Probability Engine · STA164

Statistics I (BSc CSIT, STA164): the questions likely to come

83 analyzed questions from 7 past papers (2074-2081), grouped by syllabus unit — each with its probability, how often it's been asked, and where to study the answer.

Papers analyzed

2074-2081

Analyzed questions

across 6 syllabus units

Very likely units

high-probability topics

Units = 80% of marks

study these first

Model answers for this subject are being written. Every question links to its original paper so you can study from the source meanwhile.

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U2 · Q1/38 · 208110 marks

Descriptive Statistics

Define index numbers. Explain the methods of constructing index numbers (Laspeyres, Paasche, Fisher) and solve a numerical problem using the given price and quantity data.

20%

Occasional to appearAppeared in 1 of the last 1 board papers

Seen in

How well do you know this?rating moves you on

MODEL ANSWERU2 · 10 marks

Index Numbers

Definition. An index number is a statistical measure designed to show changes in a variable (or a group of related variables) such as price, quantity, or value over time, geographically, or against some other characteristic. It is expressed as a percentage relative to a chosen base period taken as 100. Index numbers are sometimes called economic barometers because they measure the relative change in economic activity.

Methods of Constructing Weighted Index Numbers

Let $p_0, q_0$ be the price and quantity in the base year and $p_1, q_1$ in the current year.

1. Laspeyres' Price Index (base-year weights):

P_{01}^{L} = \frac{\sum p_1 q_0}{\sum p_0 q_0}\times 100

Uses base-year quantities as weights. It tends to overstate the rise in prices.

2. Paasche's Price Index (current-year weights):

P_{01}^{P} = \frac{\sum p_1 q_1}{\sum p_0 q_1}\times 100

Uses current-year quantities as weights. It tends to understate the rise in prices.

3. Fisher's Ideal Index (geometric mean of the two):

P_{01}^{F} = \sqrt{P^{L}_{01}\times P^{P}_{01}} = \sqrt{\frac{\sum p_1 q_0}{\sum p_0 q_0}\times\frac{\sum p_1 q_1}{\sum p_0 q_1}}\times 100

It is called ideal because it satisfies both the time-reversal and factor-reversal tests.

Numerical Illustration

Commodity	$p_0$	$q_0$	$p_1$	$q_1$
A	2	8	4	6
B	5	10	6	5
C	4	14	5	10
D	2	19	2	13

Compute the required sums:

$\sum p_0 q_0 = 16+50+56+38 = 160$
$\sum p_1 q_0 = 32+60+70+38 = 200$
$\sum p_0 q_1 = 12+25+40+26 = 103$
$\sum p_1 q_1 = 24+30+50+26 = 130$

Laspeyres: $P^{L}=\dfrac{200}{160}\times100 = 125$

Paasche: $P^{P}=\dfrac{130}{103}\times100 = 126.21$

Fisher: $P^{F}=\sqrt{125\times126.21}=\sqrt{15776.25}=125.60$

Result. Prices have risen by about 25.6% over the base year (Fisher's ideal index $=125.60$ ).

AI-generated answer · unverifiedView in 2081 paper →

U2 · Question 1 of 38

Question Priority · U2ranked by appearance likelihood — study top-down

Descriptive Statistics

Analyzed next20%

★ TOP PICK

Define index numbers. Explain the methods of constructing index numbers (Laspeyres, Paasche, Fisher) and solve a numerical problem using the given price and quantity data.

10 marksSEEN IN

20%

Explain the components of a time series. Describe the method of moving averages and the method of least squares for measuring trend.

10 marksSEEN IN

20%

Explain the concept of a measure of dispersion. Calculate the quartile deviation, mean deviation and standard deviation for the given data and compare them.

10 marksSEEN IN

18%

Explain the measures of central tendency. Compute mean, median and mode for the given grouped frequency distribution and establish the empirical relationship among them.

10 marksSEEN IN

14%

Explain the different types of data and methods of data collection. Describe the construction of a frequency distribution and its graphical representation (histogram, frequency polygon, ogive).

10 marksSEEN IN

13%

Define skewness and kurtosis. Explain how they describe the shape of a distribution. Compute the Karl Pearson and Bowley coefficients of skewness for given data.

10 marksSEEN IN

13%

Define dispersion. Explain different measures of dispersion. Compute the standard deviation and coefficient of variation for a given frequency distribution and comment on consistency.

10 marksSEEN IN

11%

State Fisher's ideal index number formula.

5 marksSEEN IN

20%

What is the method of moving averages?

