Question

Find the mean, the median, and the mode of the collection of numbers. $$-4,8,9,-6,-2,1$$

Short answer

The mean is 1, the median is -0.5, and there is no mode.

Step-by-step solution

Calculate the Sum

The sum of all numbers in the collection can be calculated as: -4 + 8 + 9 - 6 - 2 + 1 = 6.

Calculate the Mean

The mean of a collection of numbers can be found by dividing the sum of the numbers by the count of numbers. There are six numbers in the collection. Thus, the mean would be \( \frac{6}{6} = 1 \).

Arrange the numbers in ascending order

To find the median, we need to sort the collection of numbers from smallest to largest: -6, -4, -2, 1, 8, 9.

Find the Median

The median is the middle number in an ordered set. If there are an even number of items in the set, then the median is the mean of the two middle numbers. In this case, we have six numbers, so the median is the mean of the third and fourth numbers, -2 and 1. The median therefore is \( \frac{-2 + 1}{2} = -0.5 \).

Find the Mode

The mode is the number(s) that occurs most frequently in the data set. In this case, all numbers are unique, which means there is no mode.