Statistics Test

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Statistics Test - 24

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Weekly Quiz Competition

Question 1
1 / -0

The median class of the frequency distribution given below is _______.
Class $$0 - 10$$ $$10 - 20$$ $$20 - 30$$ $$30 - 40$$ $$40 - 50$$
Frequency 7 $$15$$ $$13$$ $$17$$ $$10$$

A
$$40 - 50$$

B
$$30 - 40$$

C
$$20 - 30$$

D
$$10 - 20$$

Solution

$$C.I$$ $$Frequency$$ $$Cumulative\,frequency$$
$$0-10$$ $$7$$ $$7$$
$$10-20$$ $$15$$ $$22$$
$$20-30$$ $$13$$ $$35$$
$$30-40$$ $$17$$ $$52$$
$$40-50$$ $$10$$ $$62$$
$$N=62$$
We have, $$N = 62$$
$$\therefore \quad \displaystyle\frac{N}{2} = 31$$
Cumulative frequency just greater than $$\cfrac N2$$ is $$35$$.
So the corresponding median class is $$20-30$$
Question 2
1 / -0

Size $$6$$ $$7$$ $$8$$ $$9$$ $$10$$
No. of Shoes $$4$$ $$5$$ $$1$$ $$2$$ $$1$$
Find the mode.

A
$$7$$

B
$$8$$

C
$$6$$

D
$$10$$

Solution

Size $$6$$ $$7$$ $$8$$ $$9$$ $$10$$
No. of size $$4$$ $$5$$ $$1$$ $$2$$ $$1$$
Mode is the quantity which is higher in frequency.
Here, $$7$$ occurs for $$5$$ times.
$$\therefore$$ Mode is $$7$$.
Question 3
1 / -0

The mode of the following data 8, 7, 9, 8, 7, 8, 10, 7, 10, 6, 7, 6, 10, 8, 6, 8 is ____

A
6

B
7

C
10

D
8

Solution

Arranging the given number in ascending order,
$$6,6,6,7,7,7,7,8,8,8,8,8,9,10,10,10$$
$$\Rightarrow$$ The number which occurs maximum times is called mode.
$$\Rightarrow$$ So, here we can see number $$8$$ occurs maximum times i.e $$5\,times$$.
$$\therefore$$ $$Mode=8$$
Question 4
1 / -0

Find the modal class
Test Scores Frequency Greater than Cummulative frequency
$$91-100$$ $$9$$ $$20$$
$$81-90$$
$$6$$ $$11$$
$$71-80$$ $$3$$ $$5$$
$$61-70$$ $$0$$ $$2$$
$$51-60$$ $$2$$ $$2$$

A
$$81-90$$

B
$$91-100$$

C
$$61-70$$

D
$$71-80$$

Solution

$$\Rightarrow$$ We know that modal class is a group that has highest frequency.
$$\Rightarrow$$ Here, in given frequency table we can see class interval $$91-100$$ has highest frequency i.e. $$9$$
$$\therefore$$ Modal class $$=91-100$$
Question 5
1 / -0

Median of the following freq. dist.
$$x_i$$ $$3$$ $$6$$ $$10$$ $$12$$ $$7$$ $$15$$
$$f_i$$ $$3$$ $$4$$ $$2$$ $$8$$ $$13$$ $$10$$

A
$$7$$

B
$$10$$

C
$$8.5$$

D
None of these

Solution

$$C.I$$ $$Frequency$$ $$Cumulative\,frequency$$
$$3$$ $$3$$ $$3$$
$$6$$ $$4$$ $$7$$
$$10$$ $$2$$ $$9$$
$$12$$ $$8$$ $$17$$
$$7$$ $$13$$ $$30$$
$$15$$ $$10$$ $$40$$
Here $$N=40$$,
then $$\dfrac{N}{2}=\dfrac{40}{2}=20$$
$$\dfrac{N}{2}+1=\dfrac{42}{2}=21$$
As the corresponding median to $$30$$ which is nearest to $$21$$ is $$7$$, so required result is $$7$$.
Question 6
1 / -0

In a batch of $$13$$ students, $$4$$ have failed. The marks of successful candidates are $$41, 57, 36, 35, 71, 50,$$ and $$40$$. The median marks are

A
$$40$$

B
$$50$$

C
$$38$$

D
cannot be determined

Solution

In question, it is given that their are $$13$$ students in a batch.
Out of $$13$$, $$4$$ students have failed and $$7$$ passed students marks are given.
We have to determine median marks, but we cannot find median marks here, because to find median we have know the marks of $$13$$ students , but in question only $$7$$ students' marks are given.
Question 7
1 / -0

Find the mean of the data given below, if following are the marks obtained by students in a class test in the mathematics subject.
Marks: 10 20 30 40 50 60
Number of student 5 12 32 40 45 48

