Statistics Test

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Statistics Test - 45

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Weekly Quiz Competition

Question 1
1 / -0

The choices of the fruits of 42 students in a class are as follows:
A, O, B, M, A, G, B, G, A, G, B, M. A, O, M, A, B, G, M, B, A, O, M, O, G, B, O, M, G, A, A, B, M, O, M, G, B, A, M, O, M, O,
where A, B, G, M, and O stands for Apple, Banana, Grapes, Mango and Orange respectively.
which fruit is liked
by most of the students?

A
O

B
G

C
M

D
A

Solution

The number of $$A$$ appearing in the list is $$9$$

The number of $$B$$ appearing in the list is $$8$$

The number of $$G$$ appearing in the list is $$7$$

The number of $$M$$ appearing in the list are $$10$$

The number of $$O$$ appearing in the list are $$8$$

So, $$M$$ appeared the most, and $$M$$ stands for Mango.

So, Mango $$M$$ is the fruit that is liked by most of the students.
Question 2
1 / -0

The median of the data : $$ 3,4,5,6,7,3,4$$ is

A
5

B
3

C
4

D
6

Solution

Rearranging the given data into ascending order, we get
$$3,3,4,4,5,6,7,$$
Total number of observations $$=7$$ which is odd
Hence, the $$4^{th}$$ term is the median.
$$\therefore$$ Median $$=4$$

Hence, option (C) is the correct answer.
Question 3
1 / -0

What is the mode of $$19, 19, 15, 20, 25, 15, 20, 15$$?

A
$$15$$

B
$$20$$

C
$$19$$

D
$$25$$

Solution

Since observation $$15$$ is occuring the most in the data:
$$19,19,15,20,25,15,20,15$$

So, the mode of the given data is $$15$$
.
Hence, the correct alternative answer is (A).
Question 4
1 / -0

If maximum cost of any times is Rs. 500 and minimum Rs 75, the coefficient of range will be -

A
$$ 0.739$$

B
$$0.937$$

C
$$7.39$$

D
$$73.9$$

Solution

Range coefficient
$$\dfrac{500 - 75}{500 + 75} = \dfrac{425}{575} = 0.739$$
Question 5
1 / -0

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

A
$$ 3/4$$

B
$$5/6$$

C
$$7/5$$

D
$$5/7$$

Solution

Coefficient of Range
$$= \dfrac{60 - 10}{60 + 10} = \dfrac{50}{70} = \dfrac{5}{7}$$
Thus (D) is correct
Question 6
1 / -0

Marks obtained by students are $$ 25, 35, 45 $$ and $$55 $$ their mean deviation is -

A
$$10$$

B
$$1$$

C
$$0$$

D
$$40$$

Solution

$$\bar{x} = \dfrac{25 + 35 + 45 + 55}{4} = \dfrac{160}{4} = 40$$
Mean $$ = 40 $$
Mean deviation $$ = \dfrac{\sum |x_{i}-\bar{x}}{N} = \dfrac{40}{4} = 10$$
Question 7
1 / -0

coefficient of Range can be defined as -

A
$$\dfrac{H - L}{2} $$

B
$$\dfrac{H + L }{2} $$

C
$$\dfrac{H - L}{H + L}$$

D
$$\dfrac{H + L}{H - L}$$

Solution

Thus (C) is correct
Question 8
1 / -0

In a series $$\sum x^{2} = 100, n = 5 $$ and $$\sum x = 20 $$ , then standard deviation is

A
16

B
2

C
4

D
8

Solution

Standard deviation
$$\sigma \sqrt{\dfrac{\sum x^{2}}{n} - \left ( \dfrac{\sum }{n} \right )^{2}} = \sqrt{\dfrac{100}{5} - \left ( \dfrac{20}{5} \right )^{2}} $$
$$\sqrt{20-16} = \sqrt{4} = 2 $$
Question 9
1 / -0

If $$ N = 10 \sum x = 120 $$ and $$ \sigma _{x} = 60 $$ , the variation coefficient is -

A
$$5$$

B
$$50$$

C
$$500$$

D
$$0.5$$

Solution

Variation coefficient
$$= \dfrac{\sigma _{x}}{Mean} \times 100$$
$$ = \dfrac{60 \times 10}{120} \times = 500$$
Question 10
1 / -0

Standard deviation of data $$6, 10, 4, 7, 4, 5$$ is -

A
$$\sqrt{\dfrac{13}{3}} $$

B
$$\dfrac{13}{3} $$

C
$$\sqrt{26} $$

D
$$\dfrac{\sqrt{26}}{6}$$

Solution

Mean $$(\bar{x}) = \dfrac{6+ 10 + 4 + 7 + 4 + 5}{6} = \dfrac{36}{6} = 6 $$
Standard deviation $$(\sigma ) = \sqrt{\dfrac{1}{N} \times \sum (x_{1} - \bar{x})^{2}} $$
$$=\sqrt{\dfrac{1}{6} \times 26} = \sqrt{\dfrac{13}{3}}$$

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Re-Attempt Weekly Quiz Competition

Statistics Test - 45

Result

Statistics Test - 45

Score

-

Rank

-

SHARING IS CARING

Question 1

O

G

M

A

Solution

Question 2

5

3

4

6

Solution

Question 3

$$15$$

$$20$$

$$19$$

$$25$$

Solution

Question 4

$$ 0.739$$

$$0.937$$

$$7.39$$

$$73.9$$

Solution

Question 5

$$ 3/4$$

$$5/6$$

$$7/5$$

$$5/7$$

Solution

Question 6

$$10$$

$$1$$

$$0$$

$$40$$

Solution

Question 7

$$\dfrac{H - L}{2} $$

$$\dfrac{H + L }{2} $$

$$\dfrac{H - L}{H + L}$$

$$\dfrac{H + L}{H - L}$$

Solution

Question 8

16

2

4

8

Solution

Question 9

$$5$$

$$50$$

$$500$$

$$0.5$$

Solution

Question 10

$$\sqrt{\dfrac{13}{3}} $$

$$\dfrac{13}{3} $$

$$\sqrt{26} $$

$$\dfrac{\sqrt{26}}{6}$$

Solution

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