Statistics Test

Result

Statistics Test - 54

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Weekly Quiz Competition

Question 1
1 / -0

In a frequency distributions, mode is $$7.88$$, mean is $$8.32$$, then median is

A
$$8.17$$

B
$$7$$

C
$$7.17$$

D
$$8.27$$

Solution

Using the Empirical Formula,
$$\begin{array} { l } { 3 \text { Median = Mode + 2 Mean } } \\ { \Rightarrow \text { Median } = \dfrac { \text { Mode } + 2 \text { Mean } } { 3 } }\end{array}$$

On substituting the values, we get
$$\begin{array} { l } { \Rightarrow \dfrac { 7.88 + 2 ( 8.32 ) } { 3 } }\\{ \Rightarrow \dfrac { 7.88 + 16.64 } { 3 } } \\ { \Rightarrow \dfrac { 24.52 } { 3 } } \\ { \Rightarrow 8.173\approx 8.17 } \end{array}$$
Question 2
1 / -0

The median class of the following distribution is ..............
x 5-10 10-20 20-30 30-40 40-50 50-60
f 4 8 12 16 9 5

A
20-30

B
5-10

C
50-60

D
30-40

Solution

To find the median class:
First add the total number of frequencies.
Here, $$f = 54$$
$$=$$ $$\dfrac{Total \space\ number\space\ of \space\ frequency }{2}$$
$$=$$ $$\dfrac{54 }{2} =27$$
Hence, the value 27 lies in the class interval 30-40 from the cummulative frequency table.
Question 3
1 / -0

Mode of the data $$3,2,3,2,3,5,6,6,5,3,2,5$$ is

A
$$3$$

B
$$2$$

C
$$5$$

D
$$6$$
Question 4
1 / -0

The modal class of the given frequency distribution is
Marks Obtained $$10-20$$ $$20-30$$ $$30-40$$ $$40-50$$
Cumulative Frequency $$7$$ $$35$$ $$27$$ $$34$$

A
$$10-20$$

B
$$30-40$$

C
$$20-30$$

D
$$40-50$$

Solution

The modal class is the class with the highest frequency.

From the table,
Highest frequency $$=35$$

The frequency $$35$$ belongs to class $$20-30.$$

Hence the modal class is $$20-30$$
Question 5
1 / -0

.

A
5

B
4

C
6

D
7
Question 6
1 / -0

The median wage of the worker in the following table is

Wages/Week
(Rs.) no. of workers c.f

50-59 15 15

60-69 40 55

70-79 50 105

80-89 60 165

90-99 45 210

100-109 40 250

110-119 15 265

A
Rs.$$80.08$$

B
Rs.$$82.08$$

C
Rs. $$84.08$$

D
Rs. 81.04$$
Question 7
1 / -0

Mode of the data $$3,2,5,2,3,5,6,6,5,3,5,2,5$$ is

A
$$6$$

B
$$4$$

C
$$3$$

D
$$5$$

Solution

$${\textbf{Step -1: Find the number used maximum times.}}$$
$${\text{Given numbers: 3,2,5,2,3,5,6,6,5,3,5,2,5}} $$

$$ {x_i}:{\text{2 3 5 6}} $$

$$ {f_i}:{\text{3 3 5 2 }} $$

$$\rightarrow {x_i} = {\text{Given numbers}} $$
$$\rightarrow {f_i} = {\text{how many times Given number is written}} $$

$$ {\text{Mode of the data is the maximum times a number is repeated in the given data}}{\text{.}} $$

$${\text{Since 5 is repeated maximum times in the given data, mode is 5.}}$$

$$ {\textbf{Hence, The correct answer is option D}} $$
Question 8
1 / -0

The ages of 40 girls in a class are given below:
Age (in years) 14 15 16 17 18
Number of girls 5 8 15 10 2
Find the mean age.

A
13.9

B
14.9

C
15.9

D
16.9

Solution
Question 9
1 / -0

$$9898, 8998, 9889, 8899, 9988, 8989, 9998$$.
If the numbers above are arranged in an ascending or descending order. Which number will appear in the middle place?

A
$$9889$$

B
$$8998$$

C
$$8899$$

D
$$9898$$

Solution
Question 10
1 / -0

The median and mode respectively of a frequency distribution are $$26$$ and $$29$$. Then its mean is

A
$$27.5$$

B
$$24.5$$

C
$$28.4$$

D
$$25.8$$

Solution

Here we can use direct formula,

$$ 3 \times Median - 2 \times Mean = Mode$$
$$ 3 \times 26 - 2 \times Mean = 29$$
$$ 78 - 29 = 2 \times Mean$$
$$ Mean = \dfrac{49}{2}$$
$$ Mean = 24.5$$

Option B is correct

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Re-Attempt Weekly Quiz Competition

Marks Obtained	$$10-20$$	$$20-30$$	$$30-40$$	$$40-50$$
Cumulative Frequency	$$7$$	$$35$$	$$27$$	$$34$$

Wages/Week (Rs.)	no. of workers	c.f
50-59	15	15
60-69	40	55
70-79	50	105
80-89	60	165
90-99	45	210
100-109	40	250
110-119	15	265

x	5-10	10-20	20-30	30-40	40-50	50-60
f	4	8	12	16	9	5

Age (in years)	14	15	16	17	18
Number of girls	5	8	15	10	2

Statistics Test - 54

Result

Statistics Test - 54

Score

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Rank

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Question 1

$$8.17$$

$$7$$

$$7.17$$

$$8.27$$

Solution

Question 2

20-30

5-10

50-60

30-40

Solution

Question 3

$$3$$

$$2$$

$$5$$

$$6$$

Question 4

$$10-20$$

$$30-40$$

$$20-30$$

$$40-50$$

Solution

Question 5

5

4

6

7

Question 6

Rs.$$80.08$$

Rs.$$82.08$$

Rs. $$84.08$$

Rs. 81.04$$

Question 7

$$6$$

$$4$$

$$3$$

$$5$$

Solution

Question 8

13.9

14.9

15.9

16.9

Solution

Question 9

$$9889$$

$$8998$$

$$8899$$

$$9898$$

Solution

Question 10

$$27.5$$

$$24.5$$

$$28.4$$

$$25.8$$

Solution

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