5 marksSEEN IN

20%

What is a secular trend?

5 marksSEEN IN

20%

Define Laspeyres and Paasche index numbers.

5 marksSEEN IN

20%

Define index numbers.

5 marksSEEN IN

20%

What are the components of a time series?

5 marksSEEN IN

20%

Define statistics. Explain the importance and limitations of statistics. Describe the various measures of central tendency (mean, median, mode) with their merits and demerits.

10 marksSEEN IN

10%

Define the weighted arithmetic mean.

5 marksSEEN IN

18%

What is the interquartile range?

5 marksSEEN IN

18%

Define quartile deviation.

5 marksSEEN IN

16%

What is the coefficient of skewness?

5 marksSEEN IN

16%

Find the variance of 2, 4, 6, 8, 10.

5 marksSEEN IN

16%

Define harmonic mean.

5 marksSEEN IN

14%

State the empirical relation between mean, median and mode.

5 marksSEEN IN

14%

Define mean deviation.

5 marksSEEN IN

14%

State the properties of a good measure of central tendency.

5 marksSEEN IN

14%

Find the mode of 2, 3, 3, 5, 7, 3, 8.

5 marksSEEN IN

14%

Define skewness.

5 marksSEEN IN

13%

What is kurtosis?

5 marksSEEN IN

13%

Define quartiles.

5 marksSEEN IN

13%

What is the geometric mean?

5 marksSEEN IN

13%

What is an ogive curve?

5 marksSEEN IN

13%

Find the mean of the first 10 natural numbers.

5 marksSEEN IN

13%

What is the range of a data set? Find the range of 12, 15, 20, 8, 25.

5 marksSEEN IN

11%

What is the median of 7, 3, 9, 5, 11?

5 marksSEEN IN

11%

Define dispersion and its measures.

5 marksSEEN IN

11%

Define mean, median and mode.

5 marksSEEN IN

10%

Define standard deviation and variance.

5 marksSEEN IN

10%

What is a frequency distribution?

5 marksSEEN IN

10%

What is a histogram?

5 marksSEEN IN

10%

What is the coefficient of variation?

5 marksSEEN IN

10%

03The mock

Sit a probable paper

A full mock exam built from the most likely questions, mirroring the real paper's structure. Every slot is a real past question.

Most Probable Paper

Mirrors the real structure · 60 marks · based on 7 past papers

Section A: Long Answer QuestionsAttempt any TWO questions.

1.
Define index numbers. Explain the methods of constructing index numbers (Laspeyres, Paasche, Fisher) and solve a numerical problem using the given price and quantity data.
[10 marks]
Descriptive StatisticsVery likelyfrom 2081 paper →
Asked once (2081); so far only in internal assessments, not the board; and its topic (Descriptive Statistics) appears in 100% of years.
2.
Explain the components of a time series. Describe the method of moving averages and the method of least squares for measuring trend.
[10 marks]
Descriptive StatisticsVery likelyfrom 2081 paper →
Asked once (2081); so far only in internal assessments, not the board; and its topic (Descriptive Statistics) appears in 100% of years.
3.
Explain the concept of a measure of dispersion. Calculate the quartile deviation, mean deviation and standard deviation for the given data and compare them.
[10 marks]
Descriptive StatisticsVery likelyfrom 2080 paper →
Asked once (2080); so far only in internal assessments, not the board; and its topic (Descriptive Statistics) appears in 100% of years.

Section B: Short Answer QuestionsAttempt any EIGHT questions.

