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?
Answer
(D)
3
2
What is the first step in calculating the median?
Answer
(B)
Ordering values
3
Which average is the easiest to find in a small number of samples?
Answer
(B)
The mode
4
What is the main purpose of the section titled 'Which average to use when comparing data?'
Answer
(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?
Answer
(B)
To identify the most frequently occurring value.
6
In the context of grouped data, what do class intervals represent?
Answer
(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?
Answer
(D)
35
8
In a frequency table, what does the frequency of a class interval represent?
Answer
(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?
Answer
(B)
Limit the choices
10
How should the questions be when you are designing a questionnaire?
Answer
(C)
Make the questions clear and concise
11
What are the two factors that the data collected can sometimes be based on?
Answer
(B)
The colour of a car and where it was made
12
If a value occurs most frequently, what is it?
Answer
(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?
Answer
(D)
Mean
14
What does the term 'skewness' refer to in a dataset?
Answer
(C)
The symmetry or asymmetry of the data distribution
15
What are the properties of a right-skewed distribution?
Answer
B
C
16
If a survey is asking for an age range, and if it is to be accurate, what must be considered?
Answer
(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?
Answer
(B)
3
18
When constructing a frequency table, which are important elements to consider?
Answer
A
B
19
What does a frequency table contain?
Answer
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?
Answer
(B)
2
21
What is a key difference between discrete and continuous data?
Answer
(B)
Discrete data can only be whole numbers; continuous data can take decimal values.
22
What is a disadvantage of the mean?
Answer
(B)
The mean has a disadvantage that it uses every data value.
23
What should you consider when designing a questionnaire?
Answer
A
B
24
When designing a questionnaire, what should you avoid?
Answer
(C)
Leading questions.
25
In a left-skewed distribution, the mean is generally:
Answer
(C)
Less than the median.
26
Which of the following is the simplest type of average?
Answer
(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?
Answer
(B)
4
28
If the mode of a data set is 5 and the range is 10, what can you conclude?
Answer
(B)
The dataset contains at least one 5.
29
What do the class boundaries represent in a frequency table for continuous data?
Answer
(B)
The exact limits of each class.
30
What is the use of the 'More than' category?
Answer
(A)
To record all the responses that don't fit into the existing rows.
31
What should you avoid when writing a questionnaire?
Answer
(C)
Asking leading questions.
32
What does a small range tell you about the data?
Answer
(A)
The data is clustered.
33
When can the mode be used for a small number of samples?
Answer
(D)
When you have a small dataset and easy to identify.
34
What is the primary use of a frequency table?
Answer
(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?
Answer
(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?
Answer
(C)
Median
37
Which statement is true about continuous data?
Answer
(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?
Answer
(A)
To organize data, including tallies, and frequencies.
39
Which statement is correct when comparing the mean, median, and mode in a symmetrical distribution?
Answer
(C)
Mean = Median = Mode
40
If you want to know the relationship between two different factors, what do you use?
Answer
(B)
A two-way table.
41
Which type of average is not affected by extreme values?
Answer
(C)
Median
42
What do the mode, median, and mean do?
Answer
B
D
43
What is the main goal of data summarization using statistical measures?
Answer
(C)
To simplify and condense a dataset for easier understanding.
44
Which of the following is an advantage of the mean?
Answer
(B)
It is easy to calculate and understand.
45
What is the purpose of a Two-way table?
Answer
(C)
To analyse two factors.
46
When might the mode not be a useful measure of central tendency?
Answer
(B)
When there is no mode.
47
In the context of frequency tables, what does 'class width' refer to?
Answer
(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?
Answer
B
C
49
In a two-way table, how is the total number calculated?
