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
Understanding the Mode in Data Sets
The question asks us to find the mode of the given set of data. The mode is a fundamental concept in statistics, representing the value that appears most frequently in a dataset. If multiple values share the highest frequency, the dataset is multimodal.
Step-by-Step Calculation of the Mode
To find the mode, we need to count how many times each number appears in the dataset. Let's list the data points provided:
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
Now, let's count the frequency of each unique number:
| Number | Frequency |
|---|---|
| 62 | 1 |
| 63 | 1 |
| 65 | 2 |
| 67 | 1 |
| 68 | 1 |
| 69 | 1 |
| 70 | 2 |
| 74 | 1 |
| 75 | 1 |
| 76 | 1 |
| 78 | 3 |
| 81 | 4 |
| 82 | 2 |
| 86 | 2 |
| 87 | 1 |
| 90 | 2 |
Identifying the Most Frequent Value
By examining the frequency table, we can see which number occurs most often. The number 81 appears 4 times, which is more than any other number in the dataset.
Therefore, the mode of this data is 81.
Important Questions from Elementary Statistics
- 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: - What is the mode of the following data?
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 - 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
