Mathematics for IGCSE & O level - Categorical, Numerical And Grouped Data (Section 8)

1
What is the purpose of calculating the median of a dataset?
Answer
(C)
To find the middle value when the data is ordered.
2
In a grouped frequency table, the interval midpoints are used primarily for what purpose?
Answer
(B)
To estimate the mean of the data.
3
When is the median a better measure than the mean?
Answer
(C)
When the data set has extreme values (outliers).
4
What information does a frequency table provide?
Answer
(C)
How often each value (or range of values) occurs in the data.
5
What is the primary advantage of using the mode as a measure of central tendency?
Answer
(C)
It can be calculated for both numerical and categorical data.
6
If the range of the given data set is 10, what can we conclude?
Answer
A
D
7
In the context of grouped discrete data, what is the purpose of multiplying the midpoint of a class by its corresponding frequency?
Answer
(B)
To estimate the total sum of values within that class.
8
What does it mean if the data values have a greater range?
Answer
(C)
The data is less consistent.
9
Why is it often impossible to find out some statistical information?
Answer
(C)
Because you cannot find out from everyone
10
Which statistical measure is least affected by extreme values (outliers) in a data set?
Answer
(B)
Median
11
When are the mean, mode and median similar?
Answer
(D)
When the data is in order and the values are clustered together
12
What is the definition of the range?
Answer
(C)
The difference between the largest and smallest number
13
If all the values in a dataset are identical, what is the range?
Answer
(C)
0
14
In a stem-and-leaf plot, what does the 'stem' represent?
Answer
(B)
The first digit(s) of a data value
15
If the mean, median, and mode of a dataset are all equal, what can you infer about the data distribution?
Answer
(C)
The data is normally distributed.
16
If you have a small number of values, which average is best to easily identify?
Answer
(D)
The mode
17
If the mode of a dataset is 10, what does this indicate?
Answer
(B)
10 is the most frequent value.
18
What is one of the disadvantages of the mean?
Answer
(B)
It uses every data value, which can be misleading with outliers.
19
What should you do after writing a questionnaire?
Answer
(B)
Give it to a few people to test it.
20
What information can a two-way table provide?
Answer
(C)
The relationship between two factors.
21
When is the mode considered the best average?
Answer
(B)
When the data set is simple.
22
If your sample is too small, what can happen?
Answer
(A)
The data will not be accurate.
23
What are the properties of a left-skewed distribution?
Answer
B
D
24
What is the primary purpose of creating a frequency table?
Answer
(B)
To organize and summarize data.
25
If all the values in a data set are different, what is the mode?
Answer
(C)
The data set has no mode.
26
If the values are close together, what does that mean?
Answer
(B)
The data is clustered.
27
What are the components needed to estimate the mean from a frequency table?
Answer
B
C
28
What is a disadvantage of using the mean as a measure of central tendency?
Answer
(B)
It is affected by extreme values or outliers.
29
When summarizing grouped data, which of the following can be used to estimate the median?
Answer
B
C
30
What does a greater range indicate about the data?
Answer
(A)
The data values are less consistent
31
Which of the following is the correct order of calculations when estimating the mean for grouped data?
Answer
(D)
Find the midpoint, multiply by frequency for each class, add the results, and divide by the sum of frequencies.
32
If a greater range indicates data values spread out, how does that affect consistency?
Answer
(B)
The data is less consistent
33
If the mean is 25, the median is 20, and the mode is 18, what type of skewness is present?
Answer
(B)
Right (positive)
34
Which of the following statements about the mode is/are true?
Answer
A
B
D
35
How do you obtain your first step when using a pilot survey?
Answer
(B)
You ask a few people.
36
For continuous data presented in a frequency table, which values are used for calculating an estimate of the mean?
Answer
B
C
37
In a frequency table, how can you show the total number of responses in a given category?
Answer
(A)
By counting the tally marks for that category.
38
If a dataset has the values: 5, 5, 6, 7, 8, 9, 9, 10, what is the mode?
Answer
(A)
5
39
What's the goal when you are taking a survey?
Answer
(B)
To collect a smaller sample of the population.
40
If you have to make a sample, which is the thing that you have to eliminate?
Answer
(B)
Bias
41
If the mode of a set of data is 7, what does that mean?
Answer
(B)
7 is the most frequent value in the dataset.
42
Which measure of central tendency is most useful when there are outliers in your data?
Answer
(C)
Median
43
What do you need to compare when comparing data values?
Answer
(A)
You need to compare the size of the data values and how spread out the data values are using averages.
44
Which measures of average are mentioned in the text?
Answer
A
B
C
45
What are the advantages of using the median?
Answer
(A)
It is not affected by outliers.
46
What can you find from a two-way table?
Answer
A
B
C
47
Which measure of central tendency is most useful when the data has a large number of repeated values?
Answer
(C)
Mode
48
What is the correct calculation for the range?
Answer
(B)
The highest data value - lowest data value
49
What would be a disadvantage of using the mean to describe the central tendency of a dataset containing extreme outliers?
Answer
(B)
The mean would not represent the typical value.
50
What should you do with the questionnaire after you have written your questions?
Answer
(B)
Give the survey to a small group.