Statistics Test

Result

Statistics Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

Given median $$= 99.6$$ and mean $$= 101.2$$, then the mode is 96.4
If true then enter $$1$$ and if false then enter $$0$$

A
$$0$$

B
$$1$$

C
Can't determine

D
None of these

Solution

Given, Median = $$99.6$$ and Mean = $$101.2$$
$$Mode = 3 Median - 2 Mean$$
$$Mode = 3 \times 99.6 - 2 \times 101.2$$
$$Mode = 96.4$$
Question 2
1 / -0

Variable $$4$$ $$8$$ $$9$$ $$10$$ $$11$$ $$12$$ $$13$$
Frequency $$3$$ $$4$$ $$5$$ $$8$$ $$4$$ $$3$$ $$2$$
Mode of the distribution

A
$$8$$

B
$$9$$

C
$$10$$

D
None of these

Solution

We know mode of a distribution is the term corresponding to maximum frequency.
Thus in the given distribution $$8$$ is the maximum frequency and corresponding mode is $$10$$.
Question 3
1 / -0

Calculate the median for the following data.
Marks (out of 60.) $$32$$ $$27$$ $$26$$ $$24$$ $$23$$ $$21$$
Number of students $$6$$ $$4$$ $$7$$ $$9$$ $$16$$ $$2$$

A
$$22$$

B
$$23$$

C
$$24$$

D
$$25$$

Solution

Total number of students $$= 6 + 4 + 7 + 9 + 16 + 2 = 44$$

Since, the number of students is even, the median will be mean of $${(\cfrac{n}{2})}^{th}$$ and $${(\cfrac{n+2}{2})}^{th}$$ number

Median = Mean of $$(\cfrac{44}{2})^{th}$$ and $$(\cfrac{44+2}{2})^{th}$$

Here, $$22^{nd}$$ and $$23^{rd}$$ number is $$24$$ Kg if arranged in ascending order.

Hence, median = $$\cfrac{24 + 24}{2}= 24$$ kg
Question 4
1 / -0

The median for the following frequency distribution is:
$$x:$$ 1 2 3 4 5 6 7 8 9
$$f:$$ 8 10 11 16 20 25 15 9 6

A
$$6$$

B
$$5$$

C
$$7$$

D
$$4$$

Solution

here,
$$\Sigma f =120$$
$$N=120 \Rightarrow even$$
$$\dfrac N2=\dfrac {120} {2}=60$$
In cumulative frequency we select $$65$$ as it is closer to $$60$$.
Corresponding $$x $$ value is $$5$$
hence option $$B$$ is correct.
Question 5
1 / -0

Determine the mode of the following data.
Marks 10 16 12 19 13 20 11 14
Number of Students 3 3 4 2 6 1 5 2

A
$$12$$

B
$$13$$

C
$$14$$

D
$$20$$

Solution

maximum number of students got $$ 13$$ marks. Hence, $$13$$ is the mode.
Question 6
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 $$= 153$$)
Question 7
1 / -0

The mode of the following discrete series is:
$$x_i$$ 1 3 5 6 12 15
$$f_i$$ 5 7 3 8 6 5

A
$$3$$

B
$$12$$

C
$$8$$

D
$$6$$

Solution

Mode is that data which has highest frequency
We observe that the value $$6$$ has maximum frequency. So mode $$= 6$$.
Question 8
1 / -0

Find the mode for the following data :
Term
18
22
26
30
34
38
Frequency
3
5
10
2
8
2

A
$$22$$

B
$$30$$

C
$$34$$

D
None of these

Solution

Mode= $$26$$ (highest frequency =$$10$$ )
Question 9
1 / -0

While computing mean of grouped data, we assume that the frequencies are:

A
evenly distributed over all the class

B
centred at the classmarks of the class

C
centred at the upper limits of the class

D
centred at the lower limits of the class

Solution

While computing mean of grouped data, we assume that the frequencies are centred at the class marks of the class.
Hence, option B is correct.
Question 10
1 / -0

The modal class for the following frequency distribution is
Marks $$0-10$$ $$10-20$$ $$20-40$$ $$40-50$$ $$50-60$$ $$60-70$$ $$70-90$$ $$90-100$$
Number of students $$4$$ $$6$$ $$14$$ $$16$$ $$14$$ $$8$$ $$14$$ $$5$$

A
$$20-40$$

B
$$40-50$$

C
$$50-60$$

D
$$70-90$$

Solution

Since $$40-50$$ is the class of maximum frequency, so, it is the modal class.

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Re-Attempt Weekly Quiz Competition

Variable	$$4$$	$$8$$	$$9$$	$$10$$	$$11$$	$$12$$	$$13$$
Frequency	$$3$$	$$4$$	$$5$$	$$8$$	$$4$$	$$3$$	$$2$$

Marks (out of 60.)	$$32$$	$$27$$	$$26$$	$$24$$	$$23$$	$$21$$
Number of students	$$6$$	$$4$$	$$7$$	$$9$$	$$16$$	$$2$$

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

Marks	$$0-10$$	$$10-20$$	$$20-40$$	$$40-50$$	$$50-60$$	$$60-70$$	$$70-90$$	$$90-100$$
Number of students	$$4$$	$$6$$	$$14$$	$$16$$	$$14$$	$$8$$	$$14$$	$$5$$

$$x:$$	1	2	3	4	5	6	7	8	9
$$f:$$	8	10	11	16	20	25	15	9	6

$$x_i$$	1	3	5	6	12	15
$$f_i$$	5	7	3	8	6	5

Term	18	22	26	30	34	38
Frequency	3	5	10	2	8	2

Statistics Test - 16

Result

Statistics Test - 16

Score

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Rank

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Question 1

$$0$$

$$1$$

Can't determine

None of these

Solution

Question 2

$$8$$

$$9$$

$$10$$

None of these

Solution

Question 3

$$22$$

$$23$$

$$24$$

$$25$$

Solution

Question 4

$$6$$

$$5$$

$$7$$

$$4$$

Solution

Question 5

$$12$$

$$13$$

$$14$$

$$20$$

Solution

Question 6

$$38$$

$$39$$

$$40$$

$$41$$

Solution

Question 7

$$3$$

$$12$$

$$8$$

$$6$$

Solution

Question 8

$$22$$

$$30$$

$$34$$

None of these

Solution

Question 9

evenly distributed over all the class

centred at the classmarks of the class

centred at the upper limits of the class

centred at the lower limits of the class

Solution

Question 10

$$20-40$$

$$40-50$$

$$50-60$$

$$70-90$$

Solution

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