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The mode of 10, 12, 11, 10, 15, 20, 19, 21, 11, 9, 10 is 10 because it has the highest frequency. The mode is the value that occurs most frequently in a given data set. It is one of the measures of central tendency, along with mean and median, and helps to identify the most common or popular value in the data. If no value is repeated, there is no mode, but if multiple values have the same highest frequency, the data is multimodal. Now let us look at the steps to find the mode of 10, 12, 11, 10, 15, 20, 19, 21, 11, 9, 10.
Complete Answer:
Here are the steps to find the mode of 10, 12, 11, 10, 15, 20, 19, 21, 11, 9, 10
Step 1: Organise the data
Write the given data in ascending order for clarity: 9, 10, 10, 10, 11, 11, 12, 15, 19, 20, 21.
Step 2: Create a Frequency Table
We list each unique value and count how many times it occurs:
| Value (x) | Frequency (f) |
| 9 | 1 |
| 10 | 3 |
| 11 | 2 |
| 12 | 1 |
| 15 | 1 |
| 19 | 1 |
| 20 | 1 |
| 21 | 1 |
Step 3: Identify the Mode
From the table, we observe that the value 10 has the highest frequency of 3. This means 10 appears more often than any other number in the data set.
Thus, the mode of the given data is 10 because it has the highest frequency.
What is Mode?
The mode is a measure of central tendency that identifies the most frequently occurring value in a dataset. It represents the value or category that appears the most. Unlike the mean (average) or median (middle value), the mode is not affected by extreme values, making it especially useful for categorical and discrete data.
How is Mode Calculated?
Understand how Mode is calculated to find the mode of 10, 12, 11, 10, 15, 20, 19, 21, 11, 9, 10.
To calculate the mode, follow these steps:
1. Organise the Data: Arrange the values in ascending order if they are numerical.
2. Count Frequencies: Identify how many times each value occurs.
3. Identify the Value with the Highest Frequency: The value that appears the most is the mode.
- If one value has the highest frequency, the data is unimodal.
- If two or more values share the highest frequency, the data is bimodal or multimodal.
- If no value repeats, the data set has no mode.
Example:
Given the data: 5, 8, 8, 10, 5, 5, 12
- Organize: 5, 5, 5, 8, 8, 10, 12
- Count:
- 5 occurs 3 times
- 8 occurs 2 times
- 10 and 12 occur 1 time each
- The mode is 5, as it has the highest frequency.
Applications of Mode
Mode is a simple yet powerful tool to identify trends and patterns in data, providing practical insights for decision-making in various fields. Here are the common applications of Mode:
- Corporations use mode to identify the most popular product or service, such as the best-selling colour of a car or the most preferred size of a clothing item.
- Also, academic institutions use mode to determine the most common grade or score achieved by students in exams to analyse performance.
- In addition, mode helps to identify the most frequent symptoms or diseases in a particular group of patients for targeted treatments.
- Additionally, retailers use mode to find the most popular products, enabling better inventory management and sales forecasting.
- Furthermore, in surveys and opinion polls, mode represents the most common response, helping to shape policies and decisions.
- Moreover, city planners use mode to determine the most common mode of transport (e.g., bus, car, train) for better infrastructure development.
Common Doubts:
