Class 9 Maths Chapter 13 Assertion and Reason Questions - Statistics

Q1: Assertion: Median = ((n+1)/2)th value if n is odd.
Reason: If the number of runs scored by 11 players of a cricket team of India are 5, 19, 42, 11, 50, 30, 21, 0, 52, 36, 27, then median is 30.
(a) both Assertion and reason are correct and reason is correct explanation for Assertion
(b) both Assertion and reason are correct but reason is not correct explanation for Assertion
(c) Assertion is correct but reason is false
(d) both Assertions and reason are false
Ans: (b)
The assertion about the formula for calculating the median when the number of observations is odd is correct. However, the reason given is not a correct explanation for the assertion. The median is not simply the middle value; it is the value that divides the data into two equal halves, with half the values above and half below. In this case, the median value would be 30, but the given reason doesn't accurately explain why.

Q2: Assertion: Median of the given data 34, 31, 42, 43, 46, 25, 39, 45, 32 is 39.
Reason: When the number of observations (n) is even, arrange the numbers in ascending order; then the median is the mean of the (n/2)th and (n/2 + 1)th terms.
(a) both Assertion and reason are correct and reason is correct explanation for Assertion
(b) both Assertion and reason are correct but reason is not correct explanation for Assertion
(c) Assertion is correct but reason is false
(d) both Assertions and reason are false
Ans: (b)
The assertion is correct, as the median of the given data is indeed 39. However, the reason provided doesn't accurately explain the calculation of the median for even observations. The correct formula for the median of even observations is the average of the two middle values, which is not accurately represented by the reason provided.

Q3: Assertion: Mean of n observations = Number of observations / Sum of observations.
Reason: If the mean of five observations x, x + 2, x + 4, x + 6, x + 8 is 11, then the mean of the last three observations is 8.
(a) both Assertion and reason are correct and reason is correct explanation for Assertion
(b) both Assertion and reason are correct but reason is not correct explanation for Assertion
(c) Assertion is correct but reason is false
(d) both Assertions and reason are false
Ans: (c)
The assertion is correct, as the formula for the mean of n observations is accurate. However, the reason provided is incorrect. The mean of the last three observations cannot be determined solely based on the mean of the first five observations as mentioned.

Q4: Assertion: The median of the following observation 0, 1, 2, 3, x, x + 2, 8, 9, 11, 12 arranged in ascending order is 63, then the value of x is 62.
Reason: Median of n even observations is (((n)/2)th term + (n/2 + 1)th term) / 2.
(a) both Assertion and reason are correct and reason is correct explanation for Assertion
(b) both Assertion and reason are correct but reason is not correct explanation for Assertion
(c) Assertion is correct but reason is false
(d) both Assertions and reason are false
Ans: (a)
Both the assertion and reason are correct. The median of even observations is calculated by taking the average of the two middle terms. In this case, when x = 62, the median is indeed 63.

Q5: Assertion: The following data of wages per day: 8, 4, 7, 5, 8, 8, 5, 7, 9, 5, 7, 9, 10, 8 has a mode of 8.
Reason: Mode = Highest observation – Lowest observation.
(a) both Assertion and reason are correct and reason is correct explanation for Assertion
(b) both Assertion and reason are correct but reason is not correct explanation for Assertion
(c) Assertion is correct but reason is false
(d) both Assertions and reason are false
Ans: (c)
The assertion is correct, as the mode of the given data is indeed 8. However, the reason provided is incorrect. The mode is not calculated by subtracting the lowest observation from the highest observation.

Q6: Assertion: If the value of mode and mean is 60 and 66 respectively, then the value of median is 64.
Reason: Median = (mode + 2 * mean).
(a) both Assertion and reason are correct and reason is correct explanation for Assertion
(b) both Assertion and reason are correct but reason is not correct explanation for Assertion
(c) Assertion is correct but reason is false
(d) both Assertions and reason are false
Ans: (c)
The assertion about the relationship between mode, mean, and median is incorrect. The reason given is not a valid formula for calculating the median. The median is not directly related to the mode and mean in this manner.

Q7: Assertion: If mean and median of an asymmetrical distribution are 58 and 61 respectively, then Mode = 67.
Reason: For an asymmetrical distribution, Mode = 3 * Median - 2 * Mean.
(a) both Assertion and reason are correct and reason is correct explanation for Assertion
(b) both Assertion and reason are correct but reason is not correct explanation for Assertion
(c) Assertion is correct but reason is false
(d) both Assertions and reason are false
Ans: (a)
The assertion is correct, as the given relationship between mean, median, and mode holds true for an asymmetrical distribution. The reason provided correctly explains how to calculate the mode for such a distribution using the median and mean values.

Q8: Assertion: The median of 83, 37, 70, 29, 45, 63, 41, 70, 34, 54 is 49.5.
Reason: The median of n odd number of observations is ((n+1)/2)th term.
(a) both Assertion and reason are correct and reason is correct explanation for Assertion
(b) both Assertion and reason are correct but reason is not correct explanation for Assertion
(c) Assertion is correct but reason is false
(d) both Assertions and reason are false
Ans: (b)
The assertion is correct, as the median of the given data is indeed 49.5. However, the reason provided does not explain why the median of odd observations is the ((n+1)/2)th term. The correct explanation involves rearranging the data in ascending order and finding the middle term.

Q9: Assertion: Range = Maximum value – Minimum value.
Reason: The range of the first 6 multiples of 6 is 9.
(a) both Assertion and reason are correct and reason is correct explanation for Assertion
(b) both Assertion and reason are correct but reason is not correct explanation for Assertion
(c) Assertion is correct but reason is false
(d) both Assertions and reason are false
Ans: (c)
The assertion is correct, as the range is indeed calculated as the difference between the maximum and minimum values. However, the reason provided is incorrect. The range of the first 6 multiples of 6 is 30 (36 - 6), not 9.

Q10: Assertion: Mode of given data 110, 120, 130, 120, 110, 140, 130, 120, 140, 120 is 120.
Reason: The observation with the maximum frequency is called the mode.
(a) both Assertion and reason are correct and reason is correct explanation for Assertion
(b) both Assertion and reason are correct but reason is not correct explanation for Assertion
(c) Assertion is correct but reason is false
(d) both Assertions and reason are false
Ans: (a)
Both the assertion and reason are correct. The mode is the value that appears most frequently in a data set, which in this case is 120 due to its higher frequency compared to other values.