The answer is: " 33 " .
→ The mode for the given data set is: " 33 " .
Step-by-step explanation:
The "mode" refers to the number that occurs most frequently within a data set.
Given the data set:
" {18, 16, 11, 45, 33, 16, 33, 14, 18, 33} " ;
→ We are asked to find the "mode" .
To do so, it is often help to rewrite the data set in order from values in least to greatest [or, for that matter, from greatest to least],
Let us rewrite the data set, in order from least to greatest; as follows:
→ " {11, 14, 16, 16, 18, 18, 45, 33, 33, 33} " ;
→ Note: How to do the above? Examine each value within the number set, and determine the smallest value, and note how many times it occurs in the data set, and "to rewrite our data set from least to greatest".
We start by typing the "lowest value" [in this case, "11"] ; and type it the number of times it occurs in the data set (in this case, the value of "11" appears only "one time" — so we begin rewriting the data with writing the number "11" only one time; then cross that value of the list of values in the data set; and then look for the "next lowest number" within the values in the data set— and so-forth:
Start by re-writing as: " { 11, _ , _ , _ , _ , _ , _ , _ , _ , _ } " ;
and then checking to make sure that we have accounted for each value in the "originally written version" of the data set — and for the appropriate number of times of occurring, and the the "rewritten data set" is, in fact, written in order of "least value to greatest value" [or, for that matter, in order of "greatest value to least value".].
For the purposes of this very example, we shall rewrite the data set in order from "least value to greatest value" ; as follows:
→ " {11, 14, 16, 16, 18, 18, 33, 33, 33, 45 .} "
Note that:
The value: "11" occurs only One Time. The value: "14" occurs only One Time. The value: "16" occurs Twice (Two Times.). The value: "18" occurs Twice (Two Times.). The value: "33" occurs Thrice (Three Times.). The value: "45" occurs Once (One Time.).
So, the value occur the greatest number of times, is: " 33 " .
→ The value: "33" ; is the only value within the data set that occurs "Thrice" [three times].
No other value within the given data set occurs "thrice [three times]" ; or: "[more than three times]."
→ As such, the answer is: " 33 " .
The mode for the given data set is: " 33 " .
Hopefully, this answer—and explanation—is helpful to you!
Best wishes to you in your academic endeavors
— and within the "" community!
