Statistics Test

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Statistics Test - 45

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Weekly Quiz Competition

Question 1

1 / -0

Find the median height for the following data$$:$$

Height(cm)	$$50-100$$	$$100-150$$	$$150-200$$	$$200-250$$
Number of students	$$2$$	$$5$$	$$6$$	$$7$$

$$123.33$$ cm

$$133.33$$ cm

$$143.33$$ cm

$$153.33$$ cm

Solution

Height(cm)	Number of students(f)	Cumulative frequency(cf)
$$50-100$$	$$2$$	$$2$$
$$100-150$$	$$5$$	$$2+5=7$$
$$150-200$$	$$6$$	$$7+6=13$$
$$200-250$$	$$7$$	$$13+7=20$$
	$$n=\Sigma f=20$$ $$\displaystyle\frac{n}{2}=\frac{20}{2}=10$$

Median $$=l+\left(\displaystyle\frac{\displaystyle\frac{n}{2}-cf}{f}\right)\times h$$
$$n=\Sigma f=$$ Total number of frequency $$=20$$
$$\displaystyle\frac{n}{2}=\frac{20}{2}=10$$
So, the median class is $$150-200$$
L$$=$$ Lower limit of the median class $$=150$$
cf$$=$$ Cumulative frequency of the class preceding the median class $$=13$$
f$$=$$ Frequency of the median class $$=6$$
h$$=$$ class width$$=50$$
Therefore, Median $$=l+\left(\displaystyle\frac{\displaystyle\frac{n}{2}-cf}{f}\right)\times h$$
$$=150+\left(\displaystyle\frac{\displaystyle\frac{20}{2}-13}{6}\right)\times 50$$
$$=150+\left(\displaystyle\frac{10-13}{6}\right)\times 50$$
$$=150-16.66$$
$$=133.33$$
Hence, the median height is $$133.33$$cm

Question 2

1 / -0

Find the median of the following distribution$$:$$

Marks	$$10-20$$	$$20-30$$	$$30-40$$	$$40-50$$	$$50-60$$
Number of students	$$12$$	$$35$$	$$45$$	$$25$$	$$13$$

$$23$$

$$22$$

$$24$$

$$21$$

Solution

Marks	Students(f)	Cumulative frequency(cf)
$$10-20$$	$$12$$	$$12$$
$$20-30$$	$$35$$	$$12+35=47$$
$$30-40$$	$$45$$	$$47+45=92$$
$$40-50$$	$$25$$	$$92+25=117$$
$$50-60$$	$$13$$	$$117+13=130$$
	$$n=\Sigma f=130$$ $$\displaystyle\frac{n}{2}=\frac{130}{2}=65$$

Median $$=l+\left(\displaystyle\frac{\displaystyle\frac{n}{2}-cf}{f}\right)\times h$$
$$n=\Sigma f=$$ Total number of frequency $$=130$$
$$\displaystyle\frac{n}{2}=\frac{20}{2}=65$$
So, the median class is $$30-40$$
L$$=$$ Lower limit of the median class $$=30$$
cf$$=$$ Cumulative frequency of the class preceding the median class $$=92$$
f$$=$$ Frequency of the median class $$=45$$
h$$=$$ class width$$=10$$
Therefore, Median $$=l+\left(\displaystyle\frac{\displaystyle\frac{n}{2}-cf}{f}\right)\times h$$
$$=30+\left(\displaystyle\frac{\displaystyle\frac{130}{2}-92}{45}\right)\times 10$$
$$=30+\left(\displaystyle\frac{65-92}{45}\right)\times 10$$
$$=30-6$$
$$=24$$
Hence, the median is $$24$$.

