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 same?
Solution:
We use the basic formula and definitions of mode and median to solve the problem.
Scores of
Arranging scores in ascending order, we get =
Mode - Mode of a given data is that value of observation that has the maximum occurrence or repetition i.e., most frequent.
Therefore, 20 has the highest occurrence.
∴ Mode =
We have 15 observations given in total. Hence, the midmost observation will be the 8th observation.
Median = Middlemost observation (in this case, 8th observation)
∴ Median =
Yes, the mode and median of the given observations are the same.
Que
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?
Sol
Solution:
We use the basic formulae of mean, median and mode to solve the problem.
Total number of players =
Scores of the players = 6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15
Arranging the scores into ascending order, we get = 6,
Mean =
=
Thus, mean = 39.
Mode is the observation that occurs the highest number of times.
Here, 15 occurs 3 times in the given data.
∴ Mode =
The arranged data is: 6, 8, 10,10, 15, 15, 15, 50, 80, 100, 120
Median is the middlemost observation of the given data
There are 11 observations here. Thus the middle value is the 6th observation.
∴ Median =
Thus, Mean = 39 , Mode= 15 and median = 15. No, the mean, mode, and median are not the 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
Solution:
We use the basic formulae of mode and median to solve the question.
Mode = Mode is the observation that occurs the highest number of times
Median = Median is the middle observation
Total number of students =
Weights of 15 students = 38, 42, 35, 37, 45, 50, 32, 43,43, 40, 36, 38, 43, 38, 47.
Arranging in ascending order, we get = 32, 35,
(i) Find the mode and median of this data.
Mode is the observation that occurred highest number of times.
Thus,
∴ Mode = 38 and 43.
Also, out of the 15 observations given, the 8th observation is the mid data.
Hence, median = 40 (8th observation)
(ii) Is there more than one mode?
Yes, there are two modes
4. Find the mode and median of the data: 13, 16, 12, 14, 19, 12, 14, 13, 14.
∴ Median =
5. Tell whether the statement is true or false