Answer :
To determine the most popular color from the given data, we need to consider a statistic that identifies the value that appears most frequently. Here is the information presented in the table:
| Color | Number of Students |
|-------|--------------------|
| Red | 15 |
| Blue | 24 |
| White | 20 |
| Pink | 16 |
| Yellow| 45 |
Let's examine each statistic:
A) The Mean:
The mean, or average, is calculated by adding all the values together and dividing by the total number of values. While the mean can provide a measure of central tendency, it does not indicate which specific value appears most frequently in a data set. Thus, the mean is not useful for determining the most popular color.
B) The Median:
The median is the middle value in a list of numbers sorted in ascending order. For this data set:
- Ordered list: 15, 16, 20, 24, 45
- The median is 20 (White), the middle value.
However, the median does not consider the frequency of each value; it only identifies the central point. Hence, it does not necessarily indicate the most popular color.
C) The Mode:
The mode is the value that appears most frequently in a data set. Here, we compare the frequencies of the number of students:
- Red: 15
- Blue: 24
- White: 20
- Pink: 16
- Yellow: 45
Since 45 (Yellow) is the highest frequency, the mode shows that Yellow is chosen by the most students. Therefore, the mode effectively identifies the most popular color.
D) The Median and the Mode:
Since the median identifies only the central value without considering frequency, it does not help us find the most popular color. So, only the mode is useful in this scenario.
Thus, the correct statistic(s) to represent the most popular color is:
C) the mode
| Color | Number of Students |
|-------|--------------------|
| Red | 15 |
| Blue | 24 |
| White | 20 |
| Pink | 16 |
| Yellow| 45 |
Let's examine each statistic:
A) The Mean:
The mean, or average, is calculated by adding all the values together and dividing by the total number of values. While the mean can provide a measure of central tendency, it does not indicate which specific value appears most frequently in a data set. Thus, the mean is not useful for determining the most popular color.
B) The Median:
The median is the middle value in a list of numbers sorted in ascending order. For this data set:
- Ordered list: 15, 16, 20, 24, 45
- The median is 20 (White), the middle value.
However, the median does not consider the frequency of each value; it only identifies the central point. Hence, it does not necessarily indicate the most popular color.
C) The Mode:
The mode is the value that appears most frequently in a data set. Here, we compare the frequencies of the number of students:
- Red: 15
- Blue: 24
- White: 20
- Pink: 16
- Yellow: 45
Since 45 (Yellow) is the highest frequency, the mode shows that Yellow is chosen by the most students. Therefore, the mode effectively identifies the most popular color.
D) The Median and the Mode:
Since the median identifies only the central value without considering frequency, it does not help us find the most popular color. So, only the mode is useful in this scenario.
Thus, the correct statistic(s) to represent the most popular color is:
C) the mode
