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Quantitative Aptitude — Statics 1st grade
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Quantitative Aptitude — Statics 1st grade

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24 mins
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32
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Quantitative Aptitude — Statics 1st grade — Questions with Answers Open after you finish the quiz — all 32 questions, with answers and explanations.
Q1. Which of the following is an example of primary data?
  1. Data collected from a government census report
  2. Data published in a research journal
  3. Data collected by a researcher through direct interviews
  4. Data obtained from a newspaper article
Show answer
Answer: C. Data collected by a researcher through direct interviews
Primary data is original data collected directly by the researcher for a specific purpose. Direct interviews are a method of collecting primary data.
Q2. When is the census method of data collection generally preferred over the sampling method?
  1. When the population is very large and diverse
  2. When resources (time, money) are limited
  3. When high accuracy and detailed information about every unit are required
  4. When quick results are needed
Show answer
Answer: C. When high accuracy and detailed information about every unit are required
The census method is preferred when high accuracy and detailed information about every unit in the population are required, as it involves collecting data from every single member.
Q3. Which method of data collection is most suitable for obtaining information from illiterate respondents?
  1. Mailed questionnaire method
  2. Observation method
  3. Telephone interview method
  4. Email survey method
Show answer
Answer: B. Observation method
The observation method does not require the respondent to read or write, making it suitable for illiterate individuals. Mailed questionnaires and email surveys require literacy.
Q4. What is a major demerit of the 'Direct Personal Investigation' method of data collection?
  1. Lack of originality in data
  2. High cost and time-consuming for large areas
  3. Difficulty in understanding local language
  4. Limited scope of information
Show answer
Answer: B. High cost and time-consuming for large areas
Direct personal investigation involves the investigator personally visiting respondents. While it ensures originality and accuracy, it is very expensive and time-consuming, especially when the area of inquiry is large.
Q5. Which of the following is an example of a discrete variable?
  1. Height of students in a class
  2. Weight of apples in a basket
  3. Number of children in a family
  4. Temperature of a city
Show answer
Answer: C. Number of children in a family
A discrete variable can only take a finite or countable number of values, often whole numbers. The number of children in a family is a discrete variable, as it can only be 0, 1, 2, 3, etc., and not values like 2.5.
Q6. What is the primary purpose of a frequency distribution table?
  1. To calculate the mean of the data
  2. To present raw data in an organized and summarized form
  3. To draw a histogram
  4. To find the median of the data
Show answer
Answer: B. To present raw data in an organized and summarized form
A frequency distribution table organizes raw data into classes or categories and shows the number of observations (frequency) falling into each class, making the data easier to understand and analyze.
Q7. If the upper limit of a class is 50 and the lower limit is 40, what is the class width?
  1. 5
  2. 10
  3. 45
  4. 90
Show answer
Answer: B. 10
Class width is calculated as the difference between the upper limit and the lower limit of a class interval. So, 50 - 40 = 10.
Q8. How would the frequency '9' be represented using tally marks?
  1. |||| ||||
  2. |||| |||| |
  3. |||| |||| ||
  4. |||| |||| |||
Show answer
Answer: B. |||| |||| |
Tally marks are grouped in fives. Four vertical lines are crossed by a fifth diagonal line to represent five. So, 9 would be represented as two groups of five, with one line remaining: |||| |||| |.
Q9. What does cumulative frequency represent in a frequency distribution?
  1. The frequency of a particular class interval
  2. The total frequency of all classes up to and including the current class
  3. The ratio of a class frequency to the total frequency
  4. The midpoint of a class interval
Show answer
Answer: B. The total frequency of all classes up to and including the current class
Cumulative frequency is the running total of frequencies. It tells us the total number of observations that fall below the upper limit of a particular class interval.
Q10. How is the relative frequency of a class calculated?
  1. Class frequency multiplied by total frequency
  2. Class frequency divided by total frequency
  3. Total frequency divided by class frequency
  4. Class frequency minus cumulative frequency
Show answer
Answer: B. Class frequency divided by total frequency
Relative frequency is the proportion of observations falling into a particular class. It is calculated by dividing the frequency of that class by the total number of observations (total frequency).
Q11. Based on the bar chart showing city populations, which city has the highest population?
