# Problem of the Week Problem B and Solution Bad Moon Rising

## Problem

On May 26, 2021, a total lunar eclipse may be seen in many parts of the world. The moon will gradually become darker and then take on a rusty red colour for only 14 minutes and 30 seconds.

Below is data on this and other recent total lunar eclipses.

Month and Year Duration (in minutes)
May 2003 $$52$$
Nov 2003 $$24$$
May 2004 $$76$$
Oct 2004 $$82$$
Mar 2007 $$74$$
Aug 2007 $$90$$
Month and Year Duration (in minutes)
Feb 2008 $$50$$
Dec 2010 $$74$$
Jun 2011 $$100$$
Dec 2011 $$52$$
Apr 2014 $$78$$
Oct 2014 $$60$$
Month and Year Duration (in minutes)
Apr 2015 $$12$$
Sept 2015 $$72$$
Jan 2018 $$76$$
Jul 2018 $$104$$
Jan 2019 $$62$$
May 2021 $$14.5$$
1. What are the mean and median durations of these 18 total lunar eclipses? (Since there is an even number of eclipses listed, recall that the median is the average of the middle two numbers when the data is arranged in order.)

2. Create a bar graph showing the durations of the total eclipses in one of the three columns of given data.

3. Look up the dates and durations of the next four total lunar eclipses.

## Solution

1. To calculate the mean duration, we first need to add up all the values from the table. When we do this, we get $$1152.5$$ minutes. Then we divide this sum by the number of values in the table, which is $$18$$. So the mean duration is $$1152.5 \div 18 \approx 64.03$$, or approximately $$64$$ minutes.

To calculate the median duration, we can start by writing all the durations in order from smallest to largest. $12, 14.5, 24, 50, 52, 52, 60, 62, 72, 74, 74, 76, 76, 78, 82, 90, 100, 104$ The middle two numbers are $$72$$ and $$74$$, so the median duration is the average of these two numbers, which is $$73$$. If the average isn’t immediately obvious, you can calculate it by adding $$72$$ and $$74$$ together, and then dividing the result by $$2$$ to get $$73$$.

2. Below is a bar graph for all the given data. (Check your chosen column.)

3. According to timeanddate.com, the next four total lunar eclipses and their durations are:

Date Duration
May 16, 2022 85 minutes
November 8, 2022 85 minutes
March 14, 2025 65 minutes
September 7, 2025 82 minutes