Each part: 2 Marks

When a die is rolled once, the possible outcomes are 1, 2, 3, 4, 5 and 6

$\Rightarrow$ Total numbers on the dice = 6

(i) Multiples of 2 are  2, 4, 6

$\Rightarrow$  Numbers of Multiples of 2 = 3

Probability of getting a multiple of 2 is

$P\left(E\right)=\frac{\text{Number of multiples of 2}}{\text{Total numbers on the dice}}$

$P\left(E\right)=\frac{3}{6}=\frac{1}{2}$

(ii) Prime numbers are 2, 3, 5

$\Rightarrow$ Numbers of Multiples of 2 = 3

Probability of getting a prime number is 

$P\left(E\right)=\frac{\text{Number of prime numbers}}{\text{Total numbers on the dice}}$

$P\left(E\right)=\frac{3}{6}=\frac{1}{2}$

(i) Jammu has the largest difference in temperature i.e., Maximum temperature = ${41}^{\circ }C$ and Minimum temperature = ${26}^{\circ }C$

$\therefore$ Difference = ${41}^{\circ }C–{26}^{\circ }C={15}^{\circ }C$
 

(ii) Jammu is the hottest city as the maximum temperature is the highest among all the given cities and Bangalore is the coldest city because the minimum temperature there is lowest among all the given cities.
 

(iii) Maximum temperature of Bangalore = ${28}^{\circ }C$

 Minimum temperature of two cities whose minimum temperature is higher than the maximum temperature of Bangalore are Ahmedabad and Jaipur = ${29}^{\circ }C$
 

(iv) Mumbai has the least difference in temperature i.e., Maximum temperature = ${32}^{\circ }C$ and Minimum temperature = ${27}^{\circ }C$.

$\therefore$ Difference = ${32}^{\circ }C–{27}^{\circ }C=5^{\circ }C$

$Average=\frac{Sumofallobservations}{Totalnumberofobservations}$​​
Here, for both the cases, the total number of observations is the same and it is 7.
Average number of villians  caught by Batman  per day = $\frac{2+5+4+1+3+2+4}{7}$ = $\frac{21}{7}$ = 3.

Average number of villians  caught by Superman per day = $\frac{3+4+2+2+1+2+0}{7}$ =  $\frac{14}{7}$ = 2.

So, BATMAN's average is higher and it is 3.

Mode is the observation that occurs the most number of times. Here, 2 and 9 both occur two times. Therefore, they both are modes of the data.

The heights of the bars that are drawn side by side in the above double bar graph, correspond to the number of men and the number of women who visit the sports complex on each day of the week.
The heights of both the bars are equal on Thursday. So, on Thursday, the numbers of men and women who visited the complex are equal. 

$Mean=\frac{Sumofallobservations}{Numberofobservations}$
​$=\frac{12+86+45+78+23+56}{6}$
$=\frac{300}{6}$
= 50.                              

Range = Highest observation - Lowest observation
           = 86 - 12
           = 74

Difference between the mean and range  = 74 - 50 = 24

After arranging the data in ascending order, we get:

0,   3,   8,  12,  15,  19,   23,   24,   39,    53,  57,  64,  65.

Here, n = 13 = Odd
$Median=\frac{(n+1)}{2}{}^{th}$ observation
              $=\frac{(13+1)}{2}$
              $=7^{th}observation$
              $=23$ 
Therefore,  median of the given data is 23.

If there are 6 faces, the probability of getting one of 6 digits is $\frac{1}{6}$. So, in the case of 8 faces, probability of getting any of the 8 numbers must be $\frac{1}{8}$. Hence, the probability of getting 8 on throwing it is $\frac{1}{8}$.