Statistics Test

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Statistics Test - 52

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Question 1
1 / -0

For the next three (03) items that follow :
The number of telephone calls received in 245 successive one minute intervals at an exchange is given below in the following frequency distribution.
Number of calls 0 1 2 3 4 5 6 7
Frequency 14 21 25 43 51 40 39 12
What is the mean of the distribution?

A
3.76

B
3.84

C
3.96

D
4.05

Solution

For the given frequency distribution table
$$Mean =\cfrac {\sum {\text{number of calls}\times \text{frequency}}}{ \sum {\text{frequency}}} $$
$$Mean\quad =\cfrac { 0\times 14+1\times21 +2\times25 +3\times43 +4\times51 +5\times40 +6\times39 +7\times12 }{245 } $$
$$\therefore$$ Mean $$=3.76$$
Question 2
1 / -0

For grouped data, formula for arithmetic mean by direct method =

A
sfX / sf

B
sd / N

C
sX / N

D
None of the above

Solution

Arithmetic mean refers to the average amount in a given group of data. There are many ways to calculate arithmetic mean for grouped data like direct method where all the data are multiplied with their respective frequencies and then added up which are then divided by the summation of the frequencies or number of figures in the data in order to ascertain the mean. The formula is sfX/ sf where sfd is the summation of frequency multiplied by X for all figures and sf is the frequency or the number of element in the given data.
Question 3
1 / -0

Find the median from the following data.
Marks $$0-10$$ $$10-30$$ $$30-60$$ $$60-80$$ $$80-90$$
No. of students $$5$$ $$15$$ $$30$$ $$8$$ $$2$$

A
$$10$$

B
$$20$$

C
$$30$$

D
$$40$$

Solution

Since the class intervals are unequal so the question can be solved in following way .
Follow the image. As the median is coming $$ 40 $$ .
Hence option d is correct.
Question 4
1 / -0

Calculate Median salary from the following frequency distribution
X(Rs.in 000) 10- 20 20- 30 30- 40 40- 50 50- 60 60-70
Y(Frequency) 2 3 6 5 2 2

A
38.5

B
36.98

C
34.1

D
39.00

Solution

R.E.F image
Median is where cumulative $$ = 10 $$
Which happens in $$ 30-40 $$ which
far frequency 6. frequency 5 in $$30-40$$
make cumulative 10
Median $$ = 30+\dfrac{(10-5)}{6}\times 5 $$
$$ = 30+4.1 $$
$$ = 34.1 $$
Question 5
1 / -0

For grouped data, Arithmetic mean by Assumed Mean Method =

A
A + sd/N

B
A + sfd/sf

C
sfX/sf

D
None of these

Solution

In assumed mean method, any value can be taken as assumed mean whether it is there in the data or not but it should be centrally located in the data so that to simply the big figures in the data in order to ascertain mean of the given data through easy calculations. For grouped data, the formula for assumed mean is A+ sfd/sf where A is the assumed mean, sfd is the summation of frequency multiplied with X-A for all figures and sf is the summation of frequency or the number of element in the given data.
Question 6
1 / -0

Arithmetic mean for grouped data can be calculated by _________.

A
direct method

B
assumed mean method

C
step deviation method

D
all of the above

Solution

Arithmetic mean refers to the average amount in a given group of data. There are many ways to calculate arithmetic mean like direct method where all the data are added up and then divided by the number of figures in the data in order to ascertain the mean class or assumed mean method and step deviation method, the data of the given class is reduced into smaller units which makes it easy to do calculation and ascertain the mean of the class.
Question 7
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 two fruits are liked by an equal number of students?

A
Apple and Mango

B
Mango and Banana

C
Banana and Orange

D
Banana and Grapes

Solution

Number of students like Apple $$= 9$$
Number of students like Orange $$= 7$$
Number of students like Banana $$= 8$$
Number of students like Grapes $$= 8$$
Number of students like Mango $$= 10$$
So, Banana and Grapes are liked by equal number of students
Question 8
1 / -0

Ages of players in a cricket team are $$25, 26, 25, 27, 28, 30, 31, 27, 33, 27, 29$$.
(i) Find the mean and mode of the data. (ii) Find the minimum number of players to be added to the above team so that mode of the data changes and what must be their ages.

