Test your knowledge 20 MCQs on Organizing Qualitative Data, Frequency Distributions & Percentiles with Answers
Test your knowledge with 20 multiple-choice questions (MCQs) on organizing qualitative data, constructing frequency distributions, and computing percentiles. Includes answers and explanations for better understanding.
1. What is the primary goal of organizing qualitative data?
a) To calculate standard deviation
b) To summarize and categorize data meaningfully
c) To determine the median
d) To create scatter plots
Answer: b) To summarize and categorize data meaningfully
Explanation: Qualitative data is categorized into meaningful groups to identify patterns and trends.
2. Which of the following is NOT a type of frequency distribution?
a) Grouped frequency distribution
b) Relative frequency distribution
c) Cumulative frequency distribution
d) Standardized frequency distribution
Answer: d) Standardized frequency distribution
Explanation: There is no such thing as a standardized frequency distribution. The other three are commonly used types.
3. A grouped frequency distribution is used when:
a) Data consists of categorical values
b) Data is continuous and large
c) Data is already in relative form
d) Data consists only of whole numbers
Answer: b) Data is continuous and large
Explanation: When data has a wide range, grouping it into classes helps in summarization.
4. The sum of relative frequencies in a relative frequency distribution is always:
a) 0
b) 1
c) 100
d) Variable
Answer: b) 1
Explanation: The relative frequency represents the proportion of each class, and all proportions together add up to 1.
5. The cumulative frequency of a class is found by:
a) Multiplying frequency by class width
b) Adding the frequency of that class to all previous frequencies
c) Dividing frequency by total observations
d) Subtracting class midpoint from total observations
Answer: b) Adding the frequency of that class to all previous frequencies
Explanation: Cumulative frequency provides a running total of all frequencies up to a certain class.
6. What is the 50th percentile also known as?
a) First quartile
b) Median
c) Mean
d) Mode
Answer: b) Median
Explanation: The 50th percentile represents the middle value in an ordered dataset.
7. In a grouped frequency distribution, the class width is calculated as:
a) Range divided by number of classes
b) Sum of all class frequencies
c) Total frequency multiplied by 100
d) Highest class value minus lowest class value
Answer: a) Range divided by number of classes
Explanation: Class width helps determine the size of each interval in grouped data.
8. If a data set has 50 observations, which percentile is the 10th value in an ordered list?
a) 10th percentile
b) 20th percentile
c) 25th percentile
d) 50th percentile
Answer: b) 20th percentile
Explanation: Percentile position = (percentile rank/100) × total observations.
9. A cumulative frequency distribution is useful for:
a) Calculating mean and mode
b) Finding percentiles
c) Determining the standard deviation
d) Measuring categorical data
Answer: b) Finding percentiles
Explanation: Cumulative frequencies help in percentile calculations by showing accumulated totals.
10. Which of the following is a key characteristic of qualitative data?
a) Measurable numerical values
b) Can be grouped into categories
c) Always continuous
d) Requires arithmetic calculations
Answer: b) Can be grouped into categories
Explanation: Qualitative data represents non-numeric attributes such as colors or names.
11. The mode of a qualitative data set is:
a) The most frequently occurring category
b) The average category
c) The cumulative sum of categories
d) The relative frequency of all categories
Answer: a) The most frequently occurring category
Explanation: The mode represents the category with the highest frequency.
12. What does a relative frequency distribution show?
a) The number of occurrences of each class
b) The proportion of each class relative to the total observations
c) The sum of all class intervals
d) The range of the dataset
Answer: b) The proportion of each class relative to the total observations
Explanation: Relative frequency represents class occurrences as a fraction of the total data set.
13. A percentile rank tells us:
a) The percentage of data points below a given value
b) The middle value in the dataset
c) The total sum of all frequencies
d) The number of unique values in the data
Answer: a) The percentage of data points below a given value
Explanation: Percentile ranks indicate the relative standing of a value in a dataset.
14. What is the range of a dataset?
a) Difference between highest and lowest values
b) Sum of all values divided by total frequency
c) The middlemost value
d) The most frequently occurring value
Answer: a) Difference between highest and lowest values
Explanation: Range measures data spread and is calculated as max – min.
15. Which of the following methods is commonly used to group qualitative data?
a) Histogram
b) Pie chart
c) Frequency table
d) Line graph
Answer: c) Frequency table
Explanation: Frequency tables summarize qualitative data into categories with their counts.
16. In a cumulative frequency table, the last value should equal:
a) The highest value in the dataset
b) The total number of observations
c) The class width
d) The median
Answer: b) The total number of observations
Explanation: Cumulative frequency accumulates data up to the total count.
17. The difference between relative and cumulative frequency is:
a) Relative frequency is based on count, while cumulative frequency is based on total accumulation
b) Relative frequency adds up to the highest value, cumulative does not
c) Cumulative frequency is always less than relative frequency
d) There is no difference
Answer: a) Relative frequency is based on count, while cumulative frequency is based on total accumulation
Explanation: Relative frequency represents proportions, while cumulative frequency is a running total.
18. If the 90th percentile in a dataset is 85, this means:
a) 90% of the data values are greater than 85
b) 90% of the data values are less than or equal to 85
c) The median is 85
d) The range of data is 85
Answer: b) 90% of the data values are less than or equal to 85
Explanation: A percentile indicates the percentage of data points below a specific value.
19. What graph is commonly used to represent cumulative frequency?
a) Pie chart
b) Ogive
c) Scatter plot
d) Bar chart
Answer: b) Ogive
Explanation: An ogive is a line graph used to visualize cumulative frequencies.
20. What is the percentile rank of a value that is greater than 75% of the dataset?
a) 75
b) 25
c) 50
d) 100
Answer: a) 75
Explanation: A percentile rank of 75 means the value is higher than 75% of the observations.
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