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Statistics MATHS - Statistics

Gujarat Board (GSEB) - STD 11 Science - MATHS (GSEB - English Medium). 110 questions in this chapter.

Question types

Statistics question types

110 questions across 4 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

110
Questions
4
Question groups
5
Question types
Sample Questions

Statistics questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 2MCQ1 Mark
Let a, b, c, d, e be the observations with mean m and standard deviation s. The standard deviation of the observations a + k, b + k, c + k, d + k, e + k is:
  • ✓
    s
  • B
    ks
  • C
    s + k
  • D
    $\frac{\text{s}}{\text{k}}$

Answer: A.

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Q 3MCQ1 Mark
If n = 10, $\overline{\text{X}}=12$ and $\sum\text{x}_\text{i}^2=1530,$ then the coefficient of variation is:
  • A
    36%
  • B
    41%
  • ✓
    25%
  • D
    None of these

Answer: C.

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Q 4MCQ1 Mark
Let $\mathrm{x}_1, \mathrm{x}_2, \ldots, \mathrm{x}_{\mathrm{n}}$ be n observations. Let $\mathrm{y}_{\mathrm{i}}=\mathrm{a} \mathrm{x}_{\mathrm{i}}+\mathrm{b} \mathrm{y}_{\mathrm{i}}+\mathrm{b}$ for $\mathrm{i}=1,2,3, \ldots, \mathrm{n}$, where a and b are constants. If the mean of $x_i^{\prime} s$ is 48 and their standard deviation is 12 , the mean of $y_i$ 's 55 and standard deviation of $y_i$ 's is 15 , the values of a and b are:
  • ✓
    a = 1.25, b = -5
  • B
    a = -1.25, b = 5
  • C
    a = 2.5, b = -5
  • D
    a = 2.5, b = 5

Answer: A.

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Q 5MCQ1 Mark
If the standard deviation of a variable X is $\sigma,$ then the standard deviation of variable $\frac{\text{aX+b}}{\text{c}}$ is:
  • A
    $\text{a}\ \sigma$
  • B
    $\frac{\text{a}}{\text{c}}\sigma$
  • ✓
    $\Big|\frac{\text{a}}{\text{c}}\Big|\sigma$
  • D
    $\frac{\text{a}\sigma+\text{b}}{\text{c}}$

Answer: C.

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Q 6(Each question 1 marks)1 Mark
If $x_1, x_2, \ldots, x_n$ are $n$ values of a variable $X$ and $y_1, y_2, \ldots, y_n$ are $n$ values of variable $Y$ such that $y_i=a x_i+b, i=1,2, \ldots, n$, then write $\operatorname{Var}( Y )$ in terms of $\operatorname{Var}( X )$.
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Q 8(Each question 1 marks)1 Mark
If X and Y are two variates connected by the relation $\text{Y}=\frac{\text{aX+b}}{\text{c}}$ and $\text{Var}(\text{X})=\sigma^2,$ then write the expression for the standard deviation of Y.
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Q 11(Each question 3 marks)3 Marks
Two plants A and B of a factory show following results about the number of workers and the wages paid to them:
  Plant A Plant B
No. of workers 5000 6000
Average monthly wages ₹ 2500 ₹ 2500
Variance of distribution of wages 81 100
In which plant A or B is there greater variability in individual wages?
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Q 12(Each question 3 marks)3 Marks
The means and standard deviations of heights ans weights of 50 students of a class are as follows:
  Weights Heights
Mean 63.2kg 63.2 inch
Standard deviation 5.6kg 11.5 inch
Which shows more variability, heights or weights?
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Q 17(Each question 4 marks)4 Marks
The mean and standard deviation of 20 observation are found to be 10 and 2 respectively. On reacheking it was found that an observation 8 was incorrect. Calculate the correct and standard deviation in each of the following cases:
  1. If wrong item is omitted.
  2. If it is replaced by 12.
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Q 19(Each question 4 marks)4 Marks
Find the numberof observation lying between $\overline{\text{X}}-\text{M.D. }$and $\overline{\text{X}}-\text{M.D. }$ is the mean deviation from the mean. 34, 66, 30, 38, 44, 50, 40, 60, 42, 51
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Q 20(Each question 4 marks)4 Marks
While calculating the mean and variance of 10 readings, a student wrongly used the reading of 52 for the correct reading 25. He obtained the mean and variance as 45 and 16 respectively. Find the correct mean and the variance.
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