what is the mode in 4 6 8 6 3 6 8 7 9 4 3 8 6 8 ?
what is the mode in 4 6 8 6 3 6 8 7 9 4 3 8 6 8 ?
The Correct Answer and Explanation is:
Answer:
The mode is 6 and 8 (it’s bimodal).
Explanation
The mode of a dataset is the value (or values) that appear most frequently. Unlike the mean or median, the mode can be used for both numerical and categorical data, and there can be more than one mode if multiple values share the highest frequency. When a dataset has two modes, it’s called bimodal; if more than two, it’s multimodal.
Let’s determine the mode for this dataset:
Dataset:
4, 6, 8, 6, 3, 6, 8, 7, 9, 4, 3, 8, 6, 8
Step 1: Count the frequency of each number:
- 3 → 2 times
- 4 → 2 times
- 6 → 4 times
- 7 → 1 time
- 8 → 4 times
- 9 → 1 time
Step 2: Identify the highest frequency:
- The highest frequency is 4, and both 6 and 8 appear 4 times.
Step 3: Determine the mode:
- Since 6 and 8 both occur most frequently (and equally), this dataset has two modes: 6 and 8.
Why mode matters:
- Practical use: In real-world scenarios like marketing or quality control, the mode tells us what is “most common.” For instance, a clothing retailer might use the mode to determine the most commonly sold size.
- Skewed distributions: When data are not symmetrically distributed, the mode can give insights that the mean and median might not. For example, in income distribution, the mode might show the income level most people earn, which is often lower than the average.
- Robustness: The mode is not affected by extreme values (outliers), unlike the mean.
In this case, since both 6 and 8 are equally common and appear more than any other numbers, the correct mode is 6 and 8 — making the dataset bimodal.
