Statistics Test

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Statistics Test - 6

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Weekly Quiz Competition

Question 1
1 / -0

Let m be the mid-point and I be the upper class limit of a class in a continuous frequency distribution. The lower class limit of the class is

A
2I − m

B
m − I

C
2m − I

D
2m + I

Solution

Let the lower limit = k
Mid point = m
Upper limit = l
Mid point = (upper limit + lower limit)/2
m = (k + l)/2
2m = k + l
k = 2m - l
Therefore, lower limit = 2m - l
Question 2
1 / -0

A grouped frequency table with class intervals of equal size using 3-5 (5 included in this interval) as one of the class intervals is constructed for the following data. The frequency of the class 3-5 is

1 4 7 2 0 3 9 2 3 7 6 3 5

2 5 5 6 2 3 5 1 0 4 6 4 6

A
8

B
11

C
3

D
5

Solution

count all the numbers in the frequency table between 3 to 5.
Frequency of the numbers from 3 to 5 is 11.
Question 3
1 / -0

The given cumulative frequency distribution shows the class intervals and their corresponding cumulative frequencies. Then the frequency of class interval 20-30 is

Class 10-20 20-30 30-40

Cumulative frequency 5 14 25

A
9

B
11

C
20

D
5

Solution

A cumulative frequency distribution is the sum of the class and all classes below it in a frequency distribution.
Subtract the previous cumulative frequency (c.f) from the cumulative frequency of the current class.
So frequency of the class interval 20-30 is 14 - 5 = 9

Question 4

1 / -0

‘Less than’ cumulative frequency table for a given data is as follows. Then, the frequency of class interval 20-30 is

Marks	Less than 10	Less than 20	Less than 300	Less than 40
Cumulative frequency	3	17	37	92

20

55

34

14 Solution

A cumulative frequency distribution is the sum of the class and all classes below it in a frequency distribution.
Less than 30 has the class interval 20-30. Frequency of this class interval will be corresponding to

Marks	Cumulative frequency	Class	Frequency
Less than 10	3	1-10	3
Less than 20	17	10-20	14
Less than 30	37	20-30	20
Less than 40	92	30-40	55

37 - 17 = 20

Question 5

1 / -0

‘More than’ cumulative frequency table for a given data is as follows: Then, the frequency of the class interval 70-80 is

Marks	More than 89	More than 79	More than 69	More than 59
Cumulative frequency	8	18	30	65

35

10

22

12 Solution

A cumulative frequency distribution is the sum of the class and all classes below it in a frequency distribution.

Subtract cumulative frequency of class more than 70 from the next cummulative Frequency of class more than 69.

30 − 18 = 12

Question 6
1 / -0

In a bar graph, 0.25 cm length of a bar represents 100 people. Then, the length of bar which represents 2000 people is

A
4 cm

B
3.5 cm

C
5 cm

D
4.5 cm

Solution

Use unitary method

0.25 cm - 100 people

so 1 cm - 400 people

so for 2000 people:

2000/400 = 5cm
Question 7
1 / -0

In a bar graph if 1 cm represents 30 km, then the length of bar needed to represent 75 km is

A
2 cm

B
3 cm

C
3.5 cm

D
2.5 cm

Solution

1 cm - 30 km

so for 75 km

75/30 = 2.5cm
Question 8
1 / -0

In a bar graph, the widths of bars

A
are proportional to the corresponding frequencies

B
are proportional to the corresponding heights

C
have no significance

D
are proportional to the space between two consecutive bars

Solution

Bar graph is a pictorial representaion of data variables(x-axis versus it value on y-axis( height of the bar.

hence width of bar has no significance in bar graph.
Question 9
1 / -0

In a histogram, which of the following is proportional to the frequency of the corresponding class?

A
Width of the rectangle

B
Perimeter of the rectangle

C
Length of the rectangle

D
Area of the rectangle

Solution

In, Histogram each rectangle is drawn, where width equivalent to class interval and height euivalent to frequency of the class.

Since class interval are same across the distribution table, area of the rectangle is corresponding to frequency or height of the rectangle
Question 10
1 / -0

For drawing a frequency polygon of a continuous frequency distribution, we plot the points whose ordinates are the frequency of respective classes and abscissa are respectively

A
class marks of the classes

B
upper limits of preceeding classes

C
upper limits of the classes

D
lower limits of the classes

Solution

Frequency polygon is the line graph plotted with class marks on x-axis & frequency of the class on y-axis.

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Statistics Test - 6

Result

Statistics Test - 6

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SHARING IS CARING

Question 1

2I − m

m − I

2m − I

2m + I

Solution

Question 2

8

11

3

5

Solution

Question 3

9

11

20

5

Solution

Question 4

20

55

34

14

Solution

Question 5

35

10

22

12

Solution

Question 6

4 cm

3.5 cm

5 cm

4.5 cm

Solution

Question 7

2 cm

3 cm

3.5 cm

2.5 cm

Solution

Question 8

are proportional to the corresponding frequencies

are proportional to the corresponding heights

have no significance

are proportional to the space between two consecutive bars

Solution

Question 9

Width of the rectangle

Perimeter of the rectangle

Length of the rectangle

Area of the rectangle

Solution

Question 10

class marks of the classes

upper limits of preceeding classes

upper limits of the classes

lower limits of the classes

Solution

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