CBSE-Class-10-Maths-Assertion-and-Reason-Chapter-14-Statistics

Class 10^th Maths Chapter Assertion and Reason Questions

Assertion and Reason Questions on Statistics

Question 1

Assertion (A): The mean is affected by extreme values in a data set.
Reason (R): The mean is calculated by dividing the sum of all values by the number of values.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The mean is sensitive to extreme values because it uses all data points in its calculation.

Question 2

Assertion (A): The median is a better measure of central tendency when data is skewed.
Reason (R): The median is calculated by arranging the data in order and finding the middle value.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The median is less affected by outliers, making it more representative in skewed distributions.

Question 3

Assertion (A): The mode is the most frequently occurring value in a data set.
Reason (R): The mode can be found by organizing the data in ascending order.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: B) Both A and R are true, but R is not the correct explanation of A.
Explanation: While the mode is indeed the most frequent value, it does not necessarily require the data to be organized in order.

Question 4

Assertion (A): A data set can have more than one mode.
Reason (R): A data set is bimodal if it has two modes and multimodal if it has more than two.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: A data set can have multiple modes, which can be classified as bimodal or multimodal.

Question 5

Assertion (A): The range is a measure of dispersion in a data set.
Reason (R): The range is calculated as the difference between the maximum and minimum values.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The range measures how spread out the values are by focusing on the extremes.

Question 6

Assertion (A): The interquartile range (IQR) is a robust measure of dispersion.
Reason (R): The IQR is calculated using the first and third quartiles, excluding outliers.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The IQR focuses on the central 50% of the data, making it less sensitive to outliers.

Question 7

Assertion (A): The mean can be calculated from grouped data.
Reason (R): Grouped data summarizes information in intervals, which allows for the calculation of the mean.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The mean can be calculated using midpoints of the intervals in grouped data.

Question 8

Assertion (A): The sum of deviations of data values from the mean is always zero.
Reason (R): The mean is the point at which the total distance from all values is minimized.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: This property of the mean ensures that the sum of positive and negative deviations equals zero.

Question 9

Assertion (A): The mode is the best measure of central tendency for categorical data.
Reason (R): Categorical data does not have a meaningful average or median.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The mode effectively represents the most common category in categorical data.

Question 10

Assertion (A): The median divides a data set into two equal parts.
Reason (R): The median is the middle value when the data is arranged in order.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The median splits the data into two halves, with equal numbers of data points on either side.

Question 11

Assertion (A): Quartiles are used to summarize the spread of a data set.
Reason (R): Quartiles divide the data into four equal parts.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: Quartiles help to identify the distribution and spread of data by segmenting it into parts.

Question 12

Assertion (A): The variance is a measure of how far each number in a data set is from the mean.
Reason (R): Variance is calculated as the average of the squared deviations from the mean.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: Variance quantifies the dispersion of data points around the mean by squaring deviations.

Question 13

Assertion (A): Standard deviation is the square root of the variance.
Reason (R): Standard deviation provides a measure of dispersion in the same units as the data.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The standard deviation relates directly to the data's scale, making it more interpretable than variance.

Question 14

Assertion (A): A box plot visually represents the five-number summary of a data set.
Reason (R): The five-number summary includes minimum, first quartile, median, third quartile, and maximum.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The box plot effectively displays the five-number summary, highlighting the distribution of the data.

Question 15

Assertion (A): The data set with the smallest interquartile range (IQR) is the most consistent.
Reason (R): A smaller IQR indicates that the central 50% of data points are closer together.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: A smaller IQR reflects less variability in the middle of the data set, indicating consistency.

Question 16

Assertion (A): When comparing two data sets, a higher mean indicates a higher overall value.
Reason (R): The mean is influenced by all values in the data set.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The mean summarizes the data effectively and reflects the overall level of values in the set.

Question 17

Assertion (A): The median is not affected by extreme outliers in the data.
Reason (R): The median is determined solely by the middle value(s) in the ordered list.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: Since the median depends only on the middle value, it remains stable despite extreme values.

Question 18

Assertion (A): Cumulative frequency helps in understanding the distribution of data.
Reason (R): Cumulative frequency shows the total number of data points that fall below a certain value.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: Cumulative frequency provides insight into how data accumulates, which aids in distribution analysis.

Question 19

Assertion (A): The probability of an event is always between 0 and 1, inclusive.
Reason (R): A probability of 0 means the event will not occur, while 1 means it will definitely occur.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: This is a fundamental principle of probability, reflecting certainty and uncertainty.

Question 20

Assertion (A): Outliers can significantly affect the mean and standard deviation of a data set.
Reason (R): Outliers are extreme values that do not conform to the rest of the data.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: Outliers can skew the mean and inflate the standard deviation, impacting data interpretation.

Question 21

Assertion (A): A bar graph is used to represent categorical data.
Reason (R): In a bar graph, the height of each bar represents the frequency of each category.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: Bar graphs are effective in displaying categorical data through visual frequency representation.

Question 22

Assertion (A): A histogram is similar to a bar graph but is used for continuous data.
Reason (R): In a histogram, the bars are adjacent to each other, indicating continuous intervals.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: Histograms illustrate the frequency distribution of continuous data through connected bars.

Question 23

Assertion (A): Data can be represented using a pie chart.
Reason (R): A pie chart shows the proportional sizes of parts to a whole.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: Pie charts effectively display parts of a whole, emphasizing the distribution of categorical data.

Question 24

Assertion (A): In a frequency distribution, the class intervals should be mutually exclusive.
Reason (R): This ensures that each data point belongs to one and only one interval.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: Mutual exclusivity is crucial for accurate representation and analysis of data.

Question 25

Assertion (A): Data representation is essential in statistics for effective communication of information.
Reason (R): Graphs and charts can simplify complex data and make it more accessible.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: Visual aids enhance understanding and allow for quicker insights into data trends.

Chapter 14 Statistics

Class 10th Maths Chapter Assertion and Reason Questions