Arranged data set is:

1          4          6          6          9          12        13        19        25        33        45        56
Median: The middle most value after arranging the given data.
Here, the number of observations is 12, which is an even number. So, we take the average of the two observations in the middle to find the value of median.

Median=$\frac{12+13}{2}$=12.5. (Mean of the $6^{th}$ and $7^{th}$ observation)
Mode: The observation that occurs most often in the data set.
We can find 6 two times in the data set. This is the most repeated value in the data set. The value of the mode is 6.
i.e., Mode=6.
Difference between median and mode of the given data set=12.5-6=6.5.

Average  $=\frac{\text{Total marks}}{\text{Total number of student}}$

$65=\frac{3080+\text{Marks scored by Arjun}+\text{Marks scored by Karan}}{50}$.

Since marks scored by Arjun = Marks scored by Karan

Marks scored by Arjun + Marks scored by Karan =  2 $\times$ Marks scored by Arjun.

So, 65 $\times$ 50 = 3080 + 2 $\times$ Marks scored by Arjun. 

So, marks scored by Arjun                                    $=\frac{3250-3080}{2}=\frac{170}{2}=85$ marks.

In the 1000 observations, 9 will be the mode.

In 1020 observations, frequency of  9 = 13 + 1 = 14

In 1020 observations, frequency of 13 = 19

So, mode of the observations = 13.

Formula: 1 Mark
Result: 1 Mark

$Mean=\frac{\text{Sum of all observation}}{\text{Total number of observation}}$

$Mean=\frac{9+10+8+9+12+10}{6}=9.66$.

The mean is 9.66.

Formula: 1 Mark
Solution: 1 Mark

First five multiples of 5 are 5,10,15, 20 and 25.

$\text{Mean}=\frac{\text{Sum of all observation}}{\text{Total number of observation}}$

$\text{Mean}=\frac{5+10+15+20+25}{5}=15$

Formula: 1 Mark
Result: 1 Mark
Range is defined as the difference between the highest and the lowest observation.
Here, after arranging marks in ascending order : ( -6 ),( -1 ) , 0 , 2, 8 , 12 , 14 , 15. 
Lowest observation: (-6)
Highest observation: 15
Range = Highest observation - Lowest observation
Range = 15 - (-6) = 21

Steps: 1 Mark
Result: 1 Mark
Given runs are, 12, 32, 43, 32, 12, 32, 12, 32, 36, 54,11.
Arranging the numbers in ascending order:
11, 12, 12, 12, 32, 32, 32, 32, 36, 43, 54.
Mode of a set of observations is the observation which occurs most often.
Clearly, here, 32 runs are scored by most of the batsman.
So, the mode of the observation is 32.

Steps: 2 Marks
Result: 1 Mark
Given,
Weights of 9 different students : 54kg, 56kg , 54kg , 57kg , 54kg , 52kg , 54kg , 55kg , 59kg
Arranging the data in ascending order,
52kg, 54kg, 54kg, 54kg, 54kg, 55kg, 56kg, 57kg, 59kg
Median is the middle most observation of the given observations
$\Rightarrow$ Median = 54kg
Mode is the most repeated observation of the given observations
Clearly, 54kg is the most repeated  observation
$\Rightarrow$  Mode =  54kg