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

Answer 1

To determine the best measure of center for the given data set (2, 3, 4, 5, 6, 100), we can evaluate the mean, median, and mode:

1. **Mean**: This is calculated by summing all the values and dividing by the number of values.
\[
\text{Mean} = \frac{2 + 3 + 4 + 5 + 6 + 100}{6} = \frac{120}{6} = 20
\]
The mean is heavily influenced by the outlier (100), which skews it upwards.

2. **Median**: This is the middle value when the numbers are arranged in order. For an even number of observations, we take the average of the two middle numbers.
Arranging the data: 2, 3, 4, 5, 6, 100
The two middle numbers are 4 and 5.
\[
\text{Median} = \frac{4 + 5}{2} = \frac{9}{2} = 4.5
\]
The median is not affected by the outlier and gives a better central tendency representation.

3. **Mode**: The mode is the number that appears most frequently. In this case, each number appears only once, so there is no mode.

4. **Range**: This is the difference between the maximum and minimum values (100 - 2 = 98), but it's not a measure of center.

Given this information, **the median (4.5)** is the best representation of the typical number of pencils used, as it is not affected by the outlier and provides a better sense of the central tendency of the majority of the data.