Question 11·Medium·One-Variable Data Distributions; Measures of Center and Spread
The frequency table summarizes the 57 data values in a data set.
| Data value | Frequency |
|---|---|
| 6 | 3 |
| 7 | 3 |
| 8 | 8 |
| 9 | 8 |
| 10 | 9 |
| 11 | 11 |
| 12 | 9 |
| 13 | 0 |
| 14 | 6 |
What is the maximum data value in the data set?
(Express the answer as an integer)
For frequency-table questions asking for the maximum (or minimum) data value, ignore the frequencies except to check whether a value actually appears (frequency greater than 0). Quickly scan the data values from smallest to largest, cross out any with frequency 0, and choose the largest remaining value. Do not confuse “maximum” with the value that has the highest frequency (the mode).
Hints
Clarify the term "maximum"
Ask yourself: does "maximum data value" refer to how often a value appears, or how big the value itself is?
Use the frequency column correctly
A frequency of 0 means that data value does not occur in the data set at all. Focus only on rows where the frequency is greater than 0.
Scan for the largest valid value
Once you know which data values actually appear, look at those values and decide which one is the largest number.
Desmos Guide
Use Desmos to confirm the maximum value
In Desmos, type max(6,7,8,9,10,11,12,14) to represent all the data values that actually appear (skip the one with frequency 0). Desmos will display the largest number in this list as the result, which confirms the maximum data value from the table.
Step-by-step Explanation
Understand what the table shows
The first column lists each possible data value (6, 7, 8, ..., 14). The second column lists how many times each value appears in the data set (its frequency). For example, the 6 in the first row with a frequency of 3 means that the value 6 appears 3 times.
Recall what “maximum data value” means
The maximum data value is the largest data value that actually occurs in the set. That means you are looking for the biggest number in the first column that has a frequency greater than 0 in the second column.
Identify which values actually appear
Look down the frequency column:
- Data value 6 has frequency 3 (it appears).
- 7 has 3 (appears).
- 8 has 8 (appears).
- 9 has 8 (appears).
- 10 has 9 (appears).
- 11 has 11 (appears).
- 12 has 9 (appears).
- 13 has 0 (this value does not appear in the data set).
- 14 has 6 (appears).
So every listed value except 13 is present in the data set.
Find the largest value that appears
Now look only at the data values that actually appear: 6, 7, 8, 9, 10, 11, 12, and 14. The largest of these is 14, so the maximum data value in the data set is 14.