Mathematics for IGCSE & O level - Categorical, Numerical And Grouped Data (Section 5)
1
What is the range of the data set: 3, 3, 4, 5, 6, 6, 6, 7?
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(D)
3
2
What is the first step in calculating the median?
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(B)
Ordering values
3
Which average is the easiest to find in a small number of samples?
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(B)
The mode
4
What is the main purpose of the section titled 'Which average to use when comparing data?'
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(C)
To explain how the choice of average affects the conclusions you can draw from data.
5
What is the most important use of the mode?
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(B)
To identify the most frequently occurring value.
6
In the context of grouped data, what do class intervals represent?
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(B)
The categories or ranges into which data values are grouped.
7
If the range of a dataset is 25, and the smallest value is 10, what is the largest value?
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(D)
35
8
In a frequency table, what does the frequency of a class interval represent?
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(C)
The number of times the values fall within that interval
9
If you want to make it easier to analyse the answers to each question, what should you do when designing a questionnaire?
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(B)
Limit the choices
10
How should the questions be when you are designing a questionnaire?
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(C)
Make the questions clear and concise
11
What are the two factors that the data collected can sometimes be based on?
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(B)
The colour of a car and where it was made
12
If a value occurs most frequently, what is it?
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(B)
Mode
13
In a data set containing the ages of students, the ages are measured on a continuous scale. Which measure is best to summarize the age of students?
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(D)
Mean
14
What does the term 'skewness' refer to in a dataset?
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(C)
The symmetry or asymmetry of the data distribution
15
What are the properties of a right-skewed distribution?
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B
C
16
If a survey is asking for an age range, and if it is to be accurate, what must be considered?
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(B)
Make sure groups are distinct
17
If a dataset contains the values: 1, 2, 2, 3, 3, 3, 4, 5, what is the median?
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(B)
3
18
When constructing a frequency table, which are important elements to consider?
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A
B
19
What does a frequency table contain?
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A
B
C
20
For a dataset with a mean of 50 and a standard deviation of 5, a data value of 60 would be how many standard deviations from the mean?
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(B)
2
21
What is a key difference between discrete and continuous data?
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(B)
Discrete data can only be whole numbers; continuous data can take decimal values.
22
What is a disadvantage of the mean?
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(B)
The mean has a disadvantage that it uses every data value.
23
What should you consider when designing a questionnaire?
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A
B
24
When designing a questionnaire, what should you avoid?
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(C)
Leading questions.
25
In a left-skewed distribution, the mean is generally:
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(C)
Less than the median.
26
Which of the following is the simplest type of average?
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(A)
Mean
27
If the mean of a set of data is 25 and the sum of the data values is 100, how many data points are in the set?
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(B)
4
28
If the mode of a data set is 5 and the range is 10, what can you conclude?
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(B)
The dataset contains at least one 5.
29
What do the class boundaries represent in a frequency table for continuous data?
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(B)
The exact limits of each class.
30
What is the use of the 'More than' category?
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(A)
To record all the responses that don't fit into the existing rows.
31
What should you avoid when writing a questionnaire?
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(C)
Asking leading questions.
32
What does a small range tell you about the data?
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(A)
The data is clustered.
33
When can the mode be used for a small number of samples?
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(D)
When you have a small dataset and easy to identify.
34
What is the primary use of a frequency table?
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(C)
To organize and summarize data by showing how often each value or group of values occurs.
35
What is the purpose of a stem-and-leaf plot?
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(C)
To display the data's distribution and retain the original data values.
36
What would be the most appropriate measure of central tendency to describe the typical age of individuals in a community, knowing there is a high proportion of older individuals?
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(C)
Median
37
Which statement is true about continuous data?
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(B)
It can be measured on a scale and take on any value within a range.
38
What is the main purpose of a frequency table?
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(A)
To organize data, including tallies, and frequencies.
39
Which statement is correct when comparing the mean, median, and mode in a symmetrical distribution?
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(C)
Mean = Median = Mode
40
If you want to know the relationship between two different factors, what do you use?
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(B)
A two-way table.
41
Which type of average is not affected by extreme values?
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(C)
Median
42
What do the mode, median, and mean do?
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B
D
43
What is the main goal of data summarization using statistical measures?
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(C)
To simplify and condense a dataset for easier understanding.
44
Which of the following is an advantage of the mean?
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(B)
It is easy to calculate and understand.
45
What is the purpose of a Two-way table?
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(C)
To analyse two factors.
46
When might the mode not be a useful measure of central tendency?
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(B)
When there is no mode.
47
In the context of frequency tables, what does 'class width' refer to?
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(B)
The difference between the upper and lower class limits of a specific interval.
48
In a frequency table, what components are needed to find the estimate of the mean?
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B
C
49
In a two-way table, how is the total number calculated?
