Statistics Test

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Statistics Test - 18

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Weekly Quiz Competition

Question 1
1 / -0

In an examination, $$10$$ students scored the following marks in Mathematics: $$35, 19, 28, 32, 63, 02, 47, 31, 13, 98$$. Its range is

A
$$2$$

B
$$96$$

C
$$98$$

D
$$50$$

Solution

Range $$=$$ Maximum value of the variable $$-$$ Minimum value of the variable
$$= 98 - 2 = 96$$
Question 2
1 / -0

The mean of $$x + 3, x + 5, x + 7, x + 9$$ and $$x + 11$$ is

A
$$2x+7$$

B
$$x+8$$

C
$$x+7$$

D
None of these

Solution

The observations are : $$x+3,x+5,x+7,x+9, x+11$$
Mean = $$\dfrac{sum}{number \quad of \quad observations}$$ = $$\dfrac{x+3,x+5,x+7,x+9, x+11}{5}$$ = $$\dfrac{5x + 35}{5} = x + 7$$
Question 3
1 / -0

A histrogram consists of

A
sectors

B
rectangles

C
triangle

D
squares

Solution

A histogram is an area diagram. It can be defined as a set of rectangles with bases along with the intervals between class boundaries and with areas proportional to frequencies in the corresponding classes.
Question 4
1 / -0

Which class-interval has the maximum frequency?

A
$$0-10$$

B
$$30-40$$

C
$$10-20$$

D
$$40-50$$

Solution

We will form table from above histogram:
$$CI$$ $$Frequency$$
$$0-10$$ $$15$$
$$10-20$$ $$10$$
$$20-30$$ $$20$$
$$30-40$$ $$25$$
$$40-50$$ $$10$$
$$50-60$$ $$5$$
$$\Rightarrow$$ From above table table we can see, $$30-40$$ has frequency $$25$$ which is maximum.
$$\therefore$$ The class-interval has the maximum frequency is $$30-40$$
Question 5
1 / -0

What is frequency of the class- interval $$20-30$$ ?

A
$$25$$

B
$$20$$

C
$$5$$

D
$$10$$

Solution

$$\Rightarrow$$ In the above histogram we can see that, frequency of the class interval $$20-30$$ is $$20$$
Question 6
1 / -0

Lower class limit of $$15 -18$$ is _____

A
$$15$$

B
$$18$$

C
$$15$$ or $$18$$

D
None of these

Solution

We need to find lower class limit of $$15-18$$.
Thus, $$15$$ is lesser in $$(15-18) $$, so answer is $$15$$.

Question 7

1 / -0

Construct a frequency distribution table for the data, taking class-intervals 4-6, 6-8, ............., 14-16.

11.5
4.5
7.4
9.8
4.6
14.2
6.6
15.5

6.3
6
5.3
8.25
6.4
15.3
4.3
14.4

7.8
8.3
8.4
6.5
8.9
11.7
4.7
12.2

9.2
12.5
15.2
5.8
10.8
9.9
9.4
7.7

10.5
15.8
8.9
10.5
12.7
8.8
10.1
5.5

C.I.
Tally Marks. Frequency
4-6
6-8
8-10
10-12
12-14
14-16
$${||||}\! \! \! \! \! \! {\diagdown}\:   ||$$
$${||||}\! \! \! \! \! \! {\diagdown}\:   |||$$
$${||||}\! \! \! \! \! \! {\diagdown}\:   {||||}\! \! \! \! \! \! {\diagdown}$$
$${||||}\! \! \! \! \! \! {\diagdown}\: |$$
|||
$${||||}\! \! \! \! \! \! {\diagdown}\: |$$
7
8
10
6
3
6

