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Mathematics for IGCSE & O level - Statistical Diagrams (Section 3)

1
If there is an even number of data values, how is the median found?
Answer
(A)
By taking the mean of the middle two values
2
How do you calculate the 90th percentile using a cumulative frequency diagram?
Answer
(B)
Find the value on the x-axis corresponding to the 90th percentile on the y-axis.
3
Which feature of the data can be best observed from a histogram?
Answer
(D)
The distribution of the data
4
The value of the 90th percentile is the same as the:
Answer
(C)
9th Decile
5
What is the purpose of class intervals?
Answer
(A)
To organize continuous data into groups.
6
In the student's travel time histogram, what is the approximate number of students who took between 30 and 60 minutes?
Answer
(C)
24
7
Which of the following is most affected by extreme values in a data set?
Answer
(C)
Mean.
8
In a histogram, if the class widths are different, which of the following is plotted on the y-axis?
Answer
(C)
Frequency density.
9
Which of the following is NOT a measure of spread?
Answer
(C)
The median.
10
Which measure of spread is the most stable to outliers?
Answer
(C)
The interquartile range
11
What type of correlation is seen if the points are scattered and have no clear pattern on a scatter diagram?
Answer
(C)
No correlation
12
What is the primary use of a box plot?
Answer
B
C
13
In a positively skewed distribution, which of the following is true?
Answer
(D)
Mean > Median > Mode
14
What type of correlation is depicted by a scatter diagram where the points form a downward sloping pattern?
Answer
(C)
Strong Negative
15
What does the shape of a frequency distribution tell us?
Answer
(D)
The symmetry or skewness of the dataset.
16
If two cumulative frequency diagrams are plotted on the same axes, what can be directly compared?
Answer
(B)
The medians and interquartile ranges.
17
What is the main advantage of a box plot?
Answer
(C)
It effectively shows the spread, central tendency, and skewness of a dataset.
18
The 50th percentile is also known as:
Answer
(B)
The median
19
What is the advantage of using the median over the mean?
Answer
(B)
The median is less susceptible to the effect of outliers.
20
What does the shape of a cumulative frequency diagram reveal about the data?
Answer
(B)
The spread and skewness of the data.
21
What can be determined from a cumulative frequency diagram?
Answer
A
C
22
What is the purpose of a cumulative frequency diagram?
Answer
(B)
To estimate the median and quartiles of a dataset.
23
What is the definition of the median?
Answer
(C)
The middle value when data is ordered.
24
If a data set's interquartile range (IQR) is small, this indicates:
Answer
(B)
The data is closely clustered.
25
For grouped data, which measure of central tendency can NOT be accurately estimated from a cumulative frequency diagram?
Answer
(C)
The mean
26
What does the term 'frequency' refer to in a frequency table or histogram?
Answer
(B)
The number of times a data value occurs within a class interval.
27
If you have a frequency table for grouped data, which method is usually the best to present it visually?
Answer
(D)
A histogram
28
How is the line of best fit generally drawn on a scatter diagram?
Answer
(C)
Approximating the general trend of the data
29
If a scatter diagram displays no correlation, what will it look like?
Answer
(C)
Points scattered randomly.
30
In statistics, what does 'percentile' represent?
Answer
(C)
A value below which a certain percentage of data falls.
31
What is the relative frequency?
Answer
(A)
Frequency / Total Frequency
32
What does a box plot visually represent about a dataset?
Answer
A
C
D
33
When is the mean of a dataset equal to the median?
Answer
(B)
When the data is symmetrical.
34
How would a positively skewed data set be represented in a cumulative frequency diagram?
Answer
(A)
A steep slope initially, then a more gradual slope.
35
If all the bars in a histogram have the same width, the height of each bar directly represents:
Answer
(B)
The frequency.
36
Which statistical diagrams can be used to identify a relationship (correlation) between two sets of data?
Answer
(B)
Scatter diagrams
37
What does the lower quartile of a data set represent?
Answer
(B)
The value below which 25% of the data falls.
38
If the interquartile range (IQR) is large, it indicates:
Answer
(B)
The data is spread out over a wider range.
39
Which of the following statements is true about histograms?
Answer
A
C
D
40
Which of the following is NOT a characteristic of a histogram?
Answer
(D)
Used for categorical data.
41
In a histogram, what does the vertical axis represent?
Answer
(C)
Frequency density
42
What is the main purpose of using class intervals in a frequency table?
Answer
(B)
To categorize and summarize data.
43
In the histogram representing the time taken to travel to school, how many students took between 15 and 25 minutes?
Answer
(B)
9
44
In a histogram, if the class intervals have equal widths, then which of the following is true?
Answer
(A)
Frequency is directly proportional to the height of the bars.
45
If the class widths in a histogram are not equal, the area of each bar represents:
Answer
(B)
The frequency.
46
Which of the following statements about histograms is true?
Answer
(C)
The area of each bar represents the frequency.
47
If a class width in a histogram is doubled, what happens to the height of the corresponding bar if the frequency stays the same?
Answer
(B)
It halves
48
If a scatter diagram shows a positive correlation, what can you infer about the relationship between the variables?
Answer
(C)
As one variable increases, the other also tends to increase.
49
If the mean is greater than the mode, what type of skewness is typically present?
Answer
(A)
Positive skew