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 which measure of center accurately represents the typical number of pencils used, let's analyze the data: 2, 3, 4, 5, 6, 100.
1. **Mean**:
The mean is calculated by adding all the values and dividing by the number of values.
\[
\text{Mean} = \frac{2 + 3 + 4 + 5 + 6 + 100}{6} = \frac{120}{6} = 20
\]
2. **Median**:
The median is the middle value when the data is arranged in order. The ordered list is 2, 3, 4, 5, 6, 100. Since there is an even number of values (6), the median will be the average of the third and fourth values:
\[
\text{Median} = \frac{4 + 5}{2} = \frac{9}{2} = 4.5
\]
3. **Mode**:
The mode is the value that appears most frequently. In this case, each value appears once, so there is no mode.
4. **Range**:
The range is the difference between the largest and smallest values:
\[
\text{Range} = 100 - 2 = 98
\]
Given the extreme outlier (100) in the data set, the **mean** (20) is considerably higher than the other values, which do not represent the typical usage. The **median** (4.5) is much more representative of the central tendency for this data set, as it is not affected by the outlier.
Thus, the best measure of center that represents the typical number of pencils used is the **Median**.
1. **Mean**:
The mean is calculated by adding all the values and dividing by the number of values.
\[
\text{Mean} = \frac{2 + 3 + 4 + 5 + 6 + 100}{6} = \frac{120}{6} = 20
\]
2. **Median**:
The median is the middle value when the data is arranged in order. The ordered list is 2, 3, 4, 5, 6, 100. Since there is an even number of values (6), the median will be the average of the third and fourth values:
\[
\text{Median} = \frac{4 + 5}{2} = \frac{9}{2} = 4.5
\]
3. **Mode**:
The mode is the value that appears most frequently. In this case, each value appears once, so there is no mode.
4. **Range**:
The range is the difference between the largest and smallest values:
\[
\text{Range} = 100 - 2 = 98
\]
Given the extreme outlier (100) in the data set, the **mean** (20) is considerably higher than the other values, which do not represent the typical usage. The **median** (4.5) is much more representative of the central tendency for this data set, as it is not affected by the outlier.
Thus, the best measure of center that represents the typical number of pencils used is the **Median**.