Statistics Test

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Statistics Test - 47

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Weekly Quiz Competition

Question 1
1 / -0

Find the mode for the following data$$:$$
X $$2$$ $$3$$ $$5$$ $$10$$ $$11$$
Frequency $$0$$ $$1$$ $$3$$ $$2$$ $$5$$

A
$$3$$

B
$$5$$

C
$$10$$

D
$$11$$

Solution

Mode for the discrete series is the variable which has the highest frequency.
From the given distribution table, the highest frequency is $$5$$ which is associated with the variable $$11$$
Therefore, the mode is $$11$$
Question 2
1 / -0

Find the mode for the following data$$:$$
$$X_i$$ $$20$$ $$30$$ $$40$$ $$50$$ $$60$$ $$70$$ $$80$$ $$90$$
Frequency $$0$$ $$1$$ $$1$$ $$0.5$$ $$0.75$$ $$0.15$$ $$1$$ $$0$$

A
$$30$$

B
$$40$$

C
$$80$$

D
All the above

Solution

Mode for the discrete series is the variable which has the highest frequency.
From the given distribution table, the highest frequency is $$1$$ which is associated with the variables $$30,40$$ and $$80$$
Therefore, the mode is $$30,40$$ and $$80$$

Question 3

1 / -0

Find the median of the following data.

Maths marks	$$60-65$$	$$65-70$$	$$70-75$$	$$75-80$$	$$80-85$$	$$85-90$$	$$90-95$$
No. of students	$$8$$	$$12$$	$$14$$	$$8$$	$$5$$	$$6$$	$$4$$

$$73.05$$

$$72.54$$

$$63.54$$

$$91.09$$

Solution

Converting the given data into a frequency distribution table

Maths marks	No. of students (f)	c.f.
$$60-65$$	$$ 8$$	$$8 $$
$$ 65-70 $$	$$12$$	$$20$$
$$ 70-75$$	$$14$$	$$34$$
$$75-80$$	$$8$$	$$42$$
$$80-85$$	$$ 5$$	$$47$$
$$85-90$$	$$ 6$$	$$53$$
$$90-95$$	$$4$$	$$57$$
	$$\text{N}=\Sigma \text{f} = 57$$

Here, $$\text{N=57}$$

$$\implies \cfrac{N}{2} = \cfrac{57}{2}=28.5$$

$$\implies$$In the above table $$70-75$$ is the median class and the respective c.f. is $$20$$ (cumulative frequency of the class preceding the median class)

Acc to ques,

$$l = 70$$ (lower limit of median class)

c.f. $$=20$$

$$h = l_2-l_1 = 5$$ (width of class interval of median class)

$$f = 14$$ (frequency of median class)

$$\text{Median} = l+ \cfrac{\cfrac{N}{2} - c.f.}{f} \times h = 70 + \cfrac{28.5-20}{14} \times 5 $$

$$\implies$$ Median $$= 73.05$$

Question 4
1 / -0

Find the median of the following data.
Group $$6-8$$ $$8-10$$ $$10-12$$ $$12-14$$ $$14-16$$ $$16-18$$ $$18-20$$
Frequencies $$12$$ $$20$$ $$16$$ $$15$$ $$17$$ $$8$$ $$12$$

A
$$12.58$$

B
$$12.266$$

C
$$11.345$$

D
$$14.87$$

Solution

Converting the given data into frequency distribution table:

Group Frequency
$$(f)$$ $$cf$$
6-8 12 12
8-10 20 32
10-12 16 48
12-14 15 63
14-16 17 80
16-18 8 88
18-20 12 100
$$\Sigma f = 100$$
Here, $$N=100$$
Hence the median class $$= \cfrac{N}{2} = \cfrac{100}{2}=50$$
In the above table $$12-14$$ is the median class and the respective $$cf$$ is $$20$$ (nearest to the value of $$50$$)
According to the question:
$$l_1 = 12$$ (lower limit of median class)
$$\text{cf}=48$$ (cf= cumulative frequency preceding the median class)
$$i = l_2-l_1 = 2$$ (width of class interval of median class)
$$f = 15$$ (frequency of median class)
$$\text{Median} = l_1 + \cfrac{\cfrac{N}{2} - C}{f} \times i = 12 + \cfrac{50-48}{15} \times 2 $$
$$\text{Median}= 12.266$$
Hence, option (B) is the correct answer.

Question 5

1 / -0

The following frequency distribution is classified according to the number of mangoes in different branches. Calculate the median of the mangoes in each branch

Number of Mangoes	$$0-10$$	$$10-20$$	$$20-30$$	$$30-40$$	$$40-50$$	$$50-60$$	$$60-70$$
Branch	$$5$$	$$4$$	$$6$$	$$2$$	$$4$$	$$3$$	$$1$$

$$37.68$$
37.68

$$36.87$$
36.87

$$38.76$$
38.76

$$25.83$$
37.86

Solution

Number of mangoes	Branch (f)	cf
0-10	5	5
10-20	4	9
20-30	6	15
30-40	2	17
40-50	4	21
50-60	3	22
60-70	1	25

So $$n=25$$

So, $$\cfrac { n }{ 2 } =\cfrac { 25 }{ 2 } =12.5$$

$$12.5$$ is nearest to $$15(cumulative frequency)$$

Observation lies in the class $$20-30$$

$$l=20,cf=9,f=6,h=5$$

$$Median==l+\left( \cfrac { \cfrac { n }{ 2 } -cf }{ f } \right) \times h\\ =20+\left( \cfrac { 12.5-9 }{ 6 } \right) \times 10\\ =20+\cfrac { 3.5 }{ 6 } \times 10\\ =20+\cfrac { 35 }{ 6 } =20+5.83\\ =\quad 25.83\quad Ans$$

