Question
A teacher collected data on the number of pencils used by students in a month. The data is:
2, 3, 4, 5, 6, 100
Which measure of center is the best representation of the typical number of pencils used?
(4 Points)
Mean
Median
Mode
Range
2, 3, 4, 5, 6, 100
Which measure of center is the best representation of the typical number of pencils used?
(4 Points)
Mean
Median
Mode
Range
Answers
GPT-4o mini
To determine the best measure of center for the given data set (2, 3, 4, 5, 6, 100), we need to analyze each option:
1. **Mean**: The mean is calculated by adding all the values together and dividing by the count of values.
\[
\text{Mean} = \frac{2 + 3 + 4 + 5 + 6 + 100}{6} = \frac{120}{6} = 20
\]
The mean (20) is heavily influenced by the outlier (100) and does not accurately reflect the typical number of pencils used by most students.
2. **Median**: The median is the middle value when the data is ordered. For an even number of observations, it is the average of the two middle values.
Ordered data: 2, 3, 4, 5, 6, 100.
\[
\text{Median} = \frac{4 + 5}{2} = 4.5
\]
The median (4.5) is more representative of the typical usage since it is not influenced by the outlier.
3. **Mode**: The mode is the value that appears most frequently. In this data set, there are no repeating values, so there is no mode.
4. **Range**: The range is the difference between the maximum and minimum values, calculated as 100 - 2 = 98. The range provides insight into the spread of the data but does not represent a measure of central tendency.
Given these calculations, the **median** (4.5) is the best measure of center for this data set, as it better represents the typical number of pencils used by students without being affected by the outlier.
**Answer: Median**
1. **Mean**: The mean is calculated by adding all the values together and dividing by the count of values.
\[
\text{Mean} = \frac{2 + 3 + 4 + 5 + 6 + 100}{6} = \frac{120}{6} = 20
\]
The mean (20) is heavily influenced by the outlier (100) and does not accurately reflect the typical number of pencils used by most students.
2. **Median**: The median is the middle value when the data is ordered. For an even number of observations, it is the average of the two middle values.
Ordered data: 2, 3, 4, 5, 6, 100.
\[
\text{Median} = \frac{4 + 5}{2} = 4.5
\]
The median (4.5) is more representative of the typical usage since it is not influenced by the outlier.
3. **Mode**: The mode is the value that appears most frequently. In this data set, there are no repeating values, so there is no mode.
4. **Range**: The range is the difference between the maximum and minimum values, calculated as 100 - 2 = 98. The range provides insight into the spread of the data but does not represent a measure of central tendency.
Given these calculations, the **median** (4.5) is the best measure of center for this data set, as it better represents the typical number of pencils used by students without being affected by the outlier.
**Answer: Median**