Compute the MODE for the final grades of the 1st quarter for 39 students. Analyze the data for mean and median based on the provided statistics.
Understand the Problem
The question is asking to compute the mode of a set of ungrouped data, and to analyze additional data to find the mean and median. It involves statistical calculations based on provided data.
Answer
The mode is 82, 83, 84, 86, 91, 93.
Answer for screen readers
The mode of the ungrouped data is 82, 83, 84, 86, 91, 93 (multimodal).
Steps to Solve
- Identifying the Data Set for Mode Calculation
The given grades are:
93, 90, 95, 84, 79, 82, 93, 92, 95, 91, 91, 86,
81, 84, 88, 89, 93, 89, 82, 90, 84, 92, 91, 92,
86, 91, 86, 83, 87, 88, 82, 85, 88, 83, 79, 83
- Finding the Mode
The mode is the number that appears most frequently in the data set.
- Count the frequency of each unique number.
- The number with the highest frequency is the mode.
Here's how the counts look:
79: 3 times
81: 2 times
82: 4 times
83: 4 times
84: 4 times
86: 3 times
89: 3 times
90: 3 times
91: 4 times
92: 3 times
93: 4 times
95: 2 times
In this data, 82, 83, 84, 86, 91, and 93 all occur 4 times.
- Concluding the Mode
Since multiple numbers appear most frequently, this data set is multimodal. Thus, the modes are:
82, 83, 84, 86, 91, 93.
The mode of the ungrouped data is 82, 83, 84, 86, 91, 93 (multimodal).
More Information
The mode is a measure of central tendency that identifies the value that occurs most frequently in a data set. In cases where more than one value appears with the same highest frequency, the set is described as multimodal.
Tips
- Neglecting Frequency Counts: Ensure you account for all occurrences accurately.
- Assuming Uniqueness: Sometimes, students may expect a singular mode even in multimodal situations. Be aware that multiple modes can exist.
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