What is the mode of the given data?
23
Finding the Mode of Given Data
The mode of a dataset is the value that appears most frequently in the set. To find the mode, we need to count how many times each number occurs in the given data.
The given data set is: 21, 22, 23, 23, 24, 21, 22, 23, 21, 23, 24, 23, 21, 23
Let's list the unique numbers present in the data and count their frequency:
| Number | Frequency (Count) |
|---|---|
| 21 | Let's count: 21 appears at positions 1, 6, 9, 13. So, 4 times. |
| 22 | Let's count: 22 appears at positions 2, 7. So, 2 times. |
| 23 | Let's count: 23 appears at positions 3, 4, 8, 10, 12, 14. So, 6 times. |
| 24 | Let's count: 24 appears at positions 5, 11. So, 2 times. |
Now, we compare the frequencies of each number:
- Frequency of 21 is 4.
- Frequency of 22 is 2.
- Frequency of 23 is 6.
- Frequency of 24 is 2.
The number with the highest frequency is 23, which appears 6 times. Therefore, the mode of the given data is 23.
Revision Table: Key Statistical Measures
| Measure | Definition | How to Find |
|---|---|---|
| Mean (Average) | The sum of all values divided by the number of values. | Sum all numbers, then divide by the total count of numbers. |
| Median | The middle value in a dataset that is ordered from least to greatest. | Order the data, find the middle value. If there's an even number of data points, average the two middle values. |
| Mode | The value that appears most frequently in a dataset. | Count the frequency of each value and identify the one with the highest count. A dataset can have one mode, multiple modes, or no mode. |
Additional Information on Mode and Data Analysis
Understanding the mode is an important part of basic data analysis. The mode tells us which value is the most common in a dataset. This is especially useful for categorical data (like favorite colors or types of cars) where the mean or median might not make sense.
- A dataset can have one mode (unimodal), two modes (bimodal), or more than two modes (multimodal) if multiple values share the highest frequency.
- If all values in a dataset appear with the same frequency, the dataset has no mode.
- The mode is one of the measures of central tendency, alongside the mean and median, which helps describe the center or typical value of a dataset.
For the given data set {21, 22, 23, 23, 24, 21, 22, 23, 21, 23, 24, 23, 21, 23}, we systematically counted each occurrence to find the mode, which is 23.
Important Questions from Elementary Statistics
What is the mode of the given data?
3, 0, 1, 0, 2, 1, 2, 0, 1, 2, 1, 1, 1, 3, 2A bowler has taken 0, 3, 2, 1, 5, 3, 4, 5, 5, 2, 2, 0, 0, 1 and 2 wickets in 15 consecutive matches. What is the mode of the given data?
The data given below shows the number of people who have saved a certain amount of money.
Saving (In Rs.)
Number of people
5
1
15
3
20
4
25
2
30
1
35
1
40
2
What is the median of the given data?
If the ratio of mean and median of a certain data is 4 : 5, then find the ratio of its mean and mode.
Given below is the marks obtained by 20 students in mathematics out of 30 marks.
7, 9, 12, 12, 13, 12, 14, 14, 14, 14, 15, 16, 17, 18, 18, 19, 20, 18, 20, 13. Then (2 × median — mode) of the data is equal to:
