Question 8·Medium·One-Variable Data Distributions; Measures of Center and Spread
The table shows the frequency of values in a data set.
| Value | Frequency |
|---|---|
| 19 | 7 |
| 21 | 1 |
| 23 | 7 |
| 25 | 4 |
What is the minimum value of the data set?
(Express the answer as an integer)
For questions asking for the minimum or maximum from a frequency table, focus first on the Value column and identify the smallest (for minimum) or largest (for maximum) value that has a positive frequency. Frequencies tell you how often each value occurs, but they do not change which value is smallest or largest, so you rarely need to do any arithmetic—just read and compare the listed values carefully.
Hints
Focus on the definition of minimum
The minimum of a data set is the smallest data value that appears, not the smallest frequency.
Look at the correct column
Pay attention to the "Value" column when deciding what the minimum is. Ask yourself: which of these values is the smallest, as long as it appears at least once?
Compare the listed values
The values in the table are 19, 21, 23, and 25. Think about how you would list these numbers from least to greatest.
Desmos Guide
List the data values in Desmos
In a Desmos expression line, type the list of data values from the table (ignoring frequencies) as a list, for example: A = [19, 21, 23, 25].
Use Desmos to find the minimum
On the next line, type min(A). The number that Desmos outputs is the smallest value in the list, which matches the minimum of the data set in the table.
Step-by-step Explanation
Understand what the table represents
The table lists each possible value in the data set (19, 21, 23, 25) and how many times each value occurs (its frequency). A value with frequency 7 appears 7 times in the data set, and so on.
Recall the definition of the minimum
The minimum of a data set is the smallest value that appears in the data set. It does not matter how many times each value appears for finding the minimum; we just need to know which value is smallest, as long as its frequency is greater than 0.
Identify the smallest value in the table
From the "Value" column, the data values are 19, 21, 23, and 25. The smallest of these numbers is , and its frequency is 7 (so it does occur in the data set). Therefore, the minimum value of the data set is 19.