A
$$44.5$$

B
$$43.846$$

C
$$46.86$$

D
$$44.96$$

Solution

Mean $$=$$ $$ \dfrac{Total\, marks\, obtained \, by \, students}{Total \, students}$$
Mean $$=$$ $$ \dfrac{50+240+960+1600+2250+2880}{5+12+32+40+45+48}$$
Mean $$=$$ $$ \dfrac{7980}{182}$$
Mean $$=$$$$ 43.846 $$
$$ \boxed{\therefore Mean = 43.846}$$
Question 8
1 / -0

Mode of the distribution is:

Marks 4 5 6 7 8
No. of students 3 5 10 6 1

A
$$6$$

B
$$10$$

C
$$8$$

D
$$4$$

Solution

Mode is the class that has the maximum frequency.

Here, we can see that the maximum number of students (10 students) have scored 6 marks.

$$\therefore$$ Mode $$=6$$

Question 9

1 / -0

The value of median of

Income In Rs	1000	1100	1200	1300	1400	1500
No. of persons	14	26	21	18	28	15

$$1300$$

$$1200$$

$$1250$$

$$1150$$

Solution

$$Income$$ $$(in\,Rs.)$$	$$No.\,of\,persons$$	$$c.f$$
$$1000$$	$$14$$	$$14$$
$$1100$$	$$26$$	$$40$$
$$1200$$	$$21$$	$$61$$
$$1300$$	$$18$$	$$79$$
$$1400$$	$$28$$	$$107$$
$$1500$$	$$15$$	$$122$$
	$$N=122$$

$$Median=\dfrac{1}{2}\left[\left(\dfrac{122}{2}\right)^{th}term+\left(\dfrac{122}{2}+1\right)^{th}term\right]$$

$$=\dfrac{1}{2}\left[61^{th}term+62^{th}term\right]$$

$$61^{th}term=1200$$ and $$62^{th}term=1300$$

$$\therefore$$ $$Median=\dfrac{1}{2}[1200+1300]$$

$$\therefore$$ $$Median=1250$$

Question 10
1 / -0

The value of $$p$$, for which the following date
$$3,5,0,7,5,3,5,6,p,7,6,4,9$$ has mode $$5$$ is

A
$$9$$

B
$$7$$

C
$$5$$

D
$$6$$

Solution

We have,

$$3,5,0,7,5,3,5,6,p,7,6,4,9$$

So,

Ascending order

$$0,3,3,4,5,5,5,6,6,7,7,9,p$$

So,

$$ \text{mode}=5 $$

$$ p=5 $$

Hence, this is the answer.

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Class	$$0 - 10$$	$$10 - 20$$	$$20 - 30$$	$$30 - 40$$	$$40 - 50$$
Frequency	7	$$15$$	$$13$$	$$17$$	$$10$$

$$C.I$$	$$Frequency$$	$$Cumulative\,frequency$$
$$0-10$$	$$7$$	$$7$$
$$10-20$$	$$15$$	$$22$$
$$20-30$$	$$13$$	$$35$$
$$30-40$$	$$17$$	$$52$$
$$40-50$$	$$10$$	$$62$$
	$$N=62$$

Size	$$6$$	$$7$$	$$8$$	$$9$$	$$10$$
No. of Shoes	$$4$$	$$5$$	$$1$$	$$2$$	$$1$$

Test Scores	Frequency	Greater than Cummulative frequency
$$91-100$$	$$9$$	$$20$$
$$81-90$$	$$6$$	$$11$$
$$71-80$$	$$3$$	$$5$$
$$61-70$$	$$0$$	$$2$$
$$51-60$$	$$2$$	$$2$$

$$x_i$$	$$3$$	$$6$$	$$10$$	$$12$$	$$7$$	$$15$$
$$f_i$$	$$3$$	$$4$$	$$2$$	$$8$$	$$13$$	$$10$$

Marks:	10	20	30	40	50	60
Number of student	5	12	32	40	45	48

Statistics Test - 24

Result

Statistics Test - 24

Score

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Question 1

$$40 - 50$$

$$30 - 40$$

$$20 - 30$$

$$10 - 20$$

Solution

Question 2

$$7$$

$$8$$

$$6$$

$$10$$

Solution

Question 3

6

7

10

8

Solution

Question 4

$$81-90$$

$$91-100$$

$$61-70$$

$$71-80$$

Solution

Question 5

$$7$$

$$10$$

$$8.5$$

None of these

Solution

Question 6

$$40$$

$$50$$

$$38$$

cannot be determined

Solution

Question 7

$$44.5$$

$$43.846$$

$$46.86$$

$$44.96$$

Solution

Question 8

$$6$$

$$10$$

$$8$$

$$4$$

Solution

Question 9

$$1300$$

$$1200$$

$$1250$$

$$1150$$

Solution

Question 10

$$9$$

$$7$$

$$5$$

$$6$$

Solution

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