Statistics — Class 11 solved problems

15 problems from this chapter, each solved step by step.

1. Calculate the mean and variance of the first n natural numbers.

   The mean of the first n natural numbers is (n+1)/(2) and the variance is (n²-1)/(12).

2. For a statistical data x_1, x_2,, x_10 of 10 values, a student obtained the mean as 5.5 and Σ_i=1^(10) x_i² = 371. He later found that he had noted two values i

   10.9

3. The mean and standard deviation of 100 observations were calculated as 40 and 5.1, respectively by a student who took by mistake 50 instead of 40 for one observ

   The correct mean is 39.9 and the correct standard deviation is 5.09.

4. Let the mean and variance of five observations x_1=1, x_2=3, x_3=a, x_4=7 and x_5=b, with a>b, be 5 and 10 respectively. Then the variance of the observations n

   16

5. The mean of 5 observations is 4.4 and their variance is 8.24. If three of the observations are 1, 2 and 6, find the other two observations.

   The other two observations are 4 and 9.

6. If each of the observation x_1, x_2,..., x_n is increased by ' a ', where a is a negative or positive number, show that the variance remains unchanged.

   The variance remains unchanged.

7. The variance of the numbers 8, 21, 34, 47,, 320 is:

   The variance of the numbers is 8788.

8. The variance of 20 observations is 5. If each observation is multiplied by 2, find the new variance of the resulting observations.

   The new variance of the resulting observations is 20.

9. Find the mean deviation about the median for the following data: x_i: 3, 6, 9, 12, 13, 15, 21, 22 f_i: 3, 4, 5, 2, 4, 5, 4, 3.

   The mean deviation about the median is 4.967 (approximately).

10. The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake, one observation is taken as 50 instead of 40. If the correct mean

    430

11. If the mean and the variance of 6, 4, a, 8, b, 12, 10, 13 are 9 and 9.25 respectively, then a + b + ab is equal to:

    103

12. Calculate mean, variance and standard deviation for the following distribution: Classes: 30-40, 40-50, 50-60, 60-70, 70-80, 80-90, 90-100; Frequencies: 3, 7, 12

    Mean ( x) = 63.8, Variance ( ²) = 164.56, Standard Deviation () = 12.83

13. Find the mean deviation about the median for the following data: 3,9,5,3,12,10,18,4,7,19,21.

    The mean deviation about the median is approximately 5.27.

14. Find the mean deviation about the mean for the following data: 6,7,10,12,13,4,8,12.

    2.75

15. Let the mean and the standard deviation of the observations 2, 3, 3, 4, 5, 7, a, b be 4 and √2 respectively. Then the mean deviation about the mode of these obs

    1

More Class 11 chapters

• Sets19 solved
• Relations and Functions26 solved
• Trigonometric Functions33 solved
• Complex Numbers and Quadratic Equations53 solved
• Linear Inequalities9 solved
• Permutations and Combinations49 solved
• Binomial Theorem17 solved
• Sequences and Series34 solved
• Straight Lines19 solved
• Conic Sections68 solved
• Introduction to Three Dimensional Geometry6 solved
• Limits and Derivatives32 solved
• Probability8 solved

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