67, 75, 81, 70, 65, 61, 65, 84, 75, 76, 85, 89, 62, 84, 72, 74, 89, 68, 83, 60, 82, 82, 66, 77, 75
Understanding the Mode of Data
The mode is a concept in statistics that represents the value that appears most often in a set of data. Think of it as the most 'popular' or frequently occurring number in your list.
To find the mode, we need to examine the given data set and count how many times each unique number appears. The number with the highest count is the mode.
Calculating the Mode for the Dataset
Here is the dataset provided:
67, 75, 81, 70, 65, 61, 65, 84, 75, 76, 85, 89, 62, 84, 72, 74, 89, 68, 83, 60, 82, 82, 66, 77, 75
Let's count the frequency of each number:
| Number | Frequency |
|---|---|
| 60 | 1 |
| 61 | 1 |
| 62 | 1 |
| 65 | 2 |
| 66 | 1 |
| 67 | 1 |
| 68 | 1 |
| 70 | 1 |
| 72 | 1 |
| 74 | 1 |
| 75 | 3 |
| 76 | 1 |
| 77 | 1 |
| 81 | 1 |
| 82 | 2 |
| 83 | 1 |
| 84 | 2 |
| 85 | 1 |
| 89 | 2 |
By examining the frequency table, we can see:
- The number 65 appears 2 times.
- The number 82 appears 2 times.
- The number 84 appears 2 times.
- The number 89 appears 2 times.
- The number 75 appears 3 times, which is more than any other number in the dataset.
Therefore, the value that occurs most frequently is 75.
Mode Identification
The mode of the given data is the number with the highest frequency. Based on our count, the number 75 occurs 3 times, making it the most frequent value.
So, the mode of this dataset is 75.
Important Questions from Elementary Statistics
- What is the mode of the following data?
87, 65, 70, 81, 68, 62, 82, 78, 81, 82, 74, 75, 90, 67, 86, 86, 81, 90, 69, 78, 65, 78, 76, 63, 70, 81 - The marks scored by 10 students are given below.
12, 14, 14, 15, 12, 16, 12, 10, 19, 11
The mode of the given data is: - The marks scored by 10 students are given below.
10, 19, 18, 18, 13, 14, 16, 18, 16, 12
The mode of the data is: - The marks scored by 10 students are given below.
12, 13, 14, 11, 16, 11, 12, 17, 15, 12
The mode of the data is: - Find the mean deviation from the mean for the following data set.
58, 65, 42, 66, 49, 59, 44, 45, 62, 60
