Statistical Tools and Interpretation : Arithmetic mean, Median and Mode : Class 11 : Economics
Questions
Multiple-Choice Questions (MCQs)
1. What is the mode of the following dataset: 5,7,7,8,9,11,12,12,12,15?
a) 7 b) 9 c) 12 d) 15
2. In a positively skewed distribution, what is the relationship between the mean, median, and mode?
a) Mean > Median > Mode b) Mean < Median < Mode c) Mean = Median = Mode d) Median > Mean > Mode
3. If the rank correlation coefficient between marks in two subjects for a group of students is calculated to be 0.85, what is the economic interpretation of this result?
a) There is a weak positive correlation between the marks. b) There is a strong negative correlation between the marks. c) There is a strong positive correlation between the marks, suggesting that students who score high in one subject also tend to score high in the other. d) There is no correlation between the marks.
4. A scatter diagram showing a cluster of points from the top left to the bottom right indicates which type of correlation?
a) Positive correlation b) Negative correlation c) No correlation d) Perfect positive correlation
5. The prices of a basket of goods in 2024 were P0=(20,50,10) and in 2025 were P1=(25,60,12). Using the Simple Aggregative Method, what is the price index for 2025 with 2024 as the base year?
a) 116.67 b) 120.00 c) 121.25 d) 100
6. What is the main economic use of the Consumer Price Index (CPI)?
a) To measure the average change in the prices of goods at the wholesale level. b) To track changes in the prices of goods and services purchased by industrial producers. c) To measure the average change over time in the prices paid by urban consumers for a market basket of consumer goods and services. d) To calculate the rate of unemployment in an economy.
7. Which of the following is a property of a correlation coefficient (r)?
a) The value of r can be greater than +1 or less than −1. b) A value of r=0 indicates a strong linear relationship. c) A value of r=+1 indicates a perfect positive linear relationship. d) A change in the scale of measurement changes the value of r.
8. Why is the mode considered an unsuitable measure of central tendency for a dataset with multiple peaks or no repeating values?
a) Because it is difficult to calculate the mode for such datasets. b) Because it will always be equal to the mean in such cases. c) Because it may not represent the typical value of the dataset, as it can be misleading or nonexistent. d) Because it is affected by extreme values or outliers.
9. Given the following ranks for two subjects (A and B) for five students: Student 1 (A: 5, B: 4), Student 2 (A: 3, B: 3), Student 3 (A: 1, B: 2), Student 4 (A: 2, B: 1), Student 5 (A: 4, B: 5). Calculate Spearman's rank correlation coefficient.
a) 0.5 b) 0.8 c) 0.9 d) 1.0
10. What is the primary difference between a Wholesale Price Index (WPI) and a Consumer Price Index (CPI)?
a) WPI measures the prices of goods, while CPI measures the prices of services. b) WPI measures price changes at the producer/wholesale level, while CPI measures price changes at the consumer level. c) WPI is only for industrial goods, while CPI is for agricultural goods. d) WPI is used to measure inflation, while CPI is not.
Answers
1. c) 12
Rationale: The mode is the value that appears most frequently in a dataset. In this case, 12 appears three times, more than any other value.
2. a) Mean > Median > Mode
Rationale: In a positively skewed distribution, the data tail extends to the right. The mean is pulled towards this tail by higher values, making it greater than the median, which is in turn greater than the mode. 
3. c) There is a strong positive correlation between the marks, suggesting that students who score high in one subject also tend to score high in the other.
Rationale: A rank correlation coefficient of +0.85 is a strong positive value, close to +1, which indicates a strong direct relationship between the rankings.
4. b) Negative correlation
Rationale: A cluster of points from the top left to the bottom right on a scatter diagram indicates that as the value of the x-variable increases, the value of the y-variable tends to decrease, which is the definition of a negative correlation.
5. c) 121.25
Rationale: The formula for the Simple Aggregative Method is (∑P1/∑P0)×100.
∑P0=20+50+10=80
∑P1=25+60+12=97
Index = (97/80)×100=121.25
6. c) To measure the average change over time in the prices paid by urban consumers for a market basket of consumer goods and services.
Rationale: The Consumer Price Index (CPI) is a key measure of inflation from the perspective of the average consumer, tracking the cost of a standard basket of goods and services.
7. c) A value of r=+1 indicates a perfect positive linear relationship.
Rationale: The correlation coefficient (r) is always between -1 and +1. A value of +1 signifies a perfect positive linear relationship where all data points lie on a straight line with a positive slope. It is also independent of the origin and scale of measurement.
8. c) Because it may not represent the typical value of the dataset, as it can be misleading or nonexistent.
Rationale: The mode is the most frequent value. If a dataset has multiple modes (bimodal or multimodal) or no repeating values at all, the mode fails to provide a useful or unique measure of central tendency.
9. b) 0.8
Rationale: Use Spearman's rank correlation formula: 1−6∑d2/(n(n2−1)).
Calculate the difference in ranks (d) for each student: 1,0,−1,1,−1.
Calculate the sum of the squared differences (∑d2): 12+02+(−1)2+12+(−1)2=1+0+1+1+1=4.
With n=5, the coefficient is 1−(6×4)/(5(52−1))=1−24/(5×24)=1−24/120=1−0.2=0.8.
10. b) WPI measures price changes at the producer/wholesale level, while CPI measures price changes at the consumer level.
Rationale: The Wholesale Price Index (WPI) tracks the price of goods at a wholesale stage, typically between businesses, while the Consumer Price Index (CPI) measures prices at the retail level paid by the end consumer. Both are important indicators of inflation but from different stages of the supply chain.
