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Mathematics for IGCSE & O level - Statistical Diagrams (Section 5)

1
In a scatter diagram, what does a weak negative correlation suggest about the relationship between the two variables?
Answer
(B)
As one variable increases, the other decreases, but not strongly.
2
What does the height of a bar in a histogram represent when the class intervals are of equal width?
Answer
(A)
The frequency.
3
Which statistical diagrams are suitable for representing categorical data?
Answer
A
B
4
In a cumulative frequency diagram, what does the y-axis typically represent?
Answer
(B)
Cumulative frequency
5
How is the mode determined from a frequency table or histogram?
Answer
(B)
The most frequent value.
6
Which of the following measures is least affected by extreme values in a data set?
Answer
(D)
Median
7
Which of the following is a characteristic of positive correlation?
Answer
(A)
Data points going from bottom left to top right
8
Which of the following statements about cumulative frequency diagrams is correct?
Answer
(C)
They are used to estimate the median.
9
Which of the following are key features of a histogram?
Answer
A
B
C
10
If the bars of a histogram have varying widths, the y-axis represents:
Answer
(B)
Frequency density
11
What is the definition of frequency density?
Answer
(A)
Frequency divided by class width
12
What does the upper quartile represent?
Answer
(C)
The value below which 75% of the data falls.
13
What is the interquartile range (IQR)?
Answer
(C)
The range of the middle 50% of the data.
14
In statistics, what is the definition of the range?
Answer
(B)
The difference between the maximum and minimum values.
15
What is the advantage of representing data using a cumulative frequency diagram?
Answer
(B)
It allows for the easy estimation of the median and quartiles.
16
Which of the following best describes what a scatter diagram shows?
Answer
(B)
The relationship between two variables
17
What is the relationship between the frequency and the area of a bar in a histogram when class widths are not equal?
Answer
(B)
Frequency is proportional to the area
18
What does a horizontal section in a cumulative frequency diagram indicate?
Answer
(B)
No values in that interval.
19
What is the purpose of a line of best fit on a scatter diagram?
Answer
(B)
To estimate the relationship between the variables
20
What information can be obtained from the cumulative frequency curve?
Answer
A
C
21
In a cumulative frequency table, the cumulative frequency represents...
Answer
(B)
The sum of the frequencies up to and including a particular class interval
22
What is indicated if, in a scatter diagram, the points are clustered closely to the line of best fit?
Answer
(B)
A strong correlation
23
Which of the following correctly describes the median?
Answer
B
C
24
Which of the following can be used to represent data distribution?
Answer
A
B
25
Which of the following elements are needed to calculate the probability in the tree diagram?
Answer
A
B
C
26
What is the formula used to estimate the frequency from a frequency density graph?
Answer
(C)
Frequency = Class Width x Frequency Density
27
Which of the following best describes the shape of a cumulative frequency curve?
Answer
(B)
An increasing curve.
28
If a data set has a median of 50 and a lower quartile of 30, what is the value of the 50th percentile?
Answer
(B)
50
29
What does a straight, sloping line in a cumulative frequency diagram indicate about the data distribution?
Answer
(A)
Data is evenly distributed in that interval.
30
Which of the following methods are usually the best for representing data?
Answer
A
C
31
Which of the following are ways to describe the spread of a data set?
Answer
A
B
D
32
When the class intervals have equal widths, how does the height of a bar in a histogram relate to the frequency?
Answer
(A)
The height is directly proportional to the frequency.
33
In a cumulative frequency diagram, the upper quartile can be found by...
Answer
(C)
reading off the value corresponding to 75% of the total frequency.
34
Which statement is true concerning the range of a dataset?
Answer
(B)
The range is very susceptible to extreme values or outliers.
35
Which measure would be most useful in describing the spread of data if the data has significant outliers?
Answer
(B)
The interquartile range (IQR)
36
What does the interquartile range (IQR) measure?
Answer
(B)
The spread of the middle 50% of the data.
37
Which graphical representation is MOST suitable for displaying continuous data?
Answer
(C)
Histogram
38
Which statement best describes the relationship between frequency density, frequency, and class width in a histogram?
Answer
(B)
Frequency = Frequency density * Class width
39
What is the relationship between a cumulative frequency diagram and a frequency table?
Answer
(B)
A cumulative frequency diagram is based on the cumulative frequencies from a table.
40
What is the purpose of using frequency density in a histogram?
Answer
(B)
To accurately represent frequency when class intervals have different widths.
41
What information can a cumulative frequency diagram provide?
Answer
C
D
42
Which statements are correct about the shape of cumulative frequency diagrams?
Answer
C
D
43
The value at the 75th percentile represents which quartile?
Answer
(C)
Third (Upper) Quartile.
44
Which diagrams are typically used for categorical data?
Answer
B
C
45
How can the interquartile range (IQR) be calculated?
Answer
(B)
Q3 - Q1
46
What is the range of the data?
Answer
(A)
the difference between the highest and lowest values
47
Which of the following is NOT directly obtainable from a histogram?
Answer
(C)
The median.
48
Which of the following would be appropriate uses of a cumulative frequency diagram?
Answer
A
B
C
49
How are the median and the 50th percentile related?
Answer
(A)
They are the same.
50
Which of the following is a measure of central tendency?
Answer
(D)
Median