C.I.
Tally Marks. Frequency
4-6
6-8
8-10
10-12
12-14
14-16
$${||||}\! \! \! \! \! \! {\diagdown}\:   ||$$
$${||||}\! \! \! \! \! \! {\diagdown}\:   |||$$
$${||||}\! \! \! \! \! \! {\diagdown}\:   {||||}\! \! \! \! \! \! {\diagdown}$$
$${||||}\! \! \! \! \! \! {\diagdown}\: |$$
|||
$${||||}\! \! \! \! \! \! {\diagdown}\: |$$
7
10
8
6
3
6

C.I.
Tally Marks. Frequency
4-6
6-8
8-10
10-12
12-14
14-16
$${||||}\! \! \! \! \! \! {\diagdown}\:   ||$$
$${||||}\! \! \! \! \! \! {\diagdown}\:   |||$$
$${||||}\! \! \! \! \! \! {\diagdown}\:   {||||}\! \! \! \! \! \! {\diagdown}$$
$${||||}\! \! \! \! \! \! {\diagdown}\: |$$
|||
$${||||}\! \! \! \! \! \! {\diagdown}\: |$$
6
8
10
8
3
3

None of these

Solution

Crete class interval in $$4 - 6$$, $$6 - 8$$ and so on and count the number of terms in between these intervals:

C.I.	Tally Marks.	Frequency
4-6 6-8 8-10 10-12 12-14 14-16	$${\|\|\|\|}\! \! \! \! \! \! {\diagdown}\: \|\|$$ $${\|\|\|\|}\! \! \! \! \! \! {\diagdown}\: \|\|\|$$ $${\|\|\|\|}\! \! \! \! \! \! {\diagdown}\: {\|\|\|\|}\! \! \! \! \! \! {\diagdown}$$ $${\|\|\|\|}\! \! \! \! \! \! {\diagdown}\: \|$$ \|\|\| $${\|\|\|\|}\! \! \! \! \! \! {\diagdown}\: \|$$	7 8 10 6 3 6

Question 8
1 / -0

How many class-intervals have equal frequency ?

A
$$2$$

B
$$1$$

C
$$3$$

D
None

Solution

$$\Rightarrow$$ In above histogram we can see, class intervals $$10-20$$ and $$40-50$$ have same frequency which is $$10$$.
$$\therefore$$ The class intervals have equal frequency are $$2$$.
Question 9
1 / -0

The difference between the greatest and the least value of the observations is known as

A
M.D.

B
S.D.

C
Range

D
Variance

Solution

The difference between the greatest and the least value of the observations is defined as $$Range$$.
Question 10
1 / -0

Find the mean of first ten odd natural numbers.

A
$$10$$

B
$$11$$

C
$$12$$

D
None of these

Solution

First 10 odd natural numbers are: $$1,3,5,7,9,11,13,15,17,19$$
Mean $$= \cfrac{\text{Sum}}{\text{Number of observations}} =\cfrac{1 + 3 + 5+ 7+9+11+13+15+17 + 19}{10} =10$$

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$$CI$$	$$Frequency$$
$$0-10$$	$$15$$
$$10-20$$	$$10$$
$$20-30$$	$$20$$
$$30-40$$	$$25$$
$$40-50$$	$$10$$
$$50-60$$	$$5$$

Statistics Test - 18

Result

Statistics Test - 18

Score

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Rank

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SHARING IS CARING

Question 1

$$2$$

$$96$$

$$98$$

$$50$$

Solution

Question 2

$$2x+7$$

$$x+8$$

$$x+7$$

None of these

Solution

Question 3

sectors

rectangles

triangle

squares

Solution

Question 4

$$0-10$$

$$30-40$$

$$10-20$$

$$40-50$$

Solution

Question 5

$$25$$

$$20$$

$$5$$

$$10$$

Solution

Question 6

$$15$$

$$18$$

$$15$$ or $$18$$

None of these

Solution

Question 7

None of these

Solution

Question 8

$$2$$

$$1$$

$$3$$

None

Solution

Question 9

M.D.

S.D.

Range

Variance

Solution

Question 10

$$10$$

$$11$$

$$12$$

None of these

Solution

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