Descriptive Statistics Test 26

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Descriptive Statistics Test 26

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Weekly Quiz Competition

Question 1
1 / -0

Find the quartile deviation of $$4, 6, 9, 12, 18, 20, 23, 27, 34, 48$$ and $$53$$

A
$$12.5$$

B
$$13$$

C
$$12$$

D
$$11.5$$

Solution

Given series of numbers is already arranged in ascending order.
Thus median is the centre value $$ = 20 $$
First Quartile $$ {Q}_{1} $$ will be the mid value of the observations to the left of $$ 20 $$ which is $$ 9 $$.
Similarly, Third Quartile $$ {Q}_{3} $$ will be the mid value of the observations to the right of $$ 20 $$ which is $$ 34 $$.
And Quartile deviation will be $$ \dfrac {{Q}_{3} - {Q}_{1}}{2} = \dfrac {34-9}{2} = \dfrac {25}{2} = 12.5 $$.
Question 2
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The line plot below shows how students scored on last week's maths test.
How many students scored 95 or higher on the test?

A
5 students

B
7 students

C
12 students

D
16 students

Solution

It is given that $$1$$ star $$= 1$$ student.
Number of students who scored $$95$$ marks or more than $$95$$ = number of students who scored $$95$$ marks + number students who scored $$100$$ marks
Students who scored $$95$$ marks $$=7$$
Students who scored $$100$$ marks $$=5$$
Total students $$=7+5=12$$
Question 3
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The standard deviation of $$3x + 5, 3x + 7, 3x + 9, 3x + 11, 3x + 13, 3x + 15$$ and $$3x + 17$$ is ...........

A
$$2$$

B
$$3$$

C
$$4$$

D
$$1$$

Solution

Mean of the given numbers is $$\bar x =\dfrac{(3x+5)+(3x+7)+(3x+9)+(3x+11)+(3x+13)+(3x+15)+(3x+17)}{7}=\dfrac{21x+77}{7}=3x+11$$

total number of values $$n=7$$

Standard deviation is given by $$SD=\sqrt{\dfrac{\sum_{i=1}^n (x_i-\bar x)^2}{n}}$$

$$\implies SD=\sqrt{\dfrac{(5-11)^2+(7-11)^2+(9-11)^2+(11-11)^2+(13-11)^2+(15-11)^2+(17-11)^2}{7}}$$

$$\implies SD=\sqrt{\dfrac{36+16+4+0+4+16+36}{7}}$$

$$\implies SD=\sqrt{\dfrac{112}{7}}$$

$$\implies SD=\sqrt{16}=4$$

Therefore the standard deviation for the given values is $$4$$
Question 4
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Directions For Questions

The pictograph given below shows how many persons travelled from city A to city B by bus on each of the days of a certain week Study the pictograph carefully and answer the questions from 6 to 8

...view full instructions

What is the total number of persons who made the journey during the week?
(Assume that one represents 10 persons)

A
200

B
400

C
600

D
900

Solution

Given that one symbol represents 10 persons and the total number of symbols in picture =$$9+4+6+4+8+6+2= 40$$
Total number of persons who made the journey during the week = $$ \displaystyle 10 \times 40 = 400 $$
Question 5
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If the lower and upper quartiles of a data are 4 and
12 then the quartile deviation is_____

A
2

B
4

C
6

D
8

Solution

Lower Quartile $$ {Q}_{1} = 4 $$

Upper Quartile $$ {Q}_{3} = 12 $$

And Quartile deviation will be $$ \frac {{Q}_{3} - {Q}_{1}}{2} = \frac {12-4}{2} = \frac {8}{2} = 4 $$
Question 6
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If the lower and upper quartiles of a data are $$4$$ and $$12$$, then the quartile deviation is ____

A
$$2$$

B
$$4$$

C
$$6$$

D
$$8$$

Solution

Quartile deviation is the half of the inter quartile deviation.
Inter quartile deviation is the difference between upper quartile and lower quartile.

Given that, lower quartile is $$4$$ and upper quartile is $$12$$

Therefore, Quartile deivation is $$\dfrac{\text{upper quartile - lower quartile}}{2}$$

$$\implies \text{quartile deviation} =\dfrac{12-4}2=\dfrac 82 =4$$
Question 7
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Read the graph and answer the following: The horizontal line in the graph is called:

A
X-axis

B
Y-axis

C
line

D
none

Solution

Horizontal line represents X-axis in the graph.
So, the horizontal line in the graph is called X-axis.
Question 8
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Read the graph and answer the following: The vertical line in the graph is called:

A
Y-axis

B
X-axis

C
ray

D
none of the above

Solution

In the graph, vertical line always represents Y-axis.
So, the vertical line in the graph is called Y-axis.
Question 9
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Directions For Questions

Following table and pictograph show the number of school teachers in some towns
Name of Town Number of school
Teacher
Hyderabad 4200
Delhi 2400
Chennai 3000

...view full instructions

How many school teachers does simile represent?

A
$$500$$

B
$$600$$

C
$$700$$

D
$$800$$

Solution

In the table Hyderabad town has $$4200$$ teachers which represented by $$7$$ similes in the pictograph.

Therefore, one simile represent $$\dfrac{4200}{7} = 600$$ school teachers.
Question 10
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Directions For Questions

Given table and pictograph which show the number of school teachers in some cities.
Name of city No. of School Teachers
Hyderabad 4200
Delhi 2400
Chennai 3000

...view full instructions

How many school teachers does each smile represent?

A
500

B
400

C
700

D
none of these

Solution

In the table Hyderabad town has $$4200$$ teachers which represented by $$7$$ similes in the pictograph.

Therefore, one simile represent $$\dfrac{4200}{7} = 600$$ school teachers.