In a Mathematics test 15 students scored 80 marks, 20 students scored 75 marks, 28 students scored 65 marks and 25 students scored 60 marks, mode of the score is:
65
Understanding the Mode in Mathematics Test Scores
The question asks us to find the mode of the scores obtained by students in a Mathematics test. The mode of a data set is the value that appears most frequently. In this case, the data set consists of the scores, and the frequency of each score is the number of students who achieved that score.
Identifying Scores and Frequencies
Let's list the scores and the corresponding number of students (frequency) who obtained each score:
| Score | Number of Students (Frequency) |
|---|---|
| 80 | 15 |
| 75 | 20 |
| 65 | 28 |
| 60 | 25 |
Determining the Mode of the Score
To find the mode, we need to look for the score that has the highest frequency among all the scores listed. Let's compare the frequencies:
- Frequency for score 80 is 15.
- Frequency for score 75 is 20.
- Frequency for score 65 is 28.
- Frequency for score 60 is 25.
Comparing the frequencies (15, 20, 28, and 25), we can see that the highest frequency is 28.
The score corresponding to the highest frequency (28) is 65.
Therefore, the score that occurred most frequently in the test is 65.
Conclusion: Finding the Mode
Based on the frequencies of the scores, the mode of the score is the score with the highest number of students. In this case, the score 65 was achieved by 28 students, which is the maximum number of students for any score. Thus, the mode is 65.
Revision Table: Key Statistical Measures
| Measure | Definition | How to find (Simple Data) |
|---|---|---|
| Mean | The average value of a data set. | Sum of all values divided by the number of values. $\text{Mean} = \frac{\sum x}{n}$ |
| Median | The middle value of a data set when arranged in order. | Arrange data in order. If $n$ is odd, median is the $\left(\frac{n+1}{2}\right)^{\text{th}}$ value. If $n$ is even, median is the average of the $\left(\frac{n}{2}\right)^{\text{th}}$ and $\left(\frac{n}{2}+1\right)^{\text{th}}$ values. |
| Mode | The value that appears most frequently in a data set. | Identify the value(s) with the highest frequency. A data set can have one mode (unimodal), multiple modes (multimodal), or no mode. |
| Range | The difference between the highest and lowest values. | Highest value - Lowest value. |
Additional Information: Mode in Different Data Types
- The mode is the only measure of central tendency that can be used for nominal data (categorical data that cannot be ordered, e.g., favorite color).
- In grouped frequency distributions, the mode falls within the modal class, which is the class interval with the highest frequency. A formula is then used to estimate the mode more precisely.
- For continuous data represented by a histogram, the mode is typically estimated as the midpoint of the tallest bar (the modal class).
- Understanding the mode helps identify the most common observation or category in a data set, providing insight into typical values or preferences.
Important Questions from Measures of Central Tendency
A random sample of 20 people is classified in the following table according to their ages:
Age
Frequency
15 – 25
2
25 – 35
4
35 – 45
6
45 – 55
5
55 - 65
3
What is the mean age of this group of people?
The median of the following observations 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33 is 58. If 92 is replaced by 99 and 41 by 43 in the above data. The new median is:
If the difference of mode and median is 36, then the difference of median and mean is:
If the mode of the scores 10, 12, 13, 15, 15, 13, 12, 10, x is 15, then what is the value of x?
A, B, C are three sets of values of x:
A: 2, 3, 7, 1, 3, 2, 3
B: 7, 5, 9, 12, 5 3, 8
C: 4, 4, 11, 7, 2, 3, 4
Select the correct statement from among the following