A
(i) Mean $$= 25,$$ Mode $$= 36$$
(ii) $$3$$ players of age $$25$$ years each

B
(i) Mean $$= 23,$$ Mode $$= 32$$
(ii) $$4$$ players of age $$25$$ years each

C
(i) Mean $$= 28,$$ Mode $$= 27$$
(ii) $$2$$ players of age $$25$$ years each

D
(i) Mean $$= 30,$$ Mode $$= 25$$
(ii) $$1$$ players of age $$25$$ years each

Solution

Mean of the data $$=\dfrac{25+26+25+27+28+30+31+27+33+27+29} {11} =28$$
Mode is tha data which is repeated frequently, in this question $$27$$ is repeated three times therefore the mode is $$27$$
As there are $$2$$ player's with age $$25$$ we need to add minimum $$2$$ players with age $$25$$ then the mode changes to $$25$$

Question 9

1 / -0

The following is the distribution of weekly wages of workers in a factory. Calculate the arithmetic mean of the distribution.

Weekly Wages (Rs.)	No. of Workers
$$240-269$$	$$7$$
$$270-299$$	$$19$$
$$300-329$$	$$27$$
$$330-359$$	$$15$$
$$360-389$$	$$12$$
$$390-419$$	$$12$$
$$420-449$$	$$8$$

$$352.3$$

$$344.5$$

$$226.7$$

$$336.7$$

Solution

Mean refers to the average amount in a given group of data. In this measure of central tendency, all the data are added up and then divided by the number of figures in the data in order to ascertain the mean.

Weekly Wages (Rs.)	No. of Workers(f)	Mid points (x)	fx
240−270	7	255	1785
270−300	19	285	5415
300−330	27	315	8505
330−360	15	345	5175
360−390	12	375	4500
390−420	12	405	4860
420−450	8	435	3480

Mean= summation of fx / summation of f

= 33720 / 100

= 337.20

Question 10
1 / -0

If the mode of five observations, in order, $$0, 2, 3, m, 5$$ is $$3$$ then $$m =$$ _______.

A
$$5$$

B
$$2$$

C
$$3$$

D
$$0$$

Solution

If the mode of five observation, in order, $$0, 2, 3, m, 5$$ is $$3$$,
then $$m = 3$$.

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Marks	$$0-10$$	$$10-30$$	$$30-60$$	$$60-80$$	$$80-90$$
No. of students	$$5$$	$$15$$	$$30$$	$$8$$	$$2$$

X(Rs.in 000)	10- 20	20- 30	30- 40	40- 50	50- 60	60-70
Y(Frequency)	2	3	6	5	2	2

Number of calls	0	1	2	3	4	5	6	7
Frequency	14	21	25	43	51	40	39	12

Statistics Test - 52

Result

Statistics Test - 52

Score

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Rank

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SHARING IS CARING

Question 1

3.76

3.84

3.96

4.05

Solution

Question 2

sfX / sf

sd / N

sX / N

None of the above

Solution

Question 3

$$10$$

$$20$$

$$30$$

$$40$$

Solution

Question 4

38.5

36.98

34.1

39.00

Solution

Question 5

A + sd/N

A + sfd/sf

sfX/sf

None of these

Solution

Question 6

direct method

assumed mean method

step deviation method

all of the above

Solution

Question 7

Apple and Mango

Mango and Banana

Banana and Orange

Banana and Grapes

Solution

Question 8

(i) Mean $$= 25,$$ Mode $$= 36$$(ii) $$3$$ players of age $$25$$ years each

(i) Mean $$= 23,$$ Mode $$= 32$$(ii) $$4$$ players of age $$25$$ years each

(i) Mean $$= 28,$$ Mode $$= 27$$(ii) $$2$$ players of age $$25$$ years each

(i) Mean $$= 30,$$ Mode $$= 25$$(ii) $$1$$ players of age $$25$$ years each

Solution

Question 9

$$352.3$$

$$344.5$$

$$226.7$$

$$336.7$$

Solution

Question 10

$$5$$

$$2$$

$$3$$

$$0$$

Solution

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(i) Mean $$= 25,$$ Mode $$= 36$$
(ii) $$3$$ players of age $$25$$ years each

(i) Mean $$= 23,$$ Mode $$= 32$$
(ii) $$4$$ players of age $$25$$ years each

(i) Mean $$= 28,$$ Mode $$= 27$$
(ii) $$2$$ players of age $$25$$ years each

(i) Mean $$= 30,$$ Mode $$= 25$$
(ii) $$1$$ players of age $$25$$ years each