Title 13.STATISTICS.pdf ✅

13 . STATISTICS-MCQS TYPE (1.) The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was recorded as 50 instead of 40 . Then the correct variance is [15 APRIL 2023 (MORNING)] (a.) 14 (b.) 11 (c.) 12 (d.) 13 (2.) Let the mean of 6 observations 1,2,4,5x and y 5 and their variance be 10 . Then their mean deviation about the mean is equal to [11 APRIL 2023 (AFTERNOON)] (a.) 7 3 (b.) 10 3 (c.) 8 3 (d.) 3 (3.) Let 1 2 100 x , x , , x  be in an arithmetic progression, with 1 x 2 = and their mean equal to 200. If y i x i i i = − ( ) , 1 i 100   , then the mean of 1 2 100 y , y , .y  is : [11 APRIL 2023 (MORNING)] (a.) 10051.50 (b.) 10100 (c.) 10101.50 (d.) 10049.50 (4.) Let sets A and B have 5 elements each. Let mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements in sets A and B be 12 and 20 respectively. A new set C of 10 elements is formed by subtracting 3 from each element of A and adding 2 to each element of B . Then the sum of the mean and variance of the elements of C is [11 APRIL 2023 (MORNING)] (a.) 36 (b.) 40 (c.) 32 (d.) 38 (5.) Let the mean and variance of 12 observations be 9 2 and 4 respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is m n , where m and n are coprime, then m n + is equal to [08 APRIL 2023 (EVENING)] (a.) 316 (b.) 317 (c.) 315 (d.) 314 (6.) The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of another set of 15 numbers are 14 and 2  respectively. If the variance of all the 30 numbers in the two sets is 13 , then 2  is equal to : [06 APRIL 2023 (MORNING)] (a.) 12 (b.) 10 (c.) 11 (d.) 9 (7.) Let the mean and standard deviation of marks of class A of 100 students be respectively 40 and ( 0)  , and the mean and standard deviation of marks of class B of n students be respectively 55 and 30− . If the mean and variance of the marks of the combined class of 100+ n students are respectively 50 and 350 , then the sum of variances of classes A and B is: [31 Jan 2023(Evening)] (a.) 500 (b.) 650 (c.) 450 (d.) 900

(a.) Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for statement-1. (b.) Statement-1 is true, statement-2 is true, statement-2 is not a correct explanation for statement-1. (c.) Statement- 1 is true, statement- 2 is false. (d.) Statement- 1 is false, statement-2 is true. (14.) All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given? [JEE (Main)-2013] (a.) Mean (b.) Median (c.) Mode (d.) Variance (15.) The variance of first 50 even natural numbers is [JEE (Main)-2014] (a.) 437 (b.) 437 4 (c.) 833 4 (d.) 833 (16.) The mean of the data set comprising of 16 observations is 16 . If one of the observation valued 16 is deleted and three new observations valued 3 , 4 and 5 are added to the data, then the mean of the resultant data, is [JEE (Main)-2015] (a.) 16.8 (b.) 16.0 (c.) 15.8 (d.) 14.0 (17.) If the standard deviation of the number 2,3 , a and 11 is 3.5 , then which of the following is true? [JEE (Main)-2016] (a.) 2 3 32 84 0 a a − + = (b.) 2 3 34 91 0 a a − + = (c.) 2 3 23 44 0 a a − + = (d.) 2 3 26 55 0 a a − + = (18.) If ( ) 9 1 5 9 i i x  − = = and ( ) 2 9 1 5 45 i i x  − = = , then the standard deviation of the 9 items 1 2 9 x x x , , .,  is [JEE (Main)-2018] (a.) 9 (b.) 4 (c.) 2 (d.) 3 (19.) 5 students of a class have an average height 150 cm and variance 2 18 cm . A new student, whose height is 156 cm , joined them. The variance (in 2 cm ) of the height of these six students is [JEE (Main)-2019] (a.) 18 (b.) 20 (c.) 22 (d.) 16 (20.) A data consists of n observations 1 2 , , , n x x x  If ( ) 2 1 1 9 n i i x n  + = = and ( ) 2 1 1 5 n i i x n  − = = , then the standard deviation of this data is [JEE (Main)-2019] (a.) 7 (b.) 5 (c.) 5 (d.) 2 (21.) The mean of five observations is 5 and their variance is 9.20 . If three of the given five observations are 1,3 and 8 , then a ratio of other two observations is [JEE (Main)-2019] (a.) 4:9 (b.) 6:7 (c.) 10:3 (d.) 5:8