Class 11 Economics Short Questions with Answers - Measures of Central Tendency

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Q1. What do you mean by central tendency?
Ans: A central tendency is a statistical term that describes a typical value within a set of data. It helps to summarise a large dataset by providing a single representative value. The main measures of central tendency include:

• Arithmetic Mean: The sum of all values divided by the number of values.
• Median: The middle value when the data is arranged in order.
• Mode: The value that appears most frequently in the dataset.

Q2. In how many parts is the statistical average divided?
Ans: Statistical average is divided into two main parts:

• Mathematical average
• Positional average

Q3. What are the types of positional averages?
Ans:

• Median: The middle value when data is arranged in order.
• Mode: The value that appears most frequently in a dataset.
• Partition values: These include:
  - Quartiles: Divide data into four equal parts.
  - Deciles: Divide data into ten equal parts.
  - Percentiles: Divide data into one hundred equal parts.

Q4. State the main functions of averages.
Ans: The main functions of averages are:

• Facilitate Comparisons: Averages simplify data, making it easier to compare. For instance, comparing the average per capita income of different countries helps identify those with the highest and lowest economic growth.
• Help in Policy Formulation: Averages assist governments in creating policies. For example, if low literacy rates are found in certain areas, targeted policies can be developed to enhance educational services.
• Basis for Statistical Analysis: Averages provide a foundation for statistical analysis, allowing for meaningful inferences to be drawn from the data.
• Represent the Whole Series: Averages encapsulate the overall data series, offering a single representative value.

Q5. State the properties of an ideal average.
Ans: The following are the main properties of an ideal average:

• Easy to Compute: The average should be simple to calculate and understand. Complex calculations can limit its use to experts only.
• Rigid Definition: An average must have a clear definition to avoid bias. This ensures it consistently yields a specific figure.
• Represent the Whole Series: It should include all observations in the series. Ignoring any items can make the average unrepresentative.
• Open to Further Algebraic Treatment: An average should allow for additional mathematical analysis to enhance its utility.
• Not Affected by Sampling Fluctuations: Averages from independent samples should be similar. Averages with minimal fluctuation are preferred.

Q6. Define Arithmetic mean
Ans: The arithmetic mean is calculated by:

• Adding up all the values of the observations.
• Dividing the total by the number of observations.

Q7. State the types of arithmetic mean.
Ans: There are two types of arithmetic mean:

• Simple arithmetic mean
• Weighted arithmetic mean

Q8. What is weighted arithmetic mean?
Ans: The weighted arithmetic mean is a type of average that considers the importance of different items by assigning them specific weights. This allows for a more accurate representation of data when some items are more significant than others.

• It is calculated by multiplying each item by its weight.
• The total of these products is then divided by the sum of the weights.
• This method is useful in scenarios where certain values need to be prioritised.

For example, if you want to find the average price of two commodities, mangoes and potatoes, you might assign a higher weight to potatoes if they are more important in your budget. The formula would look like this: Weighted Mean = (W₁P₁ W₂P₂) / (W₁ W₂)

Q9. What are the merits of arithmetic mean?
Ans: The merits of the arithmetic mean include:

• Simple to understand and calculate.
• Considers all items in a series, representing the whole data set.
• Stable average, not easily influenced by sample fluctuations.
• Possesses various algebraic features useful for advanced statistical analysis.
• Provides a definite number, not just an estimate.
• Facilitates comparison between different groups.
• Accuracy can be verified.

Q10. What are the demerits arithmetic mean?
Ans: The following are the demerits of the arithmetic mean:

• Extreme values can significantly skew the mean, making it unrepresentative of the overall data set.
• It may yield unrealistic results, such as an average of 4.5 children per family, which is not possible.
• The arithmetic mean is only suitable for quantitative data.
• It is not appropriate for analysing ratios, rates, or percentages.

Q11. Write a short note on weighted arithmetic mean.
Ans: The weighted arithmetic mean is a type of average that considers the relative importance of different items by assigning them weights. This is useful when certain items contribute more significantly to the overall average than others. For example:

• If a person spends on food (f), clothes (c), and entertainment (e), the simple arithmetic mean would be calculated as:
• (f c e) / 3.
• However, if food is deemed more important, weights can be assigned based on the amount spent:
• The weighted mean would then be:
• (fq1 cq2 eq3) / (q1 q2 q3),
• where q1, q2, and q3 represent the quantities of food, clothes, and entertainment, respectively.

In general, the formula for the weighted arithmetic mean is: (W1X1 W2X2 ... WnXn) / (W1 W2 ... Wn).

Q12. State the important features of median.
Ans: Median has the following important features:

• Easy to understand and calculate.
• Not influenced by extreme values.
• Provides a clear average.
• Can be determined graphically.
• Represents a real value within the data set.
• Can be easily calculated in open-ended series.

Q13. What are the demerits of median?
Ans:

• Lacks algebraic characteristics: The median cannot be used in further mathematical calculations.
• Estimated value: For an even number of items or in a continuous series, the median is an estimate and may not represent actual values.
• Not suitable for extreme values: When there are large differences in item values, the median may not be the best measure.
• Requires sorting: To find the median, data must be arranged in ascending or descending order, which can be time-consuming.

Q14. List the different types of modal data.
Ans:

• Uni-modal Data – data with a unique mode.
• Bi-modal Data – data with two modes.
• Multi-modal Data – data with more than two modes.