Statistics Test

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Statistics Test - 55

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following has the same mean and mode?

A
$$6,2,5,4,3,4,1$$

B
$$4,2,2,1,3,2,3$$

C
$$2,3,7,3,8,3,2$$

D
$$4,3,4,3,4,6,4$$

Solution

(a) The given data is, $$6,2,5,4,3,4,1$$
$$\Rightarrow\ Mean=\dfrac{1+2+3+4+4+5+6}{7}$$
$$=\dfrac{25}{7}$$
$$=3.57$$

$$Mode = 4$$ because it occurs two times.
Therefore, mean is not equal to mode.

(b) The given data is, $$4,2,2,1,3,2,3$$
$$\Rightarrow Mean=\dfrac{1+2+2+2+3+3+4}{7}$$
$$=\dfrac{17}{7}$$
$$=2.42$$
$$Mode = 2$$ because it occurs two times
Therefore, mean is not equal to mode.

(c) The given data is,, $$2,3,7,3,8,3,2$$
$$\Rightarrow\ Mean=\dfrac{2+2+3+3+7+8}{7}$$
$$=\dfrac{28}{7}$$
$$=4$$
$$Mode = 3$$because it occurs three times
Therefore, mean is not equal to mode

(d) The given data is,, 4,3,4,3,4,6,4
$$\Rightarrow, Mean=\dfrac{3+3+4+4+4+4+6}{7}$$
$$= \dfrac{28}{7}$$
$$=4$$
$$Mode = 4$$ because it occurs 4 times.
Therefore, mean is equal to mode.

Hence, the correct option is (D).
Question 2
1 / -0

The number of trees in different parks of a city is $$ 33,38,48,33,34,34,33$$ and $$ 24$$. The mode of this data is

A
$$24$$

B
$$34$$

C
$$33$$

D
$$48$$

Solution

The given data in ascending order is $$24,33,33,33,34,34,38$$ and $$48$$,
The mode of data is $$33$$ because the frequent of occurrence of $$33$$ is highest.
Question 3
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 fruit is liked
by most of the students?

A
O

B
G

C
M

D
A

Solution

The number of $$A$$ appearing in the list is $$9$$

The number of $$B$$ appearing in the list is $$8$$

The number of $$G$$ appearing in the list is $$7$$

The number of $$M$$ appearing in the list are $$10$$

The number of $$O$$ appearing in the list are $$8$$

So, $$M$$ appeared the most, and $$M$$ stands for Mango.

So, Mango $$M$$ is the fruit that is liked by most of the students.
Question 4
1 / -0

The median of the data : $$ 3,4,5,6,7,3,4$$ is

A
5

B
3

C
4

D
6

Solution

Rearranging the given data into ascending order, we get
$$3,3,4,4,5,6,7,$$
Total number of observations $$=7$$ which is odd
Hence, the $$4^{th}$$ term is the median.
$$\therefore$$ Median $$=4$$

Hence, option (C) is the correct answer.

Question 5

1 / -0

For the following distribution:

Marks	Number of students
Below $$10$$	$$3$$
Below $$20$$	$$12$$
Below $$30$$	$$27$$
Below $$40$$	$$57$$
Below $$50$$	$$75$$
Below $$60$$	$$80$$

The modal class is

$$10-20$$

$$20-30$$

$$30-40$$

$$50-60$$

Solution

Marks	Number of students	Cumulative Frequency
Below $$10$$	$$3$$	$$3$$
$$10-20$$	$$12-3=9$$	$$12$$
$$20-30$$	$$27-12=15$$	$$27$$
$$30-40$$	$$57-27=30$$	$$57$$
$$40-50$$	$$75-57=18$$	$$75$$
$$50-60$$	$$80-75=5$$	$$80$$

Here, we see that the highest frequency is $$30,$$ which lies in the interval $$30-40$$, and the class with the highest frequency is known as modal class.
Hence, option $$C$$ is correct.

Question 6
1 / -0

What is the mode of $$19, 19, 15, 20, 25, 15, 20, 15$$?

A
$$15$$

B
$$20$$

C
$$19$$

D
$$25$$

Solution

Since observation $$15$$ is occuring the most in the data:
$$19,19,15,20,25,15,20,15$$

So, the mode of the given data is $$15$$
.
Hence, the correct alternative answer is (A).
Question 7
1 / -0

The class whose cumulative frequency is greater than (and nearest to) $$ \dfrac{N}{2} $$, is called

A
average class

B
Modal class

C
Mean class

D
Median class

Solution

The class whose cumulative frequency is greater than (and nearest to) $$ \dfrac{N}{2} $$, is called Median class
Question 8
1 / -0

Number of students in a school according to their age are as follows :
Age (in yrs.) No. of students
8 15
9 25
10 40
11 36
12 41
13 37
14 20
15 13
16 5
17 3
Their mode is

A
41

B
12

C
3

D
17

Solution

From above table it is clear that frequency 41 is maximum and its mavimum and its corresponding age group of 12 . So its mode will be 12.
Thus (B) is correct.
Question 9
1 / -0

The mode of the data$$4, 3, 4, 5, 4, 2, 4, 1$$ will be :

A
$$1$$

B
$$2$$

C
$$5$$

D
$$4$$

Solution

Arranging the numbers with the same values together, we get
$$1,2,3,4,4,4,4,5$$
Mode of this data is $$4$$ because it occurs more frequently than other observations.

Question 10

1 / -0

Read the following news report and answer on the basis of the same: For an examination, 60 students of a school appeared. Marks obtained by the 12 students were 25 each. The number of students who scored 20 and 5 each was three more than the students who scored 25. Also, 8 students who scored 10 marks each. The students who scored 15 marks each were half the students who scored 10 each and remaining students had scored 30 each. Answer the following question:
The series so obtained from the given paragraph is:

Individual series

Discrete series

Continuous series

No series can be obtained

Solution

Marks	Number of students
5	15 = 12 + 3
10	8
15	4
20	15 = 12 + 3
25	12
30	6
Total	60

Hence, correct answer is option B.

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Re-Attempt Weekly Quiz Competition

Age (in yrs.)	No. of students
8	15
9	25
10	40
11	36
12	41
13	37
14	20
15	13
16	5
17	3

Statistics Test - 55

Result

Statistics Test - 55

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Question 1

$$6,2,5,4,3,4,1$$

$$4,2,2,1,3,2,3$$

$$2,3,7,3,8,3,2$$

$$4,3,4,3,4,6,4$$

Solution

Question 2

$$24$$

$$34$$

$$33$$

$$48$$

Solution

Question 3

O

G

M

A

Solution

Question 4

5

3

4

6

Solution

Question 5

$$10-20$$

$$20-30$$

$$30-40$$

$$50-60$$

Solution

Question 6

$$15$$

$$20$$

$$19$$

$$25$$

Solution

Question 7

average class

Modal class

Mean class

Median class

Solution

Question 8

41

12

3

17

Solution

Question 9

$$1$$

$$2$$

$$5$$

$$4$$

Solution

Question 10

Individual series

Discrete series

Continuous series

No series can be obtained

Solution

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