Statistics Test

Result

Statistics Test - 19

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Weekly Quiz Competition

Question 1
1 / -0

What is the modal class for the following distributions?
Class interval
$$22-33$$
$$33-44$$
$$44-55$$
$$55-66$$
$$66-77$$
$$77-88$$
$$88-99$$
Frequency
$$23$$
$$45$$
$$67$$
$$89$$
$$100$$
$$123$$
$$20$$

A
$$55-66$$

B
$$66-77$$

C
$$77-88$$

D
$$88-99$$

Solution

Modal class is the class which has the highest frequency.

The highest frequency is $$123$$ which is associated with the class $$77-88$$
Therefore, the modal class is $$77-88$$
Question 2
1 / -0

The marks scored by $$20$$ students in exam are given below$$:$$ Find the median.
Marks
$$50$$
$$60$$
$$70$$
$$80$$
Students
$$1$$
$$2$$
$$3$$
$$4$$

A
$$70$$

B
$$80$$

C
$$90$$

D
$$60$$

Solution

Marks
Students(f)
Cumulative frequency(cf)
$$50$$
$$1$$
$$1$$
$$60$$
$$2$$
$$1+2=3$$
$$70$$
$$3$$
$$3+3=6$$
$$80$$
$$4$$
$$6+4=10$$

$$n=\Sigma f=10$$

$$\displaystyle\frac{n}{2}=\frac{10}{2}=5$$

$$\displaystyle\frac{n}{2}=\frac{10}{2}=5$$
Therefore, the corresponding value of marks for $$5$$ is $$70$$.

Question 3

1 / -0

Number of employees	2	5	6	7	8
Daily wedges	500	750	200	400	600

Estimate the mean of the following data

$$5.53$$

$$6.53$$

$$3.45$$

$$6.45$$

Solution

Number of employees $$xi$$	Daily wedges $$fi$$	$$fixi$$
2	500	1000
5	750	3750
6	200	1200
7	400	2800
8	600	4800
	$$\sum fi=2450$$	$$\sum fixi=13550$$

First construct the following table.
Mean using direct method, $$\bar { x } =\dfrac { \sum { { f }_{ i } } { x }_{ i } }{ \sum { { f }_{ i } } } $$
$$\therefore \bar { x } =\dfrac { 13,550 }{ 2,450 } $$
$$\bar { x } =5.53$$
Mean, $$\bar { x } =5.53$$.

Question 4
1 / -0

The following table shows the scores of a group of $$20$$ football players. Identify the modal class.
Scores
$$7-14$$
$$14-21$$
$$21-28$$
$$28-35$$
$$35-42$$
Football players
$$30$$
$$40$$
$$20$$
$$60$$
$$10$$

A
$$28-35$$

B
$$21-28$$

C
$$7-14$$

D
$$35-42$$

Solution

The modal class is the class with the highest frequency. In this case, the highest frequency is $$60,$$ which is the frequency for class $$28-35$$.
Question 5
1 / -0

For the following table identify the modal class:
Length
$$6-12$$
$$12-18$$
$$18-24$$
$$24-30$$
$$30-36$$
$$36-42$$
$$42-48$$
Frequency
$$100$$
$$234$$
$$450$$
$$342$$
$$540$$
$$289$$
$$265$$

A
$$12-18$$

B
$$24-30$$

C
$$30-36$$

D
$$42-48$$

Solution

We know that, a modal class is the class which has the highest frequency.

The highest frequency in the given table is $$540$$, which is associated with the class $$30-36$$

Hence, the modal class is $$30-36$$.
Question 6
1 / -0

The mean of first 10 natural numbers is

A
$$\displaystyle \frac{5}{2}$$

B
$$\displaystyle \frac{11}{2}$$

C
$$\displaystyle \frac{13}{2}$$

D
5

Solution

The first 10 natural numbers are 1,2,3,4,5,6,7,8,9,10
Then mean of first natural numbers =$$\frac{1+2+3+4+5+6+7+8+9+10}{2}=\frac{55}{10}=5.5=\frac{11}{2}$$
Question 7
1 / -0

Consider the data: $$2, 3, 2, 4, 5, 6, 4, 2, 3, 3, 7, 8, 2, 2$$. The frequency of $$2$$ is _____