  1. Mumbai
  2. Delhi
  3. Kolkata
  4. Chennai
Show answer
Answer: B. Delhi
Looking at the bar chart, Delhi has a population of 190L, which is the highest among the listed cities.
Q12. According to the pie chart representing budget allocation, which sector received the highest percentage of the budget?
  1. Education
  2. Health
  3. Defense
  4. Infrastructure
Show answer
Answer: C. Defense
The pie chart shows Defense with 28% allocation, which is the highest among all sectors.
Q13. From the given histogram data, what is the frequency of students who scored marks between 40 and 60?
  1. 6
  2. 14
  3. 22
  4. 16
Show answer
Answer: C. 22
The data provided states that for marks 40-60, the frequency is 22.
Q14. Based on the line chart showing GDP growth, in which year was the GDP growth rate the highest?
  1. 2018
  2. 2019
  3. 2020
  4. 2021
Show answer
Answer: D. 2021
The line chart shows GDP growth rates: 2018=7.2%, 2019=6.1%, 2020=4.0%, 2021=8.9%, 2022=7.0%. The highest growth rate is 8.9% in 2021.
Q15. A frequency polygon is formed by joining the midpoints of the tops of the rectangles in a histogram with straight lines. What are these midpoints also known as?
  1. Class limits
  2. Class boundaries
  3. Class marks
  4. Frequencies
Show answer
Answer: C. Class marks
The midpoints of the class intervals are called class marks. A frequency polygon connects these class marks plotted against their respective frequencies.
Q16. Calculate the mean of the following ungrouped data: 5, 8, 10, 12, 15.
  1. 10
  2. 12
  3. 11
  4. 9
Show answer
Answer: B. 12
The mean is the sum of all observations divided by the number of observations. Sum = 5 + 8 + 10 + 12 + 15 = 50. Number of observations = 5. Mean = 50 / 5 = 10.
Q17. When is the weighted mean particularly useful?
  1. When all observations have equal importance
  2. When some observations are more important than others
  3. When dealing with qualitative data
  4. When the data is highly skewed
Show answer
Answer: B. When some observations are more important than others
The weighted mean is used when different observations have different levels of importance or influence, represented by their respective weights.
Q18. Find the mode of the following raw data: 3, 5, 7, 5, 9, 5, 12.
  1. 3
  2. 5
  3. 7
  4. 12
Show answer
Answer: B. 5
The mode is the value that appears most frequently in a data set. In this data set, 5 appears three times, which is more than any other number.
Q19. Find the median of the following ungrouped data: 10, 12, 15, 8, 20.
  1. 8
  2. 10
  3. 12
  4. 15
Show answer
Answer: C. 12
First, arrange the data in ascending order: 8, 10, 12, 15, 20. There are 5 observations (an odd number). The median is the middle value, which is the (n+1)/2-th term. (5+1)/2 = 3rd term. The 3rd term is 12.
Q20. What is the empirical relationship between Mean, Median, and Mode?
  1. Mean - Mode = 3 (Mean - Median)
  2. Mode = 3 Median - 2 Mean
  3. Median = (Mean + Mode) / 2
  4. Mean = (Mode + Median) / 2
Show answer
Answer: B. Mode = 3 Median - 2 Mean
For a moderately skewed distribution, the empirical relationship between the three measures of central tendency is approximately: Mode = 3 Median - 2 Mean.
Q21. Which of the following is the correct formula for calculating the mean of grouped data using the Direct Method?
  1. Σf / Σx
  2. Σfx / Σf
  3. A + (Σfd / Σf)
  4. A + (Σf(d/h) / Σf) * h
Show answer
Answer: B. Σfx / Σf
For grouped data, the mean (x̄) using the Direct Method is calculated as the sum of the product of frequency (f) and midpoint (x) of each class, divided by the sum of frequencies (Σf).
Q22. When is the Assumed Mean Method (Short-cut Method) for calculating the mean of grouped data generally preferred?
  1. When the frequencies are very small
  2. When the class intervals are unequal
  3. When the midpoints (x) and frequencies (f) are large numbers, making direct calculation tedious
  4. When the data is qualitative
Show answer
Answer: C. When the midpoints (x) and frequencies (f) are large numbers, making direct calculation tedious
The Assumed Mean Method simplifies calculations when the midpoints and frequencies are large, reducing the size of numbers involved in multiplication.
