Important Questions: Measures of Central Tendency | Economics Class 11 - Commerce PDF Download

Q1: What is positional average?
Ans: Positional average, also known as percentile or quantile, is a type of average calculated based on the position or rank of a value within a dataset. It provides insight into the relative standing of a particular value compared to the rest of the data points.

Q2: What are the two methods that can calculate the simple arithmetic mean in the case of an individual series?
Ans: The two methods that can calculate the simple arithmetic mean in the case of an individual series are:

• Direct method: Summing up all individual values and dividing by the total number of values.
• Shortcut method: Utilizing deviations from a convenient base value for calculation, especially when the dataset is large.

Q3: What is mode?
Ans: Mode is the value that appears most frequently in a series. In other words, it is the number that occurs with the highest frequency. A series can have one mode (unimodal) where one value occurs most frequently, or it can be bimodal or multimodal if two or more values have the same highest frequency.

Q4: What are the methods of calculating the simple arithmetic mean?
Ans: The methods of calculating the simple arithmetic mean are based on different types of data presentation:

• Individual series: Adding up all individual values and dividing by the total count.
• Discrete series: Multiplying each value by its respective frequency, summing up these products, and dividing by the total frequency.
• Frequency distribution: Multiplying each class midpoint by its frequency, summing up these products, and dividing by the total frequency to obtain the mean.

Q5: Define the partition value.
Ans: The partition value is a numerical point that divides a series into more than two parts. It essentially creates partitions or segments within the data, enabling a detailed analysis of different sections of the series.

Q6: What are the different kinds of statistical average?
Ans: The different kinds of statistical average are:

• Mathematical average: Includes mean, median, and mode, which are calculated using mathematical formulas.
• Positional average: Involves percentiles, quartiles, and other measures based on the position of values within the dataset.

Q7: Explain quartile.
Ans: A quartile is a statistical measure that divides a data set into four equal parts. There are three quartiles, denoted as Q1, Q2, and Q3. Q1 represents the 25th percentile, Q2 (the median) represents the 50th percentile, and Q3 represents the 75th percentile. These quartiles help in understanding the distribution of the data and identify outliers or extreme values.

Q8: Define the central tendency.
Ans: Central tendency is a statistical concept used to describe the center or average of a distribution. It provides a single value that represents the "typical" or "central" value of a dataset. Common measures of central tendency include mean, median, and mode.

Q9: What are the purposes of average in the statistical method?
Ans: The purposes of average in statistical methods are:

• Providing a brief description of the dataset.
• Facilitating comparison between different datasets.
• Assisting in the formulation of policies and decision-making.
• Enabling statistical analysis and interpretation of data.
• Offering a single representative value for the entire dataset.

Q10: Define median.
Ans: The median is a statistical measure that represents the middle value of a series. It is calculated by arranging the values in numerical order and selecting the middle value. If the series has an odd number of values, the median is the middle number. If the series has an even number of values, the median is the average of the two middle numbers. It divides the series into two halves, where half of the values are above it and half are below it.