Frequency Distributions
Consider the below data set.
{1, 1, 2, 3, 3, 3, 3, 5, 5, 5}
Note that in this data set, several numbers appear multiple times. The number of times any particular entry occurs in a set of data is called the __frequency__ of that entry.
Which of the following entries has the greatest frequency in the above set of data?
Incorrect.
The frequency of 1 is two because 1 appears twice in the data set. Since the frequency of 5 is three, 1 does not have the greatest frequency in the set.
What is the relative frequency of 7 in the data set {4, 6, 7, 7, 8, 4, 7, 1, 7, 8, 8, 7}?
Incorrect.
The frequency of 5 is three because 5 appears three times in the data set. Since the frequency of 3 is four, 5 does not have the greatest frequency in the set.
Incorrect.
Note that the numbers in the data set are not in numerical order. Carefully count the number of entries in the set and the number of times seven appears!
In summary:
[[summary]]
Incorrect.
Note that the denominator of the fraction must be equal to the number of elements in the data set. There are more than seven of those!
Correct.
3 has a frequency of four since it appears four times. Since 1 has a frequency of two, 2 has a frequency of one, and 5 has a frequency of three, 3 has the greatest frequency among all elements in the set.
A __frequency distribution__ is a table or graph that shows categories or values and their corresponding frequencies. For instance, the following table is a frequency distribution for the above data set.
At times, we may want to think about how often a certain value or category appears in our data set relative to the number of data points in the set. This is the __relative frequency__ of that value or category.
The relative frequency of a particular value or category in a data set is found by dividing the number of times that value or category appears in the data set by the number of points in the data set. Note that the relative frequencies of all distinct points in the set must add up to one.
Good job.
Since there are five 7s in the data set, and a total of 12 elements in the set, so the relative frequency of 7 is $$\frac{5}{12}$$.
1
3
5
$$\frac{1}{3}$$
$$\frac{5}{12}$$
$$\frac{5}{7}$$
Continue
Continue
Continue
