ECODSC-253: Statistics for Economics FYUG Even Semester Exam, 2025

Subject: Economics

Paper Code: ECODSC-253

Semester: 4th Semester (FYUG)

Exam Year: 2025

Full Marks: 70 | Pass Marks: 28

Time Duration: 3 Hours

UNIT-I

1. Answer any two of the following questions: 2 x 2 = 4

(a) What is median? Mention one use of median.

Median is the middle value of a dataset when arranged in ascending or descending order, dividing the data into two equal parts.

Use: It is used as a measure of central tendency when the data contains extreme values (outliers) as it is not affected by them.

(b) Mention two relative measures of dispersion.

  • Coefficient of Variation.
  • Coefficient of Quartile Deviation.

(c) Write two demerits of mean.

  • It is highly affected by extreme values (outliers).
  • It cannot be calculated for qualitative data or open-ended classes.

2. (a) (i) Find mean, median and mode from the following data: 4 + 4 + 2 = 10

Marks (x)fm (Mid-point)f*mcf
130-13451326605
135-13915137205520
140-14428142397648
145-14924147352872
150-15417152258489
155-15910147157099
160-1641162162100
TotalN=100Σfm=14535

Mean (X̄): Σfm / N = 14535 / 100 = 145.35

Median: N/2 = 50. Median class is 145-149.
Median = L + [(N/2 - cf)/f] * i = 144.5 + [(50 - 48)/24] * 5 = 144.5 + 0.416 = 144.92

Mode: Modal class is 140-144 (highest frequency).
Mode = L + [(f1 - f0)/(2f1 - f0 - f2)] * i = 139.5 + [(28 - 15)/(56 - 15 - 24)] * 5 = 139.5 + 3.82 = 143.32

2. (a) (ii) Mention two uses of measures of location. 2

  • To provide a single representative value for a large mass of data.
  • To facilitate comparison between different sets of data.

UNIT-II

3. Answer any two of the following questions: 2 x 2 = 4

(a) What is random experiment?

An experiment is called random if its outcome cannot be predicted with certainty, even though all possible outcomes are known in advance.

(b) Distinguish between independent and dependent events.

  • Independent: Occurrence of one event does not affect the probability of the other (e.g., tossing two coins).
  • Dependent: Occurrence of one event affects the probability of the other (e.g., drawing cards without replacement).

4. (a) (ii) Probability of tossing a die. 4

Sample space S = {1, 2, 3, 4, 5, 6}. Total outcomes = 6.

  • (1) Even number: {2, 4, 6} -> P = 3/6 = 1/2
  • (2) Odd number: {1, 3, 5} -> P = 3/6 = 1/2
  • (3) Less than 3: {1, 2} -> P = 2/6 = 1/3
  • (4) A 'six': {6} -> P = 1/6

UNIT-III

5. Answer any two of the following questions: 2 x 2 = 4

(a) Define random variable.

A random variable is a real-valued function defined over the sample space of a random experiment.

(b) Mention two properties of binomial distribution.

  • It is a discrete probability distribution.
  • Mean = np and Variance = npq.

6. (a) Discuss the properties of normal distribution. 10

  • The curve is bell-shaped and perfectly symmetrical about the mean.
  • Mean = Median = Mode.
  • The total area under the curve is equal to 1.
  • It is asymptotic to the x-axis (tails never touch the axis).
  • The points of inflection occur at X = μ ± σ.

UNIT-IV

7. Answer any two of the following questions: 2 x 2 = 4

(a) Distinguish between population and sample.

Population is the entire group you want to draw conclusions about, while a sample is the specific group you collect data from.

(c) What is sampling distribution?

It is the probability distribution of a given statistic (like the mean) based on a random sample.

8. (b) (ii) Standard Error calculation. 3

Given: N = 41, n = 5, σ = 6.25. (Sampling without replacement)

SE = (σ / √n) * √[(N - n) / (N - 1)]

SE = (6.25 / √5) * √[(41 - 5) / (41 - 1)] = (6.25 / 2.236) * √(36/40) = 2.795 * 0.948 = 2.65

UNIT-V

9. Answer any two of the following questions: 2 x 2 = 4

(a) What is statistical hypothesis?

It is an assumption or claim about a population parameter which may or may not be true and is tested using sample data.

(b) Distinguish between Type I error and Type II error.

  • Type I: Rejecting a null hypothesis when it is actually true.
  • Type II: Failing to reject a null hypothesis when it is actually false.

10. (a) (ii) Discuss the characteristics of a good estimator. 6

  • Unbiasedness: The expected value of the estimator should equal the true population parameter.
  • Consistency: As sample size increases, the estimator should approach the population parameter.
  • Efficiency: It should have the smallest variance among all unbiased estimators.
  • Sufficiency: It should utilize all information contained in the sample.

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