# Free Statistics 03 Practice Test - 9th Grade

### Question 1

The mean of the following distribution is:

xi10131619fi2576

15.2

15.35

15.55

16

#### SOLUTION

Solution :C

We know that,

Average or mean value of a given number of observations is the sum of all the observations divided by the total number of observations.

⇒Mean=∑xifi∑fi

Now,

∑xifi=20+65+112+114=311

∑fi=20

So,

Mean=∑xifi∑fi=31120=15.55

### Question 2

Find the value of 'p' if the mean of the following data is 17.

xi10p182125fi1015799

12

14

16

18

#### SOLUTION

Solution :B

Average or mean value of a given number of observations is the sum of all the observations divided by the total number of observations.

xi10p182125fi1015799xifi10015p126189225

Mean =∑xifi∑fi

∑xifi = 100 + 15p + 126 + 189 + 225

= 640 + 15p∑fi = 50

given that mean = 17

⇒ 640 + 15p = 50 x 17

⇒ 15p = 210

⇒ p = 14

### Question 3

The size of the interval in a data table depicting the entities contained in it is known as

Class mark

Class height

Class interval

Range

#### SOLUTION

Solution :C

Class interval or class size is basically the size of the interval which depicts the entities contained in it.

### Question 4

The height of 10 students in a class are (in cm):-

135, 143, 132, 149, 150, 143, 158, 124, 143, 152

Find the mode.

#### SOLUTION

Solution :B

We know that,

The mode of a set of observations is the observation that occurs most often.

We arrange the given data in the following way:

124, 132, 135, 143, 143, 143, 149, 150, 152 , 158 .

We see that in the above observation 143 is the height of the maximum number of students.

Hence, the mode of the given data is 143.

### Question 5

State true or false.

To draw a frequency polygon, we have to first draw a histogram.

False

True

#### SOLUTION

Solution :A

We don't need to draw a histogram in order to draw a frequency polygon. We can obtain the class mark corresponding to each class interval, which corresponds to the midpoint of the class interval along the x-axis and the corresponding frequency along the y-axis. The lines joining these points will constitute the frequency polygon.

### Question 6

The difference between the highest and the lowest values in the given data is called the 'range' of the data.

True

False

#### SOLUTION

Solution :A

The difference between the highest and the lowest values in the data is called the 'range' of the data.

For example,

In the following graph, the range of the height of trees

is 90 - 60 = 30 feet.

### Question 7

The following bar graph shows the favourite colours of 20 students of a class.

From the graph, it can be inferred that

#### SOLUTION

Solution :A and C

From the graph, it can be observed that:

Frequency of Blue = 6

Frequency of Orange=5

Frequency of Yellow=3

Frequency of Pink=3

Frequency of Red=2

Frequency of Green=1

Therefore, blue is most favoured colour and orange is second most favoured colour. Thus, options A and C are correct. The least favoured colour is green so option B is incorrect. Also the frequency of green and pink are different. So option D is also incorrect.

### Question 8

The frequency polygon below shows marks obtained by students of a class.

From the graph, it can be said that the maximum number of students have scored marks between ____.

#### SOLUTION

Solution :A

The peak of the frequency polygon corresponds to 60 marks. 60 is the class mark of class 55-65. Hence the class 55-65 has the maximum number of students.

### Question 9

The figure below shows a histogram of heights of cherry trees. Find the correct statement(s) among the options.

#### SOLUTION

Solution :A and C

If we add the frequencies of all the bars, total number of trees=3+3+8+10+5+2=31

The highest bar belongs to the range of 75-80 feet. So, the most common range of height is 75-80 feet.

The shortest bar belongs to the range of 85-90 feet. So, the least common range of height is 85-90 feet.

### Question 10

The table below shows the sale of shirts of various sizes in a week.

Shirt size3839404142Number sold6073899023

The size which is demanded the most is

#### SOLUTION

Solution :The frequencies of different observations are given in the table.

It can be seen that shirts of size 41 have the maximum frequency of 90.

So, the mode is 41 and size 41 is the size most in demand.