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Step-by-step NCERT solutions for Statistics (Chapter 13, NCERT Class 11 Mathematics) — every question and answer worked out in full, not just the final result. You can also read the Statistics textbook chapter.

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All 28 questions in Statistics are solved in the PDF. Here's what's inside, exercise by exercise:

Exercise 13.1

  1. Find the mean deviation about the mean for the data: 4, 7, 8, 9, 10, 12, 13, 17.
  2. Find the mean deviation about the mean for the data: 38, 70, 48, 40, 42, 55, 63, 46, 54, 44.
  3. Find the mean deviation about the median for the data: 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17.
  4. Find the mean deviation about the median for the data: 36, 72, 46, 42, 60, 45, 53, 46, 51, 49.
  5. Find the mean deviation about the mean for the data: xi : 5 10 15 20 25 fi : 7 4 6 3 5
  6. Find the mean deviation about the mean for the data: xi : 10 30 50 70 90 fi : 4 24 28 16 8
  7. Find the mean deviation about the median for the data: xi : 5 7 9 10 12 15 fi : 8 6 2 2 2 6
  8. Find the mean deviation about the median for the data: xi : 15 21 27 30 35 fi : 3 5 6 7 8
  9. Find the mean deviation about the mean for the data: Income per day (in ₹): 0-100, 100-200, 200-300, 300-400, 400-500, 500-600, 600-700, 700-800 Number of persons: 4, 8, 9, 10, 7, 5, 4, 3
  10. Find the mean deviation about the mean for the data: Height in cm: 95-105 105-115 115-125 125-135 135-145 145-155 Number of boys: 9 13 26 30 12 10
  11. Find the mean deviation about median for the following data: Marks: 0-10 10-20 20-30 30-40 40-50 50-60 Number of Girls: 6 8 14 16 4 2
  12. Calculate the mean deviation about median age for the age distribution of 100 persons given below: Age (years): 16-20 21-25 26-30 31-35 36-40 41-45 46-50 51-55 Number: 5 6 12 14 26 12 16 9 [Hint: Convert to continuous distribution by subtracting 0.5 from lower limit and adding 0.5 to upper limit.]

Exercise 13.2

  1. Find the mean and variance for the data: 6, 7, 10, 12, 13, 4, 8, 12.
  2. Find the mean and variance for the first n natural numbers.
  3. Find the mean and variance for the first 10 multiples of 3.
  4. Find the mean and variance for the following frequency distribution: xi : 6 10 14 18 24 28 30 fi : 2 4 7 12 8 4 3
  5. Find the mean and variance for the following frequency distribution: xi : 92 93 97 98 102 104 109 fi : 3 2 3 2 6 3 3
  6. Find the mean and standard deviation using the short-cut method. xi : 60 61 62 63 64 65 66 67 68 fi : 2 1 12 29 25 12 10 4 5
  7. Find the mean and variance for the following frequency distribution: Classes: 0-30 30-60 60-90 90-120 120-150 150-180 180-210 Frequencies: 2 3 5 10 3 5 2
  8. Find the mean and variance for the following frequency distribution: Classes: 0-10 10-20 20-30 30-40 40-50 Frequencies: 5 8 15 16 6
  9. Find the mean, variance and standard deviation using the short-cut method. Height (cm): 70-75 75-80 80-85 85-90 90-95 95-100 100-105 105-110 110-115 No. of children: 3 4 7 7 15 9 6 6 3
  10. The diameters of circles (in mm) drawn in a design are given below: Diameters: 33-36 37-40 41-44 45-48 49-52 No. of circles: 15 17 21 22 25 Calculate the standard deviation and mean diameter of the circles.

Miscellaneous Exercise

  1. The mean and variance of eight observations are 9 and 9.25, respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.
  2. The mean and variance of 7 observations are 8 and 16, respectively. If five of the observations are 2, 4, 10, 12, 14, find the remaining two observations.
  3. The mean and standard deviation of six observations are 8 and 4, respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations.
  4. Given that x̄ is the mean and σ² is the variance of n observations x1, x2, …, xn. Prove that the mean and variance of the observations ax1, ax2, ax3, …, axn are ax̄ and a²σ², respectively (a ≠ 0).
  5. The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases:
    • (i) If the wrong item is omitted.
    • (ii) If it is replaced by 12.
  6. The mean and standard deviation of a group of 100 observations were found to be 20 and 3, respectively. Later on it was found that three observations were incorrect, which were recorded as 21, 21 and 18. Find the mean and standard deviation if the incorrect observations are omitted.
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Read the Statistics textbook chapter / PDF, or browse all NCERT Class 11 Mathematics solutions.

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