Statistics Test

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Statistics Test - 50

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Weekly Quiz Competition

Question 1

1 / -0

What is the median salary of an employee? If the frequency table represents the number of employees and their salaries.

Salary	$$1000$$	$$500$$	$$1500$$	$$2000$$	$$3500$$
Frequency	$$2$$	$$1$$	$$5$$	$$7$$	$$2$$

$$1000$$

$$1500$$

$$500$$

$$2000$$

Solution

Salary	Frequency	position
$$1000$$	$$2$$	$$2$$
$$500$$	$$1$$	$$3$$
$$1500$$	$$5$$	$$8$$
$$2000$$	$$7$$	$$15$$
$$3500$$	$$2$$	$$17$$

Sum of frequency $$=2+1+5+7+2\\ =17(odd)$$

So Median is at $$\quad \quad \left( \cfrac { n+1 }{ 2 } \right) \\ =\quad \left( \cfrac { 17+1 }{ 2 } \right) =9$$

$$9th$$ position comes after $$8th$$ but before $$15th$$ position

$$Median=2000$$

Question 2
1 / -0

The table shows the weekly wages for the number of workers doing their work. Find the median class for the following data.

A
$$80-85$$

B
$$70-75$$

C
$$65-70$$

D
$$50-55$$
Question 3
1 / -0

If Mode $$=$$ Median $$= 10$$. Find mean.

A
3

B
5

C
10

D
9

Solution

Applying the relation between mean, median and mode formula,
$$\text{Mean} = \dfrac{(3\times \text{Median} )-\text{Mode}}{2}$$
$$=\dfrac{(3\times 10)- 10}{2}$$
$$=\dfrac{20}{2}$$
$$\boxed{\text{Mean} = 10}$$
Question 4
1 / -0

Find the median where mean and mode are given as $$10$$ and $$7$$.

A
10

B
9

C
7

D
8

Solution

Applying the relation between mean, median and mode formula,
Mode $$= 3$$ Median $$-2$$ Mean
Therefore, Median $$=$$ $$\dfrac{Mode + 2 Mean}{3}$$
$$=$$ $$\dfrac{7 + 2 \times 10}{3}$$
$$=$$ $$\dfrac{27}{3}$$
Median $$= 9$$
Question 5
1 / -0

Given mean $$= 12$$, mode $$= 3$$. Find median.

A
$$12$$

B
$$14$$

C
$$9$$

D
$$6$$

Solution

Given mean $$= 12$$, mode $$= 3$$
Applying the relation between mean, median and mode formula,
Mode $$= 3$$ Median $$-2$$ Mean
Therefore, Median $$=$$ $$\dfrac{Mode + 2 Mean}{3}$$
$$=$$ $$\dfrac{3 + 2 \times 12}{3}$$
$$=$$ $$\dfrac{27}{3}$$
$$=9$$
Hence, median is $$9$$
Question 6
1 / -0

The following table shows the number of coffees made for each hour that the coffee shop was open over $$2$$ days. Find the median class.

A
$$0-3$$

B
$$12-15$$

C
$$16-19$$

D
$$8-11$$

Solution

Number of cappuccinos Frequency Cumulative Frequency
$$0-3$$ $$2$$ $$2$$
$$4-7$$ $$3$$ $$5$$
$$8-11$$ $$8$$ $$13$$
$$12-15$$ $$3$$ $$16$$
$$16-19$$ $$2$$ $$18$$
Total $$18$$
The sum of total frequency among each class is equal to,
$$2+3+8+3+2=18$$
$$\Rightarrow N=18$$

And,
$$\dfrac N2=9$$

We can conclude that $$ 9$$ lies in the class interval $$8-11$$ from the cumulative frequency column. Hence, the median class is $$8-11.$$
Question 7
1 / -0

Calculate the mean where mode and median are given as $$12$$ and $$5$$ respectively.

