A teacher collected data on the number of pencils used by students in a month. The data is:

Question

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 analyze each measure:

1. Mean: The mean is calculated by adding all the values and dividing by the number of values.

   • Mean = (2 + 3 + 4 + 5 + 6 + 100) / 6 = 120 / 6 = 20.
   • However, the mean is heavily influenced by the outlier (100), making it not representative of the typical values in the data set.

2. Median: The median is the middle value when the data is ordered.

   • The ordered data set is: 2, 3, 4, 5, 6, 100.
   • The median is the average of the two middle numbers (4 and 5), which is (4 + 5) / 2 = 4.5.
   • The median is not influenced by the outlier and provides a better center for the majority of the data.

3. Mode: The mode is the value that appears most frequently.

   • In this data set, all numbers appear only once, so there is no mode.

4. Range: The range is the difference between the maximum and minimum.

   • Range = 100 - 2 = 98, which does not provide a measure of central tendency.

Considering all options, the median (4.5) is the best representation of the typical number of pencils used by the students, as it is not affected by the outlier and reflects the central tendency of the majority of the data.

So, the best answer is Median.