### Statistics Class 9th Mathematics Term 2 Tamilnadu Board Solution

##### Question 1.| The mean of the first 10 natural numbers isA. 25B. 55C. 5.5D. 2.5Answer:Let us list out first 10 natural numbers. They are:1, 2, 3, 4, 5, 6, 7, 8, 9, 10Total number of observations = 10Mean is given by ⇒ ⇒ ⇒ Mean = 5.5Thus, option (C) is correct.Question 2.The Arithmetic mean of integers from-5 to 5 isA. 3B. 0C. 25D. 10Answer:The integers from -5 and 5 are:-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5Total number of observations = 11Mean is given by ⇒ ⇒ Mean = 0Thus, option (B) is correct.Question 3.If the mean of x,x + 2,x + 4,x + 6,x + 8 is 20 then x isA. 32B. 16C. 8D. 4Answer:Here, total number of observations = 5And given that, mean = 20Mean is given by ⇒ ⇒ 5x + 20 = 5 × 20⇒ 5x + 20 = 100⇒ 5x = 100 – 20⇒ 5x = 80⇒ ⇒ x = 16Thus, option (B) is correct.Question 4.The mode of the data 5,5,5,5,5,1,2,2,3,3,3,4,4,4,4 isA. 2B. 3C. 4D. 5Answer:We can arrange the data in ascending form as:1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5This gives us an ease of observation.Here, 5 is coming 5 times and it is the most occurring value in the data.Since, mode is a number having the highest frequency of all numbers in the data.⇒ Mode = 5Thus, option (D) is correct.Question 5.The median of 14, 12, 10,9,11 isA. 11B. 10C. 9.5D. 10.5Answer:To find median, we need to arrange data in ascending order.We have9, 10, 11 ,12, 14Total number of observations, n = 5 (odd).When n is odd, median is found as follows. ⇒ ⇒ ⇒ Median = 3rd term⇒ Median = 11 [∵ the 3rd term in the arranged data = 11]Thus, option (A) is correct.Question 6.The median of 2,7,4,8,9,1 isA. 4B. 6C. 5.5D. 7Answer:To find median, we need to arrange data in ascending order.We have1, 2, 4, 7, 8, 9Total number of observations, n = 6 (even).When n is even, median is found as follows. ⇒ ⇒ Median = Mean of 3rd term and 4th term⇒ Median = Mean of 4 and 7 [∵ from the arranged data, 3rd term = 4 and 4th term = 7]⇒ ⇒ ⇒ Median = 5.5Thus, option (C) is correct.Question 7.The mean of first 5 whole number isA. 2B. 2.5C. 3D. 0Answer:The first whole numbers are: 0, 1, 2, 3, 4Total number of observations = 5Mean is given by ⇒ ⇒ ⇒ Mean = 2Thus, option (A) is correct.Question 8.The arithmetic mean of 10 number is-7. If 5 is added to every number, then the new Arithmetic mean isA. -2B. 12C. -7D. 17Answer:Given that, arithmetic mean of 10 numbers = -7We know, total number of observations, n = 10Then, mean is given by ⇒ ⇒ Sum of all observations = 10 × -7 = -70According to question, if 5 is added to every 10 number then,New sum of all observations = Old sum + (5 × 10)⇒ New sum = -70 + 50 = -20 ⇒ ⇒ New mean = -2Thus, option (A) is correct.Question 9.The Arithmetic mean of all the factors of 24 isA. 8.5B. 5.67C. 7D. 7.5Answer:All the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. [These numbers divide 24 completely]Total number of observations = 8Mean is given by ⇒ ⇒ Mean = 7.5Thus, option (D) is correct.Question 10.The mean of 5 numbers is 20. If one number is excluded their mean is 15. Then the excluded number isA. 5B. 40C. 20D. 10Answer:Given that, Total number of observations = 5Mean = 20So, Sum of observations can be given asSum of observations = Mean × Total number of observations [∵ ]⇒ Sum of observations = 20 × 5⇒ Sum of observations = 100Let the excluded number be x.New Sum of observations = 100 – xNew Mean = 15New total number of observations = 4Mean is given by ⇒ ⇒ 100 – x = 15 × 4⇒ 100 – x = 60⇒ x = 100 – 60 = 40⇒ The excluded number is 40.Thus, option (B) is correct.

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