## Rajasthan Board RBSE Class 11 Maths Chapter 13 Measures of Dispersion Miscellaneous Exercise

Question 1.

Marks obtain by five students in math are 20, 25, 15, 35 and 30 its range will be :

(A) 15

(B) 20

(C) 25

(D) 30

Solution:

Range = Maximum value – minimum value = 35 – 15 = 20

Thus (B) is correct.

Question 2.

Formula of inter quartile range is –

(A) Q_{3} + Q_{1}

(B) Q_{3} – Q_{1}

(C) Q_{3} – Q_{2}

(D) Q_{3} – Q_{4}

Solution:

Thus (B) is correct.

Question 3.

If maximum cost of any times is ₹ 500 and minimum ₹ 75, then coefficient of range will be –

(A) 0.739

(B) 0.937

(C) 7.39

(D) 73.9

Solution:

Range coefficient

Thus (A) is correct.

Question 4.

Coefficient of range of variable series 10, 20, 30, 40, 50, 60 is –

(A) 3/2

(B) 5/6

(C) 7/5

(D) 5/7

Solution:

Coefficient of Range

Thus (D) is correct.

Question 5.

Mean deviation is lowest from –

(A) Mean

(B) Median

(C) Mode

(D) Origin

Solution:

(B) is correct.

Use this Mean and Standard Deviation Calculator to get step-by-step calculation of the sample mean, variance and standard deviation.

Question 6.

Marks obtained by four students are 25, 35, 45 and 55 their mean deviation is –

(A) 10

(B) 1

(C) 0

(D) 40

Solution:

Mean of 25, 35, 45, 55

Question 7.

Mean deviation about median for distribution 2, 4, 5, 3, 8, 7, 8 is –

(A) 13/7

(B) 1/2

(C) 11/7

(D) 2

Solution:

Arrange in ascending order, obtained table is:

Question 8.

Mean of any variable series \(\overline { x } \) = 773 and mean deviation 64.4, then coefficient of mean deviation is –

(A) 0.065

(B) 12.003

(C) 0.083

(D) 0.073

Solution:

Mean deviation coefficient

Question 9.

Standard deviation of data 6,10,4,7,4,5 is –

Solution:

Question 10.

If standard deviation of marks obtained by students of a class is 1.4, then variable of distribution will be –

(A) 1.2

(B) 0.38

(C) 1.96

(D) 1.4

Solution:

Standard deviation

(σ) = 1.4

Variation (σ2)= (1.4)2 = 1.96

Thus (C) is correct.

Question 11.

If variance

then value of k is –

(A) 10

(B) 20

(C) 30

(D) 60

Solution:

Thus (C) is correct.

Question 12.

If coefficient of variance of a series is 30% and standard deviation is 15, then its means is –

(A) 0.5

(B) 5

(C) 2

(D) 50

Solution:

Thus (D) is correct.

Question 13.

In a series ∑x^{2} = 100, n = 5 and ∑x = 20, then standard deviation is –

(A) 16

(B) 2

(C) 4

(D) 8

Solution:

Standard deviation

Thus (B) is correct.

Question 14.

Temperature of 7 days in a city are given in centigrade 18, 12, 6, -7, -12, 5, -4. Then range in centrigrade will be –

(A) 6

(B) 30

(C) 22

(D) 14

Solution:

Range = Max. Value – Min. Value

= 18 – (- 12) = 18 + 12 = 30

Thus (B) is correct.

Question 15.

If N = 10, ∑x = 120 and σ_{x} = 60, then variation coefficient is –

(A) 5

(B) 50

(C) 500

(D) 0.5

Solution:

Variation coefficient

Thus (C) is correct.

Question 16.

Algebraic sum of deviations from mean is :

(A) Negative

(B) Positive

(C) Different in each

(D) Zero

Solution:

(C) is correct.

Question 17.

If \(\overline { x } \) = 6, ∑x = 60 and ∑x^{2} = 1000 then value σ is :

(A) 6

(B) 8

(C) 64

(D) 10

Solution:

Thus (B) is correct.

Question 18.

Coefficient of Range can be defined as –

Solution:

Thus (C) is correct.

Question 19.

If value of all the terms of a series are same, then find value of dispersion.

Solution:

Value of dispersion is zero because dispersion (deviation) cannot be find for same values.

Question 20.

Find the formula to find standard deviation in individual series.

Solution:

Question 21.

Standard deviatio of any distribution is 20.5 and arithmetic mean is 60, then find the coefficient of standard deviation.

Solution:

Question 22.

From the following distribution find inter quartile range, coefficients of inter quartile range, Quartile deviation and its coefficient.

More than digit | 0 | 15 | 30 | 45 | 60 | 75 | 90 | 105 |

No. of students | 150 | 140 | 100 | 80 | 70 | 30 | 14 | 0 |

Solution:

We prepare a table using these data:

Question 23.

Find the mean and standard deviation of the following frequency distribution by step deviation method.

Class | 1-5 | 6-10 | 11-15 | 16-20 | 21-25 | 26-30 | 31-35 |

Frequency | 5 | 7 | 18 | 25 | 20 | 4 | 1 |

Solution:

Question 24.

Find the mean deviation about mode and its coefficient from the following data –

Central size | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

Frequency | 3 | 6 | 9 | 13 | 8 | 5 | 4 |

Solution:

Here Maximum frequency is 13 and its corresponding value is 9.

∴ Mode (z) = 9

Question 25.

Find the dispersion of the following data centred size –

Central size | 32-38 | 38-44 | 44-50 | 50-56 | 56-62 | 62-68 |

No. of students | 3 | 6 | 9 | 13 | 8 | 5 |

Solution:

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