Question 3
1 / -0

Find the median class for the following data given below$$:$$
Number of cars
$$0-10$$
$$10-20$$
$$20-30$$
$$30-40$$
$$40-50$$
$$50-60$$
$$60-70$$
$$70-80$$
Frequency
$$7$$
$$9$$
$$13$$
$$21$$
$$12$$
$$15$$
$$4$$
$$12$$

A
$$30-40$$

B
$$40-50$$

C
$$50-60$$

D
$$60-70$$

Solution

To find the median class$$:$$
First add the total number of frequencies.
Here, $$f = 93$$
$$= \dfrac{(Total\quad number\quad of \quad frequency)}{2}$$
$$= (93)/2 = 46.5$$
Hence, the value 46.5 lies in the class interval 30-40 from the cummulative frequency table.
Question 4
1 / -0

From the following data identify the median class$$:$$
$$X_i$$
$$0-5$$
$$5-10$$
$$10-15$$
$$15-20$$
$$f_i$$
$$2$$
$$4$$
$$2$$
$$2$$

A
$$0-5$$

B
$$5-10$$

C
$$10-15$$

D
$$15-20$$

Solution

To find the median class$$:$$
First add the total number of frequencies.
Here, $$f = 10$$
$$= \dfrac{(Total\quad number\quad of \quad frequency )}{2}$$
So, Median class $$= \dfrac{(10 )}{2} = 5$$
Hence, the value 5 lies in the class interval 10-15 from the cummulative frequency table.
Question 5
1 / -0

A student noted that the number of cars passing through a particular spot on the road for $$200$$ periods each of $$10$$ minutes and summarized in a table given below. Find the mode of the data.
Number of cars
$$0-10$$
$$10-20$$
$$20-30$$
$$30-40$$
$$40-50$$
$$50-60$$
$$60-70$$
$$70-80$$
Frequency
$$7$$
$$9$$
$$13$$
$$21$$
$$12$$
$$15$$
$$4$$
$$12$$

A
$$34.71$$

B
$$36.47$$

C
$$42.63$$

D
$$47.26$$

Solution

Here, the maximum frequency is $$21,$$ and the class corresponding to that frequency is $$30-40$$ .
We have to apply the formula $$Mode=l+\left(\displaystyle\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$$
Where $$l$$ is the lower class limit of the modal class $$= 30$$
$$f_1$$ is the frequency of the modal class $$= 21$$
$$f_0$$ is the frequency of the class preceding the modal class in the frequency table $$= 13$$
$$f_2$$ is the frequency of the class succeeding the modal class in the frequency table $$= 12$$
$$h$$ is the class size of the modal class $$= 10$$

Thus, $$Mode$$$$=30+\dfrac{21-13}{2×21-13-12}×10$$
$$=30+\dfrac{8}{17}×10$$
$$=30+4.71$$
$$=34.71$$

Hence, the mode is $$34.71$$ .
Question 6
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What is the median class for the following data given below?
Time(min)
$$10-20$$
$$20-30$$
$$30-40$$
$$40-50$$
Running race(km)
$$10$$
$$20$$
$$3$$
$$4$$

A
$$10-20$$

B
$$20-30$$

C
$$30-40$$

D
$$40-50$$

Solution

To find the median class:
First add the total number of frequencies.
Here, $$f = 37$$
Formula to obtain the median class $$= \dfrac {(Total \quad number \quad of \quad frequency + 1)}{2}$$
So, Median class $$= \dfrac{(37 + 1)}{2} = 19$$
Hence, the median class of $$19$$ lies between the intervals $$10-20.$$
Question 7
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Identify the median class.
Farm size
$$20-50$$
$$50-80$$
$$80-110$$
$$110-140$$
$$140-170$$
Rooms
$$4$$
$$8$$
$$12$$
$$16$$
$$20$$

A
$$20-50$$

B
$$50-80$$

C
$$80-110$$

D
$$110-140$$

Solution

To find the median class:
First add the total number of frequencies.
Here, $$f = 60$$
$$=\dfrac{ (Total \quad number\quad of \quad frequency )}{2}$$
$$= (60 )/2 = 30$$
Hence, the value 30 lies in the class interval 110-140 from the cummulative frequency table.

Question 8

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Identify the median class from the given data$$:$$

Fruits	$$30-40$$	$$40-50$$	$$50-60$$	$$60-70$$	$$70-80$$	$$80-90$$	$$90-100$$
Boxes	$$1$$	$$3$$	$$6$$	$$7$$	$$8$$	$$5$$	$$7$$

$$70-80$$

$$50-60$$

$$40-50$$

$$80-90$$

Solution

$$Class$$	$$Frequency$$	$$c.f$$
$$30-40$$	$$1$$	$$1$$
$$40-50$$	$$3$$	$$4$$
$$50-60$$	$$6$$	$$10$$
$$60-70$$	$$7$$	$$17$$
$$70-80$$	$$8$$	$$25$$
$$80-90$$	$$5$$	$$30$$
$$90-100$$	$$7$$	$$37$$
	$$N=37$$

$$\Rightarrow$$ Here total frequency, $$N=37$$

so, $$\dfrac{N}{2}=\dfrac{37}{2}=18.5$$, which lies between cumulative frequencies $$17$$ and $$25$$.

