Statistics Test

Result

Statistics Test - 47

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Question 1
1 / -0

Directions For Questions

The average age of $$06$$ persons living in a house is $$23.5$$ years. Three of them are majors and their average age is $$42$$ years. The difference in ages of the three minor children is same.

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What is the median of the ages of minor children?

A
$$3$$ years

B
$$5$$ years

C
$$7$$ years

D
cannot determined due to the insufficient data

Solution
Question 2
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Variance of the first $$1$$ natural numbers is.

A
$$\sqrt{5}$$

B
$$\sqrt{10}$$

C
$$5\sqrt{2}$$

D
$$10$$
Question 3
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Mean and standard deviation of a data are $$48$$ and $$12$$ respectively. The coefficient of variation is.

A
$$42$$

B
$$25$$

C
$$28$$

D
$$48$$
Question 4
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What is the mean deviation about the mean for the data $$4, 7, 8, 9, 10, 12, 13, 17$$?

A
$$2.5$$

B
$$3$$

C
$$3.5$$

D
$$4$$

Solution

Given data is $$4,7,8,9,10,12,13,17$$

Mean of the given data =$$\dfrac {sum\ of\ all\ terms }{total\ no.\ of\ terms}$$

$$\bar{x} = \dfrac {4+7+8+9+10+12+13+17}{8}$$

= $$\dfrac {80}{8}$$

Mean = $$10$$

Mean deviation about mean = $$\dfrac {\sum \left | x_i - \bar{x} \right |}{8}$$

Where $$ \bar{x}$$ is the mean value and $$x_i$$ is the given data

By substituting the values in the formula we get =$$\dfrac {24}{8} = 3$$
Mean deviation about mean is $$3$$
Question 5
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Given $$\sum (x-\bar{x})^2=48, \bar{x}=20$$ and $$n=12$$. The coefficient of variation is.

A
$$25$$

B
$$20$$

C
$$30$$

D
$$10$$

Solution
Question 6
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If the variance of $$14, 18, 22, 26, 30$$ is $$32$$, then the variance of $$28, 36, 44, 52, 60$$ is.

A
$$64$$

B
$$128$$

C
$$32\sqrt{2}$$

D
$$32$$

Solution
Question 7
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The variance of $$10, 10, 10, 10$$ is.

A
$$10$$

B
$$\sqrt{10}$$

C
$$5$$

D
$$0$$

Solution
Question 8
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Calculate the coefficient of range from the following discrete (ungrouped) frequency distribution of marks of 60 students.
No of students Marks
9 15
10 20
15 25
14 30
12 35

A
0.3

B
0.4

C
1.5

D
0.2

Solution
Question 9
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If x is the average(arithmetic mean) of $$5$$ consecutive odd integers, what is the median of integers?

A
$$0$$

B
$$1$$

C
$$x-2$$

D
x
Question 10
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If coefficient of range is $$0.092$$ and the largest value is $$71$$, the range is?

A
$$12$$

B
$$13$$

C
$$14$$

D
$$16$$

Solution

Coefficient of range$$=\dfrac{x_m-x_0}{x_m+x_0}$$
$$0.092=\dfrac{71-x_0}{71+x_0}$$
$$0.092(71+x_0)=71-x_0$$
$$0.092x_0+x_0=71-71 \times 0.092$$
$$x_0=\dfrac{71(1-0.092)}{1.092}=59.03\approx59$$
The smallest value of data is $$59$$
But the range$$=x_m-x_0=71-59=12$$