A
$$4$$

B
$$5$$

C
$$6$$

D
$$3$$

Solution

Number of times $$ 2 $$ occurs in the given data is $$ 5 $$

So, frequency of $$ 2 $$ in given data is $$ 5 $$.
Question 8
1 / -0

The mean of 20 items of a data is 5 and if each item is multiplied by 3 then the mean will be

A
5

B
10

C
15

D
20

Solution

Given the mean of 20 items are 5
Then total of 20 items =$$20\times 3=300$$
Then new mean =$$\frac{300}{20}=15$$
If multiply each item by 3 then total of 20 items =$$100\times 5=100$$
Question 9
1 / -0

Find the median class$$:$$
Marks
$$10-20$$
$$20-30$$
$$30-40$$
$$40-50$$
$$50-60$$
Number of students
$$12$$
$$35$$
$$15$$
$$25$$
$$13$$

A
$$10-20$$

B
$$50-60$$

C
$$30-40$$

D
$$40-50$$
Question 10
1 / -0

Calculate the mode for the following data$$:$$
Distance(km) $$11$$ $$21$$ $$31$$ $$41$$ $$51$$
Number of persons $$4$$ $$6$$ $$10$$ $$20$$ $$18$$

A
$$41$$

B
$$31$$

C
$$21$$

D
$$11$$

Solution

Mode for the discrete series is the variable which has the highest frequency.
From the given distribution table, the highest frequency is $$20$$ which is associated with the variable $$41$$
Therefore, the mode is $$41$$

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Re-Attempt Weekly Quiz Competition

Class interval	$$22-33$$	$$33-44$$	$$44-55$$	$$55-66$$	$$66-77$$	$$77-88$$	$$88-99$$
Frequency	$$23$$	$$45$$	$$67$$	$$89$$	$$100$$	$$123$$	$$20$$

Marks	Students(f)	Cumulative frequency(cf)
$$50$$	$$1$$	$$1$$
$$60$$	$$2$$	$$1+2=3$$
$$70$$	$$3$$	$$3+3=6$$
$$80$$	$$4$$	$$6+4=10$$
	$$n=\Sigma f=10$$ $$\displaystyle\frac{n}{2}=\frac{10}{2}=5$$

Scores	$$7-14$$	$$14-21$$	$$21-28$$	$$28-35$$	$$35-42$$
Football players	$$30$$	$$40$$	$$20$$	$$60$$	$$10$$

Length	$$6-12$$	$$12-18$$	$$18-24$$	$$24-30$$	$$30-36$$	$$36-42$$	$$42-48$$
Frequency	$$100$$	$$234$$	$$450$$	$$342$$	$$540$$	$$289$$	$$265$$

Marks	$$10-20$$	$$20-30$$	$$30-40$$	$$40-50$$	$$50-60$$
Number of students	$$12$$	$$35$$	$$15$$	$$25$$	$$13$$

Distance(km)	$$11$$	$$21$$	$$31$$	$$41$$	$$51$$
Number of persons	$$4$$	$$6$$	$$10$$	$$20$$	$$18$$

Statistics Test - 19

Result

Statistics Test - 19

Score

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Rank

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SHARING IS CARING

Question 1

$$55-66$$

$$66-77$$

$$77-88$$

$$88-99$$

Solution

Question 2

$$70$$

$$80$$

$$90$$

$$60$$

Solution

Question 3

$$5.53$$

$$6.53$$

$$3.45$$

$$6.45$$

Solution

Question 4

$$28-35$$

$$21-28$$

$$7-14$$

$$35-42$$

Solution

Question 5

$$12-18$$

$$24-30$$

$$30-36$$

$$42-48$$

Solution

Question 6

$$\displaystyle \frac{5}{2}$$

$$\displaystyle \frac{11}{2}$$

$$\displaystyle \frac{13}{2}$$

5

Solution

Question 7

$$4$$

$$5$$

$$6$$

$$3$$

Solution

Question 8

5

10

15

20

Solution

Question 9

$$10-20$$

$$50-60$$

$$30-40$$

$$40-50$$

Question 10

$$41$$

$$31$$

$$21$$

$$11$$

Solution

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