Unlike finding a single average, where we used a one-column list of numbers, to find a weighted average we need two sets of numbers. For the purpose of this example, we’ll assume the items are shipments of tonic, dealing with a number of cases and the price per case.  For this example, we’ll include column labels. Enter the label “Price Per Case” in cell A1 and “Number of Cases” in cell B1. The first shipment was for 10 cases at $20 per case. Enter “$20” in cell A2 and “10” in cell B2. Demand for tonic increased, so the second shipment was for 40 cases. However, due to demand, the price of tonic went up to $30 per case. Enter “$30” in cell A3 and “40” in cell B3. Because the price went up, demand for tonic went down, so the third shipment was for only 20 cases. With the lower demand, the price per case went down to $25. Enter “$25” in cell A4 and “20” in cell B4. Unlike figuring a single average, Excel doesn’t have a single function to figure a weighted average. Instead you’ll use two functions:  SUMPRODUCT. The SUMPRODUCT function multiplies the numbers in each row together and adds them to the product of the numbers in each of the other rows. You specify the range of each column; since the values are in cells A2 to A4 and B2 to B4, you’d write this as “=SUMPRODUCT(A2:A4,B2:B4)”. The result is the total dollar value of all three shipments. SUM. The SUM function adds the numbers in a single row or column. Because we want to find an average for the price of a case of tonic, we’ll sum up the number of cases that were sold in all three shipments. If you wrote this part of the formula separately, it would read “=SUM(B2:B4)”.  The average per-case price is the total value of the shipment divided by the total number of cases that were sold.  The total value of the shipments is 20 x 10 + 30 x 40 + 25 x 20, or 200 + 1200 + 500, or $1900. The total number of cases sold is 10 + 40 + 20, or 70. The average per case price is 1900 / 70 = $27.14.
++++++++++
One-sentence summary -- Enter the data you want to calculate a weighted average for. Enter the formula you need to calculate the weighted average. Since an average is determined by dividing a sum of all numbers by the number of numbers, we can combine the two functions into a single formula, written as “=SUMPRODUCT(A2:A4,B2:B4)/ SUM(B2:B4)”. Observe the result in the cell you entered the formula in.


Dogs usually show their depression through their body language. Seeing your dog show symptoms of depression might be alarming, but it's normal for them to show these symptoms after a loss. However, if your dog continues to show signs of depression for longer than a month or your dog is behaving out of character, talk to your vet to discuss potential treatment options. Here are the common signs of canine depression:  Refusing to eat Refusing to engage in activities he once enjoyed A change in sleeping patterns (either sleeping more than usual or being unable to settle) A change in habits (for example, he no longer gets up to greet you upon your return home) Grief is a natural process that needs to be worked through, and numbing those feelings with medication is not the way ahead unless the depression goes on for several weeks. If, however, you have done everything right and three or four weeks down the line your dog still seems depressed, then it is worth getting him assessed by a veterinarian. One option he or she may suggest is a dog appeasing pheromone. This is marketed as Adaptil, and is available as a plug-in diffuser that infuses the pheromone into the air, or on a collar worn close to the dog's skin. Adaptil contains a synthetic analogue of the chemical messenger (pheromone) given off by a nursing doggy mom that makes her pups feel safe and content. The dog breathes the pheromone in and it activates feelings of safety and wellbeing. While this is not a quick fix, it can help to decrease anxiety levels in a stressed dog, which can help him turn a new corner and become more well-adjusted. Another option your vet may suggest is a prescription anti-depressant, usually reserved for when all else fails and the symptoms have lasted over a month. The anti-depressant medication that is licensed for use in dogs is called clomipramine, which is a tricyclic antidepressant. This works by blocking the reuptake of certain neurotransmitters (serotonin and norepinephrine) in the brain, which has an anti-anxiety effect.  The dose is 1-2mg/kg twice a day by mouth. Thus a 30kg Labrador requires half an 80mg tablet, twice a day. This drug does have side effects such as a dry mouth and constipation, and can increase the plasma levels of certain anti-epileptic drugs and so should be used with caution in these cases.
++++++++++
One-sentence summary -- Learn to recognize canine depression. Talk to your vet about dog appeasing pheromones. Talk to your vet about prescription anti-depressants.


These reports are often free and available even when you’re not operating a plane. Check with your government’s aviation office or national weather service online. The Aviation Weather Center in the U.S., for instance, offers reports. Access reports at https://www.aviationweather.gov/metar. To request a report from the weather center, select a location. You can also choose a time period if you wish to access a past report. If you’re looking at a METAR report, you will see it listed at the beginning. There are other types of reports as well. Each type of report conveys different information. Distinguish between these types of reports to get weather details you need.  METAR reports are routine hourly reports. A new METAR report is issued at the end of each hour. SPECI indicates a special, unscheduled report. SPECI reports usually happen for special conditions like low visibility and thunderstorms. TAF means terminal aerodrome forecast. TAFs are similar to METARs but less common and used to provide a forecast for a general area. The ID tag will look something like KAFF. K represents a location in the US. The letters after it tell you which station the report came from. Every country and station has its own identifying code given out by the World Meteorlogical Organization.  KAFF, for instance, represents the Air Force Academy in Colorado. EGLL is the code for London Heathrow. E represents the UK, while GLL stands for Heathrow Airport. RJAA represents Tokyo Narita Airport. Look for a series of 6 numbers followed by a Z, such as 212355Z. The first pair of numbers stands for the day of the month. The rest of the code represents the time in Zulu, also called Universal or Greenwich Mean Time. Note that the report doesn’t include information about the month or year it was issued. For example, in 212355Z, 21 shows you that the report came on the 21st day of the month. It happened at 2355Z Zulu, which would be 1755, or 11:55 AM, in Colorado Springs. In the example, the modifier is indicated by COR. If it is present, the modifier information is always listed after the time and date. You can tell it apart from the rest of the report by how short it is. It also doesn’t have any numbers in it, unlike the codes before and after it.  AUTO means the report came from an automated station. COR tells you that someone corrected the initial report. A manual observer changed something the automated station got wrong. You won’t see a modifier for reports issued by a person. If no one is on duty at the station, then you may start seeing automated reports.
++++++++++
One-sentence summary --
Obtain a METAR report from an airport aviation center. Use the initial code letters to identify the type of report. Note the station identifier after the report type. Read the next numbers to find the report’s date and time. Look for a short phrase explaining how the report was modified.