# Free Statistics 01 Practice Test - 9th Grade

### Question 1

Find the median of the following data: 13, 15, 18, 14, 22, 42, 9, 6, 15, 21.

14

15

16

17

#### SOLUTION

Solution :B

Median is the middle observation of the given data, when arranged in either ascending or descending order.

Arranging the observations in ascending order, we get

6, 9, 13 , 14, 15, 15, 18, 21, 22, 42Since, there are even number of observations.

Now median,

= Average of ( n2)^{th }observation and (n2+1)^{th}observation

= 5th term + 6th term2

= 15+152

= 15

Thus, median of the given data is 15.

### Question 2

The mean of 5 observations is 12. If the mean of the first 3 observations is 10, then find the mean of the other two.

10

12

12.5

15

#### SOLUTION

Solution :D

Let, the observations be a, b, c, d, e.

We know that,

Mean = Sum of all observationsNumber of observations

Now,

mean of 5 observations = 12

⇒a+b+c+d+e5=12

⇒a+b+c+d+e=60.....(i)

It is also given that the mean of the first three observations is 10

⇒a+b+c3=10

⇒a+b+c=30...........(ii)

From (i) and (ii) we get

d + e = 30

Hence, the mean of the other two observations i.e. 'd' and 'e' is

=d+e2=15

### Question 3

Bar graphs are usually used to represent 'categorical data' while histogram are usually used for 'continuous data' .

True

False

#### SOLUTION

Solution :A

Bar graphs are usually used to display "categorical data" i.e. data that fits into categories. Histograms, on the other hand, are usually used to present "continuous data",

### Question 4

In a cricket tournament, the total runs scored by 10 batsmen are:-

212, 134, 101, 89, 45, 121, 323, 202, 76, 87

The median of this data is

#### SOLUTION

Solution :To obtain the median of a given set of data, we have to arrange the data in ascending or descending order. After arranging in ascending order, we get

45, 76, 87, 89, 101, 121, 134, 202, 212, 323.

Here, we have even number of observations i.e. n = 10. So, we will obtain the median by taking the mean of the value of 5th and 6th observation i.e. 101+1212=111

### Question 5

A __________ is a pictorial representation of data in which rectangular bars of uniform width are drawn with equal spacing between them, with their widths usually placed on the x-axis and the frequency on the y-axis.

#### SOLUTION

Solution :A

The given description is the one about a bar graph. In a bar graph, rectangular bars of uniform width are drawn with equal spacing between them on one of the coordinate axes, usually the x-axis, to represent the type of variables. The frequency of variable is projected on the other axis i.e. the y-axis.

### Question 6

The following figure shows a histogram and corresponding frequency polygon. The data shows the number of victims suffering from a disease 'X' in various months of 2012.

Identify the correct statement(s) among the following.

#### SOLUTION

Solution :A and C

From the definition, the area under frequency polygon is same as the sum of the areas of all the bars of the histogram provided the class size of all classes is the same. Hence option A is correct.

Also, we can see that the bar of February is not the smallest. Hence, option B is incorrect.

The bar of June is highest, so option C is correct.

Also, the frequency polygon is correctly drawn joining all the class marks and starting and ending at 0 so option D is not correct.

### Question 7

In a bar graph, bars can be of unequal width.

#### SOLUTION

Solution :B

By convention, bars of all categories in a bar graph are drawn with equal width. Hence the above statement is false.

### Question 8

The data below shows the number of times of all outcomes of a dice. Find the frequency of getting a number greater than 2 but less than or equal to 5.

#### SOLUTION

Solution :D

3, 4, and 5 are the numbers greater than 2 but less than or equal to 5

So, frequency of getting 3, 4, and 5 is

= 6 + 4 + 8

= 18

Hence, the frequency of getting a number greater than 2 and less than equal to 5 is 18.

### Question 9

Histogram and bar graph are two names of the same type of graph.

#### SOLUTION

Solution :B

A bar graph is used to represent data that have different categories while histogram is used to represent classes that are continuous by bars which are side-by-side. Thus they both are different.

### Question 10

A histogram can never have gaps between two bars.

#### SOLUTION

Solution :B

A histogram can have a gap between two bars if the intermediate class has 0 frequency.