Botswana International University
of Science & Technology
School of Pure and Applied Sciences
Department of Mathematics and Statistical Science
Module Title (Code): Introduction toStatistics
(STAT 101)
Date of Test 1: March 13h, 2025
Time: 1830hrs - 1945hrs
Time Allowed: 1 hour 15 mins
Total Marks: 50
Instructions
• Answer all the questions
• Show allcaleulations clearly and ensure accuracy in table construction.
Section A: Multiple Choice Questions (15 marks)
Question 1
Which of the following is a disadvantage of using secondary data?
A. It may be outdated or not specifie
to the researcher's needs.
C. It requires mnore time and effort to
gather.
D. It is more reliable than primary
B. It is more expensive to collect.
data.
Question 2
item on the
In a factory, a quality control manager decides to inspect every 10th
method is
production line to ensure quality standards are met. Which sampling
this?
B. Stratified
A. Random
Sampling
Sampling
C. Clhuster
Sampling
D. Systematic
Sampling
Question 3
for nominal data?
Which of the following operations is NOT appropriate
B. Calculating
the mode
A. Counting
frequencies
C. Caleulating
the nean
Question 4
Given the data set 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, what is the relative
D. Creating
a bar chart
frequency of the
nurnber 3?
B. 20%
A. 10%
3
C. 30%
Ď. 40%
Question 5
Which chart is most suitable for displaving the proportion of each category in a
whole?
A. Bar chart
D. Box plot
C. Line chart
B. Piechart
Question 6
What does a Pareto chart combine?
A. Line chart and scatter plot.
C Bar chart and line chart.
B. Bar chart and pie chart.
D. Histogram and box plot.
Question 7
What is the purpose of Sturges Rule?
k
C. To find the median.
A. To calculate the mean.
B. To determine the optimal number
of class intervals.
D. To create pie charts.
Question 8
In a stem-and-leaf plot, what does the stem represent?
A. The individual data points.
C. The leading digits of the data points.
B. The cumulative frequency.
D. The trailing digits of the data points.
Question 9
Given a box plot with the following values: Q1 = 10, Q2= 15, Q3 = 20, what is the
Interquartile Range (IQR)?- 3-Oi 20-5
A. 5
B.10
C. 15
D. 20
Question 10
When comparing multiple box plots, what can you infer if one box plot has
larger IQR than the others?
a much
A. The data set has a higher median.
C. The data set is more symmetric.
B. The data set has more variability.
D. The data set has fewer outliers.
Question 11
Given a scatter plot showing the relationship between hours studied and exam scores,
what type of correlation would you expect to see?
A. Positive correlation.
C. No correlation.
B. Negative correlation.
D. Categorical correlation.
Question 12
Given the data set 10, 20. 30, 40, 100)., which measure of central tendeney IS nost
affected by the outlier (100)?
A.
Mean
B. Median
C. Mode
D. Range
Question 13
In adata set, if the 90th percentile is 85, what does this indicate about the data?
A. 85% of the data points are below
C. 10% of the data points are below
85.
85.
B. 90% of the data points are below 85D. 15% of the data points are below S5.
Question 14
Which mneasure of central tendency is most appropriate for skewed data?
A Mean
B. Median
C. Mode
D. Range
Question 15
How can measures of central tendency be used in decision-making contexts?
A, To identify trends and patterns
C. To determine the total nunber of data
points.
in data.
B. To calculate the range of data.
D. To create pie charts.
Section B: True/False Questions (10 marks)
Question 16
A frequency table can be 1sed to summarize ungrouped.
Question 17
Relative frequency is caleulated by dividing the eumnlative frequeney by
number of data points.
the total
Question 18
The mean for a frequency distribution is caleulated by multiplying the frequeney of
each class by the class midpoint and sunming the results, then dividing by the total
frequeney. T
Question 19
A Pareto chart helps identify the most significant factors in a data set. T
Question 20
Scatter plots are used to visualize the relationship between two quantitative vari
ables.
T
Question 21
A bimodal dlistribution has two distinct peaks modal.
3
Question 22
Interpolation techniques are used to estimate the median and quartiles for grouped
T
data.
Question 23
The median is represented by the length of the box in a box plot.
Question 24
Whiskers always extend to the non-negative minimum and maximun values of the
dataset.
Question 25
Outliers are data points that fall significantly outside the whiskers. T
Question 26
Primary data is collected firsthand by the researcher specifcally for their study.
Section C: Structured Question (25 marks)
Question 27
of 40
The following are data points on the percent shrinkages on drying
plastic clay specimnens:
21.5, 21.5, 17.9,
20.3, 16.8, 21.7, 19,4, 15.9, 18.3, 22/3, 17.1, 19.6,
18.1, 23.5, 19:8,
19.5, 19.7, 13,3, 20.5, 24.4, 19.8, 19.3, 17.9, 18.9,
20.1, 18.5, 17.8, 17.3,
20.4, 18.4, 19.5, 18.5, 17.4, 18.7, 18.3, 20.4,
20.0, 19.2, 18.4, 19.0
data by answering the questions
Construct a frequency distribution table for this
below.
2 marks]
class intervals.
a) Determine k, the number of
b) Calculate the range of the dataset.
2 marks]
(2 marks
width.
c) Determine a suitable class
.
d) Determine suitable class intervals
(f) for each class interval.
e) Write down frequencies
f) For each interval compute the;
(i) cumulative frequency (CF),
(ii) class mark (w),
and
(iii) class boundaries (CB)
w x f
(iv) product between class marks and frequencies
s)
shrinkage.t7
Compute mean pereent
d data?
h) What is the mode of the groupe
h
(2 marks)
(2 marks]
(2 marks]
2 marks]
2 marks)
2 marks
(3 marks]
4 marks)