What are the modes of the following sets of numbers:
a) 3, 13, 6, 8, 10, 5, 6
b)12, 0, 15, 15, 13, 19, 16, 13, 16, 16
c)8, 5, 8, 5, 7, 6, 7, 7, 5, 7, 5, 5, 6, 6, 9, 8, 9, 7, 9, 9, 6, 8, 6, 6, 7
d)5, 4, 10, 3, 3, 4, 7, 4, 6, 5, 11, 9, 5, 7
Answers
a- 6
b- 16
c-6
d-54
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The modes of the given sets of numbers are:
a) 6,
b) 16,
c) 6, 7,
d) 4, 5.
Given,
Some sets of numbers:
a) 3, 13, 6, 8, 10, 5, 6
b) 12, 0, 15, 15, 13, 19, 16, 13, 16, 16
c) 8, 5, 8, 5, 7, 6, 7, 7, 5, 7, 5, 5, 6, 6, 9, 8, 9, 7, 9, 9, 6, 8, 6, 6, 7
d) 5, 4, 10, 3, 3, 4, 7, 4, 6, 5, 11, 9, 5, 7
To find,
Mode of these sets of numbers.
Solution,
It can be seen that here, a few sets of numbers are given. For these sets, we are required to find the modes for each of them.
Now, we know that mode of a given data or a set of numbers is defined as the most repeated number or term. Or a number that appears the most number of times in a data, is the mode of that data.
To find the mode easily, data can first be arranged in ascending or descending order.
- For a) 3, 13, 6, 8, 10, 5, 6
In ascending order:
3, 5, 6, 6, 8, 10, 13.
We can see that 6 appears 2 times.
Thus, mode = 6.
- For b) 12, 0, 15, 15, 13, 19, 16, 13, 16, 16
In ascending order:
0, 12, 13, 13, 15, 15, 16, 16, 16, 19.
Here, the number that is most repeated is 16, which appears 3 times.
Thus, mode = 16.
- For c) 8, 5, 8, 5, 7, 6, 7, 7, 5, 7, 5, 5, 6, 6, 9, 8, 9, 7, 9, 9, 6, 8, 6, 6, 7
In ascending order:
5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9.
Here, we can see that there are 2 numbers, 6 and 7, which appear most as well as an equal number of times.
6, 7 appear 6 times.
Thus, mode = 6, 7.
- For d) 5, 4, 10, 3, 3, 4, 7, 4, 6, 5, 11, 9, 5, 7
In ascending order:
3, 3, 4, 4, 4, 5, 5, 5, 6, 7, 7, 9, 10, 11.
In this set again, the two numbers, 4 and 5, both appear 3 times, and a maximum number of times.
Thus, mode = 4, 5.
Therefore, the modes of the given sets of numbers are:
a) 6,
b) 16,
c) 6, 7,
d) 4, 5.
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