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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