**Data Handling**

**Exercise 3.2**

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 the same?

The scores in ascending order is 5, 9, 10, 12, 15, 16, 19, 20, 20, 20, 20, 23, 24, 25, 25.

Mode is the observation that occurs most often

Mode = 20.

The Median is the middle observation.

Here total observations are 15 therefore median is the eighth observation

Median = 20

Here both the mode and the median are the same.

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?

The runs scored in ascending order are 6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120

Mode is the observation that occurs most often

Mode = 15

The Median is the middle observation.

Here total observations are 11 therefore median is the sixth observation

Median = 15

Mean = sum of the runs scored

No. of players

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

11

= 429

11

= 39

No the mode median and the mean are not same.

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?

The weights of the students in ascending order are 32, 35, 36, 37, 38, 38, 38, 40, 42, 43, 43, 43, 45, 47, 50

Mode is the observation that occurs most often

both 38 and 43 occurs three times

Mode = 38 and 43.

The Median is the middle observation.

Here total observations are 15 therefore median is the eighth observation

Median = 40

(ii) Is there more than one mode?

Yes, there is more than one mode.

4). Find the mode and median of the data: 13, 16, 12, 14, 19, 12, 14, 13, 14

The data in ascending order is 12, 12, 13, 13, 14, 14, 14, 16, 19

Mode is the observation that occurs most often

14 occurs three times

Mode = 14

The Median is the middle observation.

Here total observations are 9 therefore median is the fifth observation

Median = 14

5). Tell whether the statement is true or false:

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

True.

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

False.

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

True.

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

False.

Mean = __6+4+3+8+9+12+13+9__

8

= __64__

8

= 8

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