Q23. In the Step Deviation Method for calculating the mean of grouped data, what does 'h' represent?
  1. Assumed mean
  2. Frequency of the class
  3. Class size or width
  4. Deviation from the assumed mean
Show answer
Answer: C. Class size or width
In the Step Deviation Method, 'h' represents the common class size or width of the class intervals, which is used to simplify the deviations.
Q24. How is the 'modal class' identified in a frequency distribution table for grouped data?
  1. The class with the lowest frequency
  2. The class with the highest cumulative frequency
  3. The class with the highest frequency
  4. The class containing the median
Show answer
Answer: C. The class with the highest frequency
The modal class is the class interval that has the highest frequency. It is the class where the mode is expected to lie.
Q25. What is the formula for frequency density?
  1. Frequency × Class width
  2. Frequency / Class width
  3. Class width / Frequency
  4. Cumulative frequency / Class width
Show answer
Answer: B. Frequency / Class width
Frequency density is used when class intervals are unequal. It is calculated by dividing the frequency of a class by its class width.
Q26. Which of the following is the correct formula for calculating the Mode of grouped data?
  1. L + [(n/2 - cf) / f] * h
  2. L + [(f1 - f0) / (2f1 - f0 - f2)] * h
  3. Σfx / Σf
  4. A + (Σfd / Σf)
Show answer
Answer: B. L + [(f1 - f0) / (2f1 - f0 - f2)] * h
The formula for Mode of grouped data is L + [(f1 - f0) / (2f1 - f0 - f2)] * h, where L is the lower limit of the modal class, f1 is the frequency of the modal class, f0 is the frequency of the class preceding the modal class, f2 is the frequency of the class succeeding the modal class, and h is the class size.
Q27. Which of the following is the correct formula for calculating the Median of grouped data?
  1. L + [(f1 - f0) / (2f1 - f0 - f2)] * h
  2. L + [(n/2 - cf) / f] * h
  3. Σfx / Σf
  4. A + (Σfd / Σf)
Show answer
Answer: B. L + [(n/2 - cf) / f] * h
The formula for Median of grouped data is L + [(n/2 - cf) / f] * h, where L is the lower limit of the median class, n is the total frequency, cf is the cumulative frequency of the class preceding the median class, f is the frequency of the median class, and h is the class size.
Q28. What is an ogive curve primarily used for in statistics?
  1. To find the mode of the data
  2. To represent the frequency distribution of discrete data
  3. To graphically determine the median and quartiles of grouped data
  4. To show the relationship between two variables
Show answer
Answer: C. To graphically determine the median and quartiles of grouped data
An ogive (cumulative frequency curve) is a graphical representation used to determine the median, quartiles, and other positional values for grouped data.
Q29. What does a point on a 'less than' ogive represent?
  1. The number of observations greater than a certain value
  2. The frequency of a specific class interval
  3. The number of observations less than or equal to the upper limit of a class interval
  4. The midpoint of a class interval
Show answer
Answer: C. The number of observations less than or equal to the upper limit of a class interval
A 'less than' ogive plots cumulative frequencies against the upper class boundaries. Thus, a point on it represents the number of observations less than or equal to that upper boundary.
Q30. What does the intersection point of 'less than' and 'more than' ogives represent?
  1. Mean
  2. Mode
  3. Median
  4. Standard Deviation
Show answer
Answer: C. Median
The intersection point of the 'less than' and 'more than' ogives graphically determines the median of the grouped data.
Q31. Which type of variable can take any value within a given range?
  1. Discrete variable
  2. Categorical variable
  3. Continuous variable
  4. Nominal variable
Show answer
Answer: C. Continuous variable
A continuous variable can take any value within a specified range, including fractions and decimals, such as height, weight, or temperature.
Q32. Which of the following is a demerit of the sampling method?
  1. It is very costly and time-consuming.
  2. It may not always provide a true representation of the population.
  3. It requires highly skilled investigators.
  4. It is suitable only for small populations.
Show answer
Answer: B. It may not always provide a true representation of the population.
While sampling is cost-effective and less time-consuming, a major demerit is the risk of sampling error, meaning the sample might not perfectly represent the entire population, leading to less accurate conclusions than a census.
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