Question 6
1 / -0

Identify the mode for the following data$$:$$
Class $$33$$ $$44$$ $$55$$ $$66$$ $$77$$ $$88$$ $$99$$
Frequency $$12$$ $$3$$ $$90$$ $$100$$ $$100$$ $$10$$ $$6$$

A
$$66$$

B
$$77$$

C
Both A and B

D
$$55$$

Solution

Mode for the discrete series is the variable which has the highest frequency.
From the given distribution table, the highest frequency is $$100$$ which is associated with the variables $$66$$ and $$77$$
Therefore, the mode is $$66$$ and $$77$$
Question 7
1 / -0

What is the mode?
Fruits $$90$$ $$80$$ $$70$$ $$60$$
Boxes $$1$$ $$12$$ $$6$$ $$7$$

A
$$80$$

B
$$70$$

C
$$60$$

D
$$90$$

Solution

Mode for the discrete series is the variable which has the highest frequency.
From the given distribution table, the highest frequency is $$12$$ which is associated with the variable $$80$$
Therefore, the mode is $$80$$
Question 8
1 / -0

Find the mode for the following set of scores.
Scores $$2$$ $$4$$ $$6$$ $$8$$ $$10$$ $$12$$ $$14$$ $$16$$
Frequency $$4$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$5$$ $$4$$

A
$$10$$

B
$$8$$

C
$$12$$

D
All the above

Solution

Mode for the discrete series is the variable which has the highest frequency.
From the given distribution table, the highest frequency is $$6$$ which is associated with the variable $$12$$
Therefore, the mode is $$12$$
Question 9
1 / -0

Identify the mode for the following data$$:$$
Height(cm) $$12$$ $$34$$ $$56$$ $$67$$ $$10$$ $$30$$
Swimmers $$1$$ $$2$$ $$6$$ $$5$$ $$4$$ $$4$$

A
$$34$$

B
$$56$$

C
$$67$$

D
$$10$$

Solution

Mode for the discrete series is the variable which has the highest frequency.
From the given distribution table, the highest frequency is $$6$$ which is associated with the variable $$56$$
Therefore, the mode is $$56$$
Question 10
1 / -0

Identify the mode for the following data$$:$$
Number $$0$$ $$3$$ $$6$$ $$9$$ $$12$$ $$15$$ $$18$$
Frequency $$4$$ $$8$$ $$9$$ $$7$$ $$10$$ $$3$$ $$10$$

A
$$18$$

B
$$12$$

C
Both A and B

D
$$6$$

Solution

Mode for the discrete series is the variable which has the highest frequency.
From the given distribution table, the highest frequency is $$10$$ which is associated with the variables $$12$$ and $$18$$
Therefore, the mode is $$12$$ and $$18$$

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$$X_i$$	$$20$$	$$30$$	$$40$$	$$50$$	$$60$$	$$70$$	$$80$$	$$90$$
Frequency	$$0$$	$$1$$	$$1$$	$$0.5$$	$$0.75$$	$$0.15$$	$$1$$	$$0$$

Group	$$6-8$$	$$8-10$$	$$10-12$$	$$12-14$$	$$14-16$$	$$16-18$$	$$18-20$$
Frequencies	$$12$$	$$20$$	$$16$$	$$15$$	$$17$$	$$8$$	$$12$$

Group	Frequency $$(f)$$	$$cf$$
6-8	12	12
8-10	20	32
10-12	16	48
12-14	15	63
14-16	17	80
16-18	8	88
18-20	12	100
	$$\Sigma f = 100$$

Class	$$33$$	$$44$$	$$55$$	$$66$$	$$77$$	$$88$$	$$99$$
Frequency	$$12$$	$$3$$	$$90$$	$$100$$	$$100$$	$$10$$	$$6$$

Scores	$$2$$	$$4$$	$$6$$	$$8$$	$$10$$	$$12$$	$$14$$	$$16$$
Frequency	$$4$$	$$2$$	$$3$$	$$4$$	$$5$$	$$6$$	$$5$$	$$4$$

Height(cm)	$$12$$	$$34$$	$$56$$	$$67$$	$$10$$	$$30$$
Swimmers	$$1$$	$$2$$	$$6$$	$$5$$	$$4$$	$$4$$

Number	$$0$$	$$3$$	$$6$$	$$9$$	$$12$$	$$15$$	$$18$$
Frequency	$$4$$	$$8$$	$$9$$	$$7$$	$$10$$	$$3$$	$$10$$

Statistics Test - 47

Result

Statistics Test - 47

Score

-

Rank

-

SHARING IS CARING

Question 1

$$3$$

$$5$$

$$10$$

$$11$$

Solution

Question 2

$$30$$

$$40$$

$$80$$

All the above

Solution

Question 3

$$73.05$$

$$72.54$$

$$63.54$$

$$91.09$$

Solution

Question 4

$$12.58$$

$$12.266$$

$$11.345$$

$$14.87$$

Solution

Question 5

$$37.68$$37.68

$$36.87$$36.87

$$38.76$$38.76

$$25.83$$37.86

Solution

Question 6

$$66$$

$$77$$

Both A and B

$$55$$

Solution

Question 7

$$80$$

$$70$$

$$60$$

$$90$$

Solution

Question 8

$$10$$

$$8$$

$$12$$

All the above

Solution

Question 9

$$34$$

$$56$$

$$67$$

$$10$$

Solution

Question 10

$$18$$

$$12$$

Both A and B

$$6$$

Solution

User

Question Analysis

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$$37.68$$
37.68

$$36.87$$
36.87

$$38.76$$
38.76

$$25.83$$
37.86