 ≈ 51%

Study the given histogram and answer the question that follows.

Q. The number of persons weighing 55 kg or more but less than 75 kg is what percentage more than the number of persons weighing 80 kg or more but less than 100 kg (correct to one decimal place)?
  • a)
    88.2%
  • b)
    77.8%
  • c)
    68.4%
  • d)
    66.7%
Correct answer is option 'B'. Can you explain this answer?

Calculation:
The number of persons weighing 55 kg or more but less than 75 kg = (25 + 35 + 52 + 48) = 160
The number of persons weighing 80 kg or more but less than 100 kg = (38 + 30 + 13 + 9) = 90
Now,
Required percentage = [(160 – 90)/90 × 100]
⇒ (70/90 × 100)
⇒ (700/9)
⇒ 77.8%
∴ The required percentage is 77.8%

The given histogram represents the marks of students in Mathematics test of a certain class. The total number of students is 350.
Study the graph and answer the question that follows.
Q. What is the ratio of the total number of students who scored 140 marks and above to the total number of students who scored marks between 60 to 120?
  • a)
    11 : 9
  • b)
    9 : 11
  • c)
    110 : 137
  • d)
    137 : 110
Correct answer is option 'C'. Can you explain this answer?

Academia Elite answered
Given:
The total number of students = 350
Calculation:
The total number of students who scored 140 marks and above = 55 + 40 + 15 = 110
The total number of students who scored marks between 60 to 120 = 32 + 45 + 60 = 137
The ratio = 110 : 137
∴ The ratio of the total number of students who scored 140 marks and above to the total number of students who scored marks between 60 to 120 is 110 : 137

The given histogram showsthe daily wages (in Rs.)of workers in a factory. Study the histogram and answerthe question that follows.
Q. The number of workers with daily wages lessthan Rs. 180 is what percentage of the number of workers with daily wages more than Rs. 190? Expressyour answer correct to one decimal place.
  • a)
    75.8%
  • b)
    85.6%
  • c)
    74.8%
  • d)
    86.7%
Correct answer is option 'C'. Can you explain this answer?

Given:
There is the histogram shows the daily wages ( in Rs.)of workers in a factory.
Calculation:
The number of workers with daily wages lessthan Rs.180= 55+ 80+ 108 = 243
The number of workers with daily wages is more than Rs. 190 = 150+ 105+ 70 = 325
The percentage = (243/325) x 100 = 74.76...% = 74.8%
∴ The number of workers with daily wages less than Rs. 180 is 74.8% of the number of workers with daily wages more than Rs. 190

The number of cars passing the road near a colony from 6 am to 12 noon has been shown in the following histogram.
What is the ratio of the number of cars passed between 6 am and 8 am to the number of cars passed between 9 am and 11 am?
  • a)
    7 : 4
  • b)
    21 : 19
  • c)
    14 : 23
  • d)
    5 : 6
Correct answer is option 'D'. Can you explain this answer?

Given:
There are the number of cars passing the road near a colony from 6 am to 12 noon has been shown in the following histogram.
Calculation:
The number of cars passed between 6 am and 8 am = 70 + 105 = 175
The number of cars passed between 9 am and 11 am = 115 + 95 = 210
The ratio = 175 : 210 = 5 : 6
∴ The ratio of the number of cars passed between 6 am and 8 am to the number of cars passed between 9 am and 11 am is 5 : 6

The following histogram shows the marks scored by 40 to student in a test of 30 marks. A student has to score a minimum of 10 marksto pass the test.
Q. How many students have passedthe test and obtained lessthan 50% marks?
  • a)
    15
  • b)
    7
  • c)
    10
  • d)
    17
Correct answer is option 'B'. Can you explain this answer?

JKL Classes answered
Given:
The total marks of the test = 30
Minimum pass marks = 10
Calculation:
50% of the total marks = (50/100) × 30 = 15
Total number of students who scored between 10 and 15 = 7
∴ A total number of 7 students have passed the test and obtained less than 50% marks.

Observe the graph and answerthe question that follows.
Q. How many students obtained marks more than 130?
  • a)
    14
  • b)
    19
  • c)
    20
  • d)
    17
Correct answer is option 'C'. Can you explain this answer?

JKL Classes answered
Calculations:
According to the question,
Students obtained 135 marks = 2
Students obtained 140 marks = 8
Students obtained 145 marks = 5
Students obtained 150 marks = 4
Students obtained 155 marks = 1
Total students obtained marks more than 130 = 2 + 8 + 5 + 4 + 1 = 20
∴ 20 students obtained marks more than 130.

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