*Q1 : The scores of 15 students (out of 35) of 15 students in Science test is as follows:*

*20, 26, 24, 21, 10, 21, 16, 11, 6, 17, 26, 21, 25, 13, 21*

*Find median and mode of this data and check if they are same.*

**Answer:**

Scores of 15 students in mathematics test are

20, 26, 24, 21, 10, 21, 16, 11, 6, 17, 26, 21, 25, 13, 21

Arranging these scores in an ascending order,

6, 10, 11, 13, 16, 17, 20, 21, 21, 21, 21, 24, 25, 26, 26

Mode of a certain data is the value of observation which repeats itself for the most number of times.

Median of a certain data is the observation which occurs in the middle when the data is sorted in an ascending order or descending order.

There are totally 15 values given in the question. Therefore 8^{th} observation is the median of the given data.

Hence, median = 21

For mode, we observe that 21 repeat 4 times (i.e., maximum number of times).

So, mode of the given data = 21

Yes, both mode and median are same.

*Q2. The runs scored by 11 players in a cricket match are as follows:*

*7, 16, 121, 51, 101, 81, 11, 16, 9, 11, 16*

*Find the median, mean and mode of the above data and check if the three are same.*

**Answer:**

The runs scored by the 11 players are

7, 16, 121, 51, 101, 81, 11, 16, 9, 11, 16

Arranging the scores in an ascending order,

7, 9, 11, 11, 16, 16, 16, 51, 81, 101, 121

Mean =

Mode of a certain data is the value of the observation which repeats itself for the most number of times.

Median of a certain data is the observation which occurs in the middle when the data is sorted in an ascending order or descending order.

There are totally 11 values given in the question. Therefore, the 6^{th} observation is the median of this data.

Median = 16

For mode, we observe that 16 repeat 3 times (i.e., maximum number of times).

So, mode of the given data = 16

We can understand from the above results that median, mode and mean are not the same.

*Q3. 15 students in a class weigh (in kg):*

*39, 43, 36, 38, 46, 51, 33, 44, 44, 41, 37, 39, 44, 39, 48*

*(i) Determine the median and mode of the above data.*

*(ii) How many modes are there?*

**Answer:**

The weights given (in kg) are

39, 43, 36, 38, 46, 51, 33, 44, 44, 41, 37, 39, 44, 39, 48

Arranging the given weights in ascending order,

33, 36, 37, 38, 39, 39, 39, 41, 43, 44, 44, 44, 46, 48, 51

Mode of a certain data is the value of observation which repeats itself for the most number of times.

Median of a certain data is the observation which occurs in the middle when the data is sorted in an ascending order or descending order.

There are totally 15 values given in the question. Therefore 8^{th} observation is the median of this data.

Hence, median = 41

For mode, we observe that both 44 and 39 repeat 3 times.

So, mode of the given data = 44 and 39.

Therefore, there are 2 modes in the above given question.

* *

*Q4: Calculate the mode and median of the following data:*

* 14, 16, 11, 13, 13, 14, 19, 13, 12. *

**Answer:**

Rearranging the given data in ascending order:

11, 12, 13, 13, 13, 14, 14, 16, 19

Mode = 13

Median = 13

*Q5. Which of the below-given statements are true? Justify your answer:*

*(i) One of the numbers is always the mode of the data.*

*(ii) One of the numbers is the mean of the data.*

*(iii) One of the numbers is always the median of the data.*

*(iv) The data 7, 5, 4, 9, 10, 13, 14, 10 has its mean value as 9.*

*Ans: *

**(i) True**

Mode of a certain data is the value of the observation, which repeats itself for the most number of times. Therefore, it is one of the observations given in the data.

**(ii) False**

Mean may or may not be one of the numbers in the data.

**(iii) True**

**(iv) True**

Mean =