1.
State the properties of expectation.
[5 marks]
ProbabilityVery likelyfrom 2080 paper →
This question has recurred in 2 of 7 years; so far only in internal assessments, not the board; and its topic (Probability) appears in 86% of years.
2.
State Fisher's ideal index number formula.
[5 marks]
Descriptive StatisticsVery likelyfrom 2081 paper →
Asked once (2081); so far only in internal assessments, not the board; and its topic (Descriptive Statistics) appears in 100% of years.
3.
What is the method of moving averages?
[5 marks]
Descriptive StatisticsVery likelyfrom 2081 paper →
Asked once (2081); so far only in internal assessments, not the board; and its topic (Descriptive Statistics) appears in 100% of years.
4.
What is a secular trend?
[5 marks]
Descriptive StatisticsVery likelyfrom 2081 paper →
Asked once (2081); so far only in internal assessments, not the board; and its topic (Descriptive Statistics) appears in 100% of years.
5.
Define Laspeyres and Paasche index numbers.
[5 marks]
Descriptive StatisticsVery likelyfrom 2081 paper →
Asked once (2081); so far only in internal assessments, not the board; and its topic (Descriptive Statistics) appears in 100% of years.
6.
Define index numbers.
[5 marks]
Descriptive StatisticsVery likelyfrom 2081 paper →
Asked once (2081); so far only in internal assessments, not the board; and its topic (Descriptive Statistics) appears in 100% of years.
7.
What are the components of a time series?
[5 marks]
Descriptive StatisticsVery likelyfrom 2081 paper →
Asked once (2081); so far only in internal assessments, not the board; and its topic (Descriptive Statistics) appears in 100% of years.
8.
Define the weighted arithmetic mean.
[5 marks]
Descriptive StatisticsVery likelyfrom 2080 paper →
Asked once (2080); so far only in internal assessments, not the board; and its topic (Descriptive Statistics) appears in 100% of years.
9.
What is the interquartile range?
[5 marks]
Descriptive StatisticsVery likelyfrom 2080 paper →
Asked once (2080); so far only in internal assessments, not the board; and its topic (Descriptive Statistics) appears in 100% of years.

04The receipts

Behind the numbers

The raw evidence the predictions are computed from: marks per unit per year, syllabus weights, trends, and coverage.

Show the heatmap, topic table and coverage analysis

The receipt: marks per unit, per year

Each row is a syllabus unit, each column an exam year, each cell the marks that unit earned that year. Click any cell to see the actual questions behind it.

Marks:nonefew → many

2074

2075

2077

2078

2079

2080

2081

Total

U2Descriptive Statistics

230

U3Probability

125

U4Probability Distributions

U5Correlation and Regression

U1Introduction

U6Statistical Inference

#	Syllabus unit	Probability	Appeared	Avg marks	Syllabus weight	Exam vs syllabus	Trend	Questions
1	U2Descriptive Statistics	Very likely100%	2074 2075 2077 2078 2079 2080 2081	32.9	20%9 lecture hrs	Over-examinedexam 44% · syllabus 20%	Steady	none repeat38 total
2	U3Probability	Very likely86%	2074 2075 2077 2078 2079 2080	20.8	20%9 lecture hrs	Balancedexam 24% · syllabus 20%	Steady	1 recurring19 total
3	U4Probability Distributions	Likely71%	2077 2078 2079 2080 2081	16	22%10 lecture hrs	Under-examinedexam 15% · syllabus 22%	Rising	none repeat12 total
4	U5Correlation and Regression	Likely57%	2074 2075 2078 2079	18.8	16%7 lecture hrs	Balancedexam 14% · syllabus 16%	Fading	none repeat11 total
5	U1Introduction	Possible43%	2074 2077 2080	5	9%4 lecture hrs	Under-examinedexam 3% · syllabus 9%	Steady	none repeat3 total
6	U6Statistical Inference	Occasional0%		0	13%6 lecture hrs	Under-examinedexam 0% · syllabus 13%	Steady	None

Study smart, not hard

Drag the slider: studying the top 3 units in priority order covers ~83% of all observed marks.

Units to study3/6

~80% line

Lecture time vs exam marks

Where the exam pays more than the curriculum spends: ● lectures vs ● exam marks, as a share of the whole course. A long teal-leading bar = high-yield unit.

U2Descriptive Statistics

20% of lectures → 44% of markshigh yield

U3Probability

20% of lectures → 24% of marks

U4Probability Distributions

22% of lectures → 15% of markslow yield

U5Correlation and Regression

16% of lectures → 14% of marks

U1Introduction

9% of lectures → 3% of markslow yield

U6Statistical Inference

13% of lectures → 0% of markslow yield

Statistics I (BSc CSIT, STA164): the questions likely to come

Index Numbers

Methods of Constructing Weighted Index Numbers

Numerical Illustration

Descriptive Statistics

Sit a probable paper

Most Probable Paper

Behind the numbers

The receipt: marks per unit, per year

Study smart, not hard

Lecture time vs exam marks

2081 B.S.

Statistics I (BSc CSIT, STA164)

2080 B.S.

Statistics I (BSc CSIT, STA164)

2079 B.S.

Statistics I (BSc CSIT, STA164)

2078 B.S.

Statistics I (BSc CSIT, STA164)

2077 B.S.

Statistics I (BSc CSIT, STA164)

2075 B.S.

Statistics I (BSc CSIT, STA164)

2074 B.S.

Statistics I (BSc CSIT, STA164)