A
$$0.5$$

B
$$1.5$$

C
$$2.5$$

D
$$3.5$$

Solution

Applying the relation between mean, median and mode formula,
Mean $$=$$ $$\dfrac{(3\times Median) -Mode}{2}$$
$$=$$ $$\dfrac{(3\times 5)-12}{2}$$
$$=$$ $$\dfrac{3}{2}$$
Mean $$= 1.5$$
Question 8
1 / -0

The total number of goals scored in each of $$43$$ soccer matches in a tournament is shown in the following table. Find the average number of goals scored per match, to the nearest $$0.1$$ goal.
Total number of goals in a match Number of matches with this total
0 4
1 10
2 5
3 9
4 7
5 5
6 1
7 2

A
$$1.0$$

B
$$2.8$$

C
$$3.0$$

D
$$6.1$$

E
$$17.14$$

Solution

Average number of goals $$=$$ $$\dfrac{\text{Total no. of goals}}{\text{total no. of matches}}$$

$$\Rightarrow \dfrac{4\times 0+10\times 1+5\times 2+9\times 3+7\times 4+5\times 5+6\times 1+7\times 2}{43}$$

$$\Rightarrow \dfrac{+10+10+27+28+25+6+14}{43}=\dfrac{120}{43}=2.79=2.8$$
Question 9
1 / -0

The mode of a data exceeds its mean by $$12$$. By how much does its mode exceed the median?

A
$$8$$

B
$$12$$

C
$$0$$

D
$$10$$

Solution

We know that,
$$3 $$Median $$=$$ Mode $$+$$ $$2$$Mean

Let,
Median $$=M$$
Mode $$=m$$
Mean $$=\overline x$$

Given: $$m=\overline x+12$$

Now,
$$3M=m+2\overline x$$
$$\Rightarrow 3M=\overline x +12+2\bar x$$
$$\Rightarrow 3M=3\overline x+12$$
$$\Rightarrow M=\overline x+4$$
$$\Rightarrow M=m-12+4$$
$$\Rightarrow M+8=m$$

So, mode exceeds median by $$8$$.
Question 10
1 / -0

The mean and median of the data are respectively $$20$$ and $$22$$.
The value of mode is:

A
$$20$$

B
$$26$$

C
$$22$$

D
$$21$$

Solution

$$\mbox {Mode = 3 Median - 2 Mean}$$
$$=3 (22) - 2(20)$$
$$=66-40$$
$$=26$$

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Re-Attempt Weekly Quiz Competition

Number of cappuccinos	Frequency	Cumulative Frequency
$$0-3$$	$$2$$	$$2$$
$$4-7$$	$$3$$	$$5$$
$$8-11$$	$$8$$	$$13$$
$$12-15$$	$$3$$	$$16$$
$$16-19$$	$$2$$	$$18$$
Total	$$18$$

Total number of goals in a match	Number of matches with this total
0	4
1	10
2	5
3	9
4	7
5	5
6	1
7	2

Statistics Test - 50

Result

Statistics Test - 50

Score

-

Rank

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SHARING IS CARING

Question 1

$$1000$$

$$1500$$

$$500$$

$$2000$$

Solution

Question 2

$$80-85$$

$$70-75$$

$$65-70$$

$$50-55$$

Question 3

3

5

10

9

Solution

Question 4

10

9

7

8

Solution

Question 5

$$12$$

$$14$$

$$9$$

$$6$$

Solution

Question 6

$$0-3$$

$$12-15$$

$$16-19$$

$$8-11$$

Solution

Question 7

$$0.5$$

$$1.5$$

$$2.5$$

$$3.5$$

Solution

Question 8

$$1.0$$

$$2.8$$

$$3.0$$

$$6.1$$

$$17.14$$

Solution

Question 9

$$8$$

$$12$$

$$0$$

$$10$$

Solution

Question 10

$$20$$

$$26$$

$$22$$

$$21$$

Solution

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