Answer: Option A. -> Blue is the favourite colour of most students.
:
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.

Answer: Option A. -> True
:
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.
 

Answer: Option A. -> Total number of trees is 31
:
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.
 

Answer: Option B. -> Median
:
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. 

Answer: Option B. -> 4.5
:
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 $(\frac{n}{2}{)}^{th}$ and $\left[\right(\frac{n}{2})+1{]}^{th}$ term. 
Here the ${\frac{10}{2}}^{th}term$= 5${}^{th}$ term = 4
$\left[\right(\frac{n}{2})+1{]}^{th}$ term.  = 6${}^{th}$ term = 5
 i.e. $\left(\frac{4+5}{2}\right)=4.5$
Hence, median of the given data $=4.5$

Answer: Option B. -> 4.5
:

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.

Answer: Option D. -> 19
:
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.

Answer: Option A. -> 16
:
A

We know that,
Mean = $\frac{Sumofallobservations}{Numberofobservations}$
Sum of values of all the observations
$=Mean\times Numberofobservation$
$=15\times 8$
$=120$
So, sum of the first eight observations
$=Mean\times Numberofobservation$
$=7\times 8$
$=56$
Sum of the last eight observations
$=Mean\times Numberofobservation$
$=10\times 8$
$=80$ 
Hence, value of the $8^{th}$observation 
$=(80+56)-120$
$=16$

Answer: Option B. -> The youngest president was 44 years old
:
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.

Answer: Option A. -> Total number of people in 0-20 age group is 10
:
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  $5\times 2=10$

Hence 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