## Chapter 3 Data Handling Exercise 3.2

**Question 1: The scores in mathematics test (out of 25) of 15 students is as follows:**

19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20

Find the mode and median of this data. Are they same?

Answer:

19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20

Find the mode and median of this data. Are they same?

Answer:

Ascending order of data: 5, 9, 10, 12, 15, 16, 19, 20, 20, 20, 20, 23, 24, 25, 25

Mode = most occurring (in ascending order)

Therefore, 20 is the mode of the given data.

Median = middlemost value of given data (in ascending order)

Therefore, 20 is the median of the given data.

Yes, both the median and mode of this data are same.

**Question 2: The runs scored in a cricket match by 11 players is as follows:**

6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15

Find the mean, mode and median of this data. Are the three same?

Answer:

6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15

Find the mean, mode and median of this data. Are the three same?

Answer:

Ascending order of the data: 6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120

Mean = sum of observations/number of observations

= 6 + 8 + 10 + 10 + 15 + 15 + 15 + 50 + 80 + 100 + 120/11

= 429/11 = 39

Therefore, the mean of the given data is 39.

Mode = most occurring (in ascending order)

Therefore, the mode of the given data is 15.

Median = middlemost value of the given data (in ascending order)

Therefore, the median of the given data is 15.

No, all of them (mean, median and mode) of this data are not same.

**Question 3: The weights (in kg.) of 15 students of a class are:**

38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47

(i) Find the mode and median of this data.

(ii) Is there more than one mode?

Answer:

38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47

(i) Find the mode and median of this data.

(ii) Is there more than one mode?

Answer:

Ascending order of the given data: 32, 35, 36, 37, 38, 38, 38, 40, 42, 43, 43, 43, 45, 47, 50

(i) Mode = most occurring (in ascending order)

Therefore, the mode of the given data is 38 and 43.

Median = middlemost value (in ascending order)

Therefore, the median of the given data is 40.

(ii) Yes, there are 2 modes for the given weights of the students.

**Question 4: Find the mode and median of the data: 13, 16, 12, 14, 19, 12, 14, 13, 14**

Answer:

Answer:

Ascending order of the given data: 12, 12, 13, 13, 14, 14, 14, 16, 19

Mode = most occurring (in ascending order)

Therefore, the mode of the given data is 14.

Median = middlemost value (in ascending order)

Therefore, the median of the given data is 14.

**Question 5: Tell whether the statement is true or false:**

(i) The mode is always one of the numbers in a data. (False

(i) The mode is always one of the numbers in a data. (

**)**

(ii) The mean is one of the numbers in a data. (True

(ii) The mean is one of the numbers in a data. (

**)**

(iii) The median is always one of the numbers in a data. (True

(iii) The median is always one of the numbers in a data. (

**)**

(iv) The data 6, 4, 3, 8, 9, 12, 13, 9 has mean 9. (False

(iv) The data 6, 4, 3, 8, 9, 12, 13, 9 has mean 9. (

**)**

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