Statistics(9th Grade > Mathematics ) Questions and answers for exam Preparation

9th Grade > Mathematics

STATISTICS MCQs

Total Questions : 53 | Page 1 of 6 pages

Question 1. Histogram and bar graph are two names of the same type of graph.

True
False
22
18

Discuss Question

Answer: Option B. -> False
:
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 2. 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

Discuss Question

Answer: Option C. -> Class interval
:
C
Class interval or class size is basically the size of the interval which depicts the entities contained in it.

Question 3. Find the value of 'p' if the mean of the following data is 17.

\begin{matrix} x_{i} & 10 & p & 18 & 21 & 25 f_{i} & 10 & 15 & 7 & 9 & 9 \end{matrix}

Discuss Question

Answer: Option B. -> 14
:
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.

\begin{matrix} x_{i} & 10 & p & 18 & 21 & 25 f_{i} & 10 & 15 & 7 & 9 & 9 x_{i} f_{i} & 100 & 15 p & 126 & 189 & 225 \end{matrix}

Mean

= \frac{\sum x_{i} f_{i}}{\sum f_{i}}

\sum x_{i}

f_{i}

= 100 + 15p + 126 + 189 + 225
= 640 + 15p

\sum f_{i}

= 50
given that mean = 17

\Rightarrow

640 + 15p = 50 x 17

\Rightarrow

15p = 210

\Rightarrow

p = 14

Question 4. 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.

Bar Graph
Histogram
Frequency Polygon
Pie Chart

Discuss Question

Answer: Option A. -> Bar Graph
:
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 5. Bar graphs are usually used to represent 'categorical data' while histogram are usually used for 'continuous data' .

True
False
12.5
15

Discuss Question

Answer: Option A. -> True
:
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 6. Find the median of the following data: 13, 15, 18, 14, 22, 42, 9, 6, 15, 21.

Discuss Question

Answer: Option B. -> 15
:
B
Median is the middle observation of the given data, when arranged in either ascending or descending order.
Arrangingthe observations in ascending order, we get
6, 9, 13 , 14, 15, 15, 18, 21, 22, 42
Since, there are even number of observations.
Now median,
= Average of (

\frac{n}{2}

)^thobservation and

(\frac{n}{2} + 1)

^thobservation
=

\frac{5^{t h} t e r m + 6^{t h} t e r m}{2}

\frac{15 + 15}{2}

= 15
Thus, median of the given data is 15.

Question 7. 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.

Discuss Question

Answer: Option D. -> 18
:
D
3, 4, and 5 are thenumbers greater than 2 but less than or equal to 5
So, frequency of getting 3,4, and5 is
= 6 + 4 + 8
= 18
Hence,the frequency of getting a number greater than 2 and less than equal to 5 is 18.

Question 8. 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

Discuss Question

Answer: Option D. -> 15
:
D
Let, the observations be a, b, c, d, e.
We know that,
Mean =

\frac{S u m o f a l l o b s e r v a t i o n s}{N u m b e r o f o b s e r v a t i o n s}

Now,
mean of 5 observations = 12

\Rightarrow \frac{a + b + c + d + e}{5} = 12

\Rightarrow a + b + c + d + e = 60

.....(i)
It is also given that the mean of the first three observations is 10

\Rightarrow \frac{a + b + c}{3} = 10

\Rightarrow 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

= \frac{d + e}{2} = 15

Question 9. 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
___.

Discuss Question

:
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 themedian bytaking the mean of the value of

5^{t h}

and

6^{t h}

observation i.e.

\frac{101 + 121}{2} = 111

Question 10. In a bar graph, bars can be of unequal width.

True
False
June has the highest frequency of victims.
The frequency graph is incorrect.

Discuss Question

Answer: Option B. -> False
:
B
By convention, bars of all categories in a bar graph are drawn with equal width. Hence the above statement is false.