And the corresponding class is $$70-80$$ .

Hence, the median class is $$70-80$$ .

Question 9
1 / -0

From the following data identify the median class$$:$$
Time(hour)
$$5-15$$
$$15-25$$
$$25-35$$
$$35-45$$
$$45-55$$
$$55-65$$
Frequency
$$20$$
$$28$$
$$17$$
$$12$$
$$6$$
$$17$$

A
$$15-25$$

B
$$25-35$$

C
$$35-45$$

D
$$45-55$$

Solution

To find the median class$$:$$
First add the total number of frequencies.
Here, $$f = 100$$
$$=\dfrac{(Total\quad number\quad of \quad frequency )}{2}$$
$$= \dfrac{(100 )}{2} = 50$$
Hence, value 50 lies in the class interval $$25-35$$ from a cumulative frequency table.
Question 10
1 / -0

Identify the median class.
X
$$5-9$$
$$9-13$$
$$13-17$$
$$17-21$$
F
$$3$$
$$8$$
$$9$$
$$4$$

A
$$5-9$$

B
$$9-13$$

C
$$13-17$$

D
$$17-21$$

Solution

To find the median class$$:$$
First add the total number of frequencies.
Here, $$f = 24$$
$$= \dfrac{(Total \quad number \quad of \quad frequency )}{2}$$
$$=\dfrac{ (24)}{2} = 12$$
Hence, the value 12 lies in the class interval 13-17 from the cummulative frequency table.

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Re-Attempt Weekly Quiz Competition

Number of cars	$$0-10$$	$$10-20$$	$$20-30$$	$$30-40$$	$$40-50$$	$$50-60$$	$$60-70$$	$$70-80$$
Frequency	$$7$$	$$9$$	$$13$$	$$21$$	$$12$$	$$15$$	$$4$$	$$12$$

$$X_i$$	$$0-5$$	$$5-10$$	$$10-15$$	$$15-20$$
$$f_i$$	$$2$$	$$4$$	$$2$$	$$2$$

Time(min)	$$10-20$$	$$20-30$$	$$30-40$$	$$40-50$$
Running race(km)	$$10$$	$$20$$	$$3$$	$$4$$

Farm size	$$20-50$$	$$50-80$$	$$80-110$$	$$110-140$$	$$140-170$$
Rooms	$$4$$	$$8$$	$$12$$	$$16$$	$$20$$

Time(hour)	$$5-15$$	$$15-25$$	$$25-35$$	$$35-45$$	$$45-55$$	$$55-65$$
Frequency	$$20$$	$$28$$	$$17$$	$$12$$	$$6$$	$$17$$

X	$$5-9$$	$$9-13$$	$$13-17$$	$$17-21$$
F	$$3$$	$$8$$	$$9$$	$$4$$

Statistics Test - 45

Result

Statistics Test - 45

Score

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Rank

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SHARING IS CARING

Question 1

$$123.33$$ cm

$$133.33$$ cm

$$143.33$$ cm

$$153.33$$ cm

Solution

Question 2

$$23$$

$$22$$

$$24$$

$$21$$

Solution

Question 3

$$30-40$$

$$40-50$$

$$50-60$$

$$60-70$$

Solution

Question 4

$$0-5$$

$$5-10$$

$$10-15$$

$$15-20$$

Solution

Question 5

$$34.71$$

$$36.47$$

$$42.63$$

$$47.26$$

Solution

Question 6

$$10-20$$

$$20-30$$

$$30-40$$

$$40-50$$

Solution

Question 7

$$20-50$$

$$50-80$$

$$80-110$$

$$110-140$$

Solution

Question 8

$$70-80$$

$$50-60$$

$$40-50$$

$$80-90$$

Solution

Question 9

$$15-25$$

$$25-35$$

$$35-45$$

$$45-55$$

Solution

Question 10

$$5-9$$

$$9-13$$

$$13-17$$

$$17-21$$

Solution

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