# Free Statistics 02 Practice Test - 9th Grade

### Question 1

Which of the following is/are a measure of central tendency?

Frequency

Median

Mean

Class Limit

#### SOLUTION

Solution :B and C

Mean, median and mode are used as measures of central tendency. Mean is the average of all the observations, mode is the observation having maximum frequency and median is the value which divides the data into two equal halves.

### Question 2

What is the median of the following data: 1, 4, 7, 3, 9, 5, 3, 2, 7, 5.

4

4.5

5

7

#### SOLUTION

Solution :B

For finding the median, the data should be arranged in ascending or descending order first.

Arranging the data in ascending order ,we get :

1, 2, 3, 3, 4, 5, 5, 7, 7, 9.

There are even number of observations.

Hence the median is the mean value of (n2)th and [(n2)+1]th term.

Here the 102thterm= 5th term = 4

[(n2)+1]th term. = 6th term = 5

i.e. (4+52)=4.5

Hence, median of the given data =4.5

### Question 3

Find the range of the following data: 26, 21, 33, 17, 14, 15, 27.

13

15

17

19

#### SOLUTION

Solution :D

The difference between the highest and lowest values in the data is called the 'range' of the data. So, here the maximum value is 33 and the minimum is 14. So the difference between them i.e. 19 is the range of the given data.

### Question 4

The mode of the given data 7, 9, 11, 13, 9 13, 9, 9, 7, 8 is

#### SOLUTION

Solution :Mode is that value of the observation which occurs most frequently i.e. an observation with maximum frequency is called mode. In the above set of observations, '9' occurs most frequently and so it is the mode of the given data.

### Question 5

The mean of 15 observations is 8. If the mean of the first eight observations is 7 and that of the last eight observations is 10, then the value of the 8th observation is _____.

16

15

#### SOLUTION

Solution :A

We know that,

Mean = Sum of all observationsNumber of observations

Sum of values of all the observations

=Mean×Number of observation

=15×8

=120

So, sum of the first eight observations

=Mean×Number of observation

=7×8

=56

Sum of the last eight observations

=Mean×Number of observation

=10×8

=80

Hence, value of the 8thobservation

=(80+56)−120

=16

### Question 6

Modes of transport of 1700 students of NIT Warangal is shown in the graph below.

Which of the following options are correct?

#### SOLUTION

Solution :A and B

We can observe from the graph:

Number of students using car = 250

Number of students using bike = 425

Number of students using bus = 350

Number of students using metro = 450

Number of students using cycle = 225

So, option A is correct. Also, cycle has the least frequency. So option B is also correct.

The frequency of metro is higher than the frequency of bike. So, option C is incorrect.

Also, D is incorrect as car doesn't have the highest frequency.

### Question 7

The graph below shows the ages of presidents of a country at the time of inauguration or start of their tenure.

Find the correct option(s) among the following.

#### SOLUTION

Solution :B

On summing up all the frequencies, we get 4+11+14+9+4+2=44. Hence the total number of presidents is 44 and option A is incorrect. The graph starts from 39 but the corresponding frequency is 0. Hence, the age of 44 is the youngest age of president. Thus, B is correct and C is incorrect. The last point on the graph having non-zero frequency is 69. 74 has zero frequency and hence option D is incorrect.

### Question 8

The graph below shows the number of people of different age groups staying in a hotel. Find the correct statement(s) among the options.

Total number of people in 0-20 age group is 10

Total number of people in 0-20 age group is 5

Maximum number of people are from age group of 21-30 years

Total number of people staying in the hotel is 35

#### SOLUTION

Solution :A and C

The number of people in a class is proportional to area.

Therefore, the class of 0-20 is twice the size of other classes.

So, total frequency of 0-20 class is 5×2=10Hence option A is correct and B is incorrect.

The class of 21-30 age group has the highest frequency.

Hence option C is correct.

On summing up all the frequencies, it can be seen that D is incorrect

### Question 9

The mean of the following distribution is

xi10131619fi2576

15.55

15.35

14.3

16

#### SOLUTION

Solution :A

Mean of ungrouped frequency distribution is given by

¯x=∑ni=1fixi∑ni=1fi

=(10×2+13×5+16×7+19×6)(2+5+7+6)

=31120

Therefore, the mean of the data is 15.55.

### Question 10

The heights (in cm) of students of a class is tabulated below.

HeightNumber of students150−1544155−1593160−1642165−1691170−1742175−1792180−1844185−1892Total20

Identify the correct option (s).

The class distribution is discontinuous

Number of students having height in range of 160-174 cm is 5

The data can not be changed into continuous class interval form

The range of data is 39

#### SOLUTION

Solution :A, B, and D

In the given table, the upper limit of a class does not coincide with the lower limit of the succeeding class, so the class intervals are not continuous and option A is correct.

Also the number of students in the range of 160 cm -174 cm = 2+1+2 = 5. Hence, option B is correct.

Also, any data having discontinuous class intervals can be converted into one with continuous class intervals. Hence, C is incorrect.

Range of data = Total width of data = 189-150 = 39.