Statistics Test

Result

Statistics Test - 12

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Weekly Quiz Competition

Question 1
1 / -0

A child says that the median of $$3, 14, 18, 20, 5$$ is $$18$$. What concept does the child missed about finding the median?

A
The order of numbers.

B
$$14$$

C
$$18$$

D
None of these

Solution

To calculate the median of any data series. The data series has to be arranged in the ascending order. The child hasn't arranged the data series in ascending order.
Question 2
1 / -0

The mean deviation of the data $$2,9,9,3,6,9,4$$ from the mean is

A
$$2.23$$

B
$$2.57$$

C
$$3.23$$

D
$$3.57$$

Solution

Given data is, 2,9,9,3,6,9,4
Here, $$\displaystyle n = 7, \bar{x}=\frac{2+9+9+3+6+9+4}{7}=6$$
$$\therefore$$ Mean deviation from mean is $$=\displaystyle \frac{1}{n}\left(\sum |x-\bar{x}|\right)=\frac{4+3+3+3+0+3+2}{7}=\frac{18}{7}=2.57$$
Question 3
1 / -0

Mode of $$2, 3, 4, 5, 0, 1, 3, 3, 4, 3\ is\ 3.$$

A
True

B
False

C
Neither

D
None

Solution

Mode is the term which appears maximum number of times.

The terms are: 2, 3, 4, 5, 0, 1, 3, 3, 4, 3
Arranging them in ascending order: 0,1,2,3,3,3,3,4,4,5
3 is occurring maximum number of times. hence mode is 3.
Question 4
1 / -0

Which one of the following statements is correct ?

A
Th Standard deviation for a given distribution is the square of the variance.

B
The standard deviation for a given distribution is the square root of the variance.

C
The standard deviation for a given distribution is equal to the variance.

D
The standard deviation for a given distribution is half of the variance.

Solution

We know $$Variance(\sigma^2)=\dfrac{\sum(x-\overline{x})^2}{n}$$
Where,
$$\sigma^2$$ is variance
$$\overline{x}$$ is mean
$$n$$ is number of observations.
Standard deviation $$(\sigma)=\sqrt{\dfrac{\sum(x-\overline{x})^2}{n}}$$
$$\therefore$$ We can see, the standard deviation for a given distribution is the square root of the variance.
Question 5
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 6
1 / -0

A student got marks in $$5$$ subjects in a monthly test is given below: $$2, 3, 4, 5, 6$$.
In these obtained marks, $$4$$ is the

A
Mean and median

B
Median but no mean

C
Mean but no median

D
Mode

Solution

Marks obtained $$= 2,3,4,5,6$$

Median is the middle term $$= 4$$.
Mean $$= \dfrac{2+3+4+5+6}{5} = 4$$.
Question 7
1 / -0

Coefficient of deviation is calculated by the formula:

A
$$\cfrac { \bar { X } }{ \sigma } \times 100$$

B
$$\cfrac { \bar { X } }{ \sigma }$$

C
$$\cfrac { \sigma } {\bar { X }} \times 100$$

D
$$\cfrac{ \sigma } { \bar { X }}$$

Solution

It is a fundamental concept.
coefficient of deviation $$=\cfrac{\sigma}{\bar{x}}\times 100$$
where $$\sigma$$ and $$\bar{x}$$ are standard deviation and mean respectively.
Question 8
1 / -0

The marks of $$20$$ students in a test were as follows:
$$5, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19, 20$$
The mode is

A
$$20$$

B
$$10$$

C
$$15$$

D
$$25$$

Solution

Terms are: $$5, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19, 20$$.
$$15$$ occurs most number of times $$(3$$ times$$)$$.
Hence, $$15$$ is the mode of the marks.
Question 9
1 / -0

The mean deviation about median from the data
$$340,150,210,240,300,310,320$$ is

A
$$50$$

B
$$52.8$$

C
$$55$$

D
$$45$$

Solution

Arrange in increasing order
150,210,240,300,310,320,340 N=number of data = 7
median (M) =300
The mean deviation about median $$= \frac{150+90+60+0+10+20+40}{7 }= 52.857$$
Question 10
1 / -0

Find the mode of:
Height ($$cm$$)
$$37$$
$$38$$
$$39$$
$$40$$
$$41$$
Number of plants $$46$$
$$89$$
$$93$$ $$90$$
$$153$$

A
$$38$$

B
$$39$$

C
$$40$$

D
$$41$$

Solution

mode $$=41$$ (highest frequency $$= 153$$)

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Height ($$cm$$)	$$37$$	$$38$$	$$39$$	$$40$$	$$41$$
Number of plants	$$46$$	$$89$$	$$93$$	$$90$$	$$153$$

Statistics Test - 12

Result

Statistics Test - 12

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Question 1

The order of numbers.

$$14$$

$$18$$

None of these

Solution

Question 2

$$2.23$$

$$2.57$$

$$3.23$$

$$3.57$$

Solution

Question 3

True

False

Neither

None

Solution

Question 4

Th Standard deviation for a given distribution is the square of the variance.

The standard deviation for a given distribution is the square root of the variance.

The standard deviation for a given distribution is equal to the variance.

The standard deviation for a given distribution is half of the variance.

Solution

Question 5

$$2x+7$$

$$x+8$$

$$x+7$$

None of these

Solution

Question 6

Mean and median

Median but no mean

Mean but no median

Mode

Solution

Question 7

$$\cfrac { \bar { X } }{ \sigma } \times 100$$

$$\cfrac { \bar { X } }{ \sigma }$$

$$\cfrac { \sigma } {\bar { X }} \times 100$$

$$\cfrac{ \sigma } { \bar { X }}$$

Solution

Question 8

$$20$$

$$10$$

$$15$$

$$25$$

Solution

Question 9

$$50$$

$$52.8$$

$$55$$

$$45$$

Solution

Question 10

$$38$$

$$39$$

$$40$$

$$41$$

Solution

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