Worksheet Solutions: Use of Statistical Tools | Economics Class 11 - Commerce PDF Download

Multiple Choice Questions

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Very Short Answers

Q1: Define 'Statistics.'
Ans: Statistics is the science of collecting, organizing, analyzing, interpreting, and presenting data to make informed decisions.

Q2: Explain the term 'Central Tendency.'
Ans: Central tendency refers to the measure that represents the center or average of a dataset. It includes mean, median, and mode.

Q3: What is the primary purpose of a histogram?
Ans: The primary purpose of a histogram is to represent the frequency distribution of data in graphical form.

Q4: Define 'Variance.'
Ans: Variance is a measure of how spread out the data points are from the mean in a dataset. It quantifies the dispersion or variability of data.

Q5: What is the significance of the coefficient of variation (CV)?
Ans: The coefficient of variation (CV) is significant because it measures the relative variability of data, allowing for comparisons between datasets with different units or scales.

Short Answers

Q1: Explain the concept of 'Measures of Dispersion' and provide examples.
Ans: Measures of dispersion quantify how data points vary or spread out in a dataset. Examples include the range, variance, and standard deviation. The range is the difference between the highest and lowest values. Variance measures the average squared deviation from the mean, and standard deviation is the square root of variance.

Q2: Describe the 'Coefficient of Variation' (CV) and its importance.
Ans: The coefficient of variation (CV) is the ratio of the standard deviation to the mean, expressed as a percentage. It is important because it helps compare the relative variability of datasets with different units or scales. A lower CV indicates less relative variability, while a higher CV suggests greater relative variability.

Q3: Explain the concept of 'Skewness' in statistics.
Ans: Skewness measures the asymmetry of the probability distribution of a dataset. A positive skew indicates that the tail on the right side is longer or fatter, while a negative skew means the left tail is longer or fatter. A perfectly symmetrical distribution has zero skewness.

Q4: Differentiate between 'Mean' and 'Median' as measures of central tendency.
Ans: Mean is the arithmetic average of a dataset and is sensitive to outliers. Median is the middle value when data is arranged in ascending or descending order and is less affected by outliers. Mean provides a balance point, while the median represents the middle value.

Q5: Explain the construction and interpretation of a 'Box-and-Whisker Plot.'
Ans: A Box-and-Whisker Plot is a graphical representation of the five-number summary of a dataset: minimum, first quartile (Q1), median, third quartile (Q3), and maximum. It helps visualize the spread and skewness of data. The box represents the interquartile range (Q3-Q1), and the whiskers extend to the minimum and maximum values. Outliers may be shown as individual points.