Riddle for the Castanauts.

[Glacier]

JagXKR and Glacier were having a heated argument at the pub last night. JagXKR smashes his pint on the floor and exclaims, "you clueless *bleep*, you'd have to be living in a cave to not notice that this has been one of the top five hottest Julys on record!"

Glacier slams both of his pints down on JagXKR's head and retorts, "no, July was actually bang on the average around here!"

GordonH wonders over from the neighbouring table, "I couldn't help but overhear your conversation. I just want to point out that you're both right."

Question: GordonH is right, but how can this be?

[neilsimon]

JagXKR and Glacier were having a heated argument at the pub last night. JagXKR smashes his pint on the floor and exclaims, "you clueless *bleep*, you'd have to be living in a cave to not notice that this has been one of the top five hottest Julys on record!"

Glacier slams both of his pints down on JagXKR's head and retorts, "no, July was actually bang on the average around here!"

GordonH wonders over from the neighbouring table, "I couldn't help but overhear your conversation. I just want to point out that you're both right."

Question: GordonH is right, but how can this be?

Maybe I'm going about this too literally, but I'm a bit of a mathematician, so you'll forgive me.
Assuming by average you mean mean, if the mean is above the median, you can have an mean/average value only shared or beaten by a small number of samples, while the vast majority of samples are below average. This does tend to require some significant values on the high end of things to keep the average above the median.

[Glacier]

You are on the right track, sort of. I hinted at the answer in the "Weather Appreciation" thread. Basically, JagXKR was talking about the average daily maximum temperature, which was the 3rd highest ever recorded in Penticton and the 5th highest in Kamloops. 31.7C in Penticton and 32.2C in Kamloops.

For interest sake, the hottest ever for Penticton was 1985 when the average daily maximum was 32.6C. For Kamloops, the hottest ever was 1960 when the average daily maximum was 33.3C.

By contrast, Glacier was referring to the average daily lows. Penticton had an average daily low of 13.4C in July and Kamloops 14.1C. The normal or average daily lows for these two cities in July are 13.3C and 14.2C. Therefore, Penticton was 0.1C above average and Kamloops was 0.1C below average. So Glacier was also right about July being average, though it looks like he was trying to get off on a technicality so to speak since no one really cares how cold it is at night when everyone is sleeping.

Again, for interest sake, the hottest ever for Penticton was 1998 at 15.8C; for Kamloops it was also 1998 at 17.1C. The coldest was 1954 at 10.4C and at both places.

[neilsimon]

You are on the right track, sort of. I hinted at the answer in the "Weather Appreciation" thread. Basically, JagXKR was talking about the average daily maximum temperature, which was the 3rd highest ever recorded in Penticton and the 5th highest in Kamloops. 31.7C in Penticton and 32.2C in Kamloops.

By contrast, Glacier was referring to the average daily lows. Penticton had an average daily low of 13.4C in July and Kamloops 14.1C. The normal or average daily lows for these two cities in July are 13.3C and 14.2C. Therefore, Penticton was 0.1C above average and Kamloops was 0.1C below average. So Glacier was also right about July being average, though it looks like he was trying to get off on a technicality so to speak since no one really cares how cold it is at night when everyone is sleeping.

Ah yes, a different solution, and one I missed. Good one!

[Glacier]

I ripped out all my carpet, and replaced it with hardwood, tile, and laminate. Now, when the project is done, my floor space has been reduce by 45 sq. ft.

How did this happen?

[Queen K]

You installed baseboards?

Did I cheat?

[GordonH]

I ripped out all my carpet, and replaced it with hardwood, tile, and laminate. Now, when the project is done, my floor space has been reduce by 350 sq. ft.

How did this happen?

Your mother in law took over 18×19.445 room. lol

[Glacier]

You installed baseboards?

Did I cheat?

Yes, and yes! You win... you cheater!

[GordonH]

My guess was based on much larger sq footage.

[Glacier]

My guess was based on much larger sq footage.

Ya, that was typo. My MIL is not that large, FYI.

[GordonH]

My guess was based on much larger sq footage.

Ya, that was typo. My MIL is not that large, FYI.

My bad Glacier, I wasn't saying your MIL was that big.... just you were giving her large room of your home.

[Glacier]

Queen K wanted to conduct an evil experiment on some Castanutters, so she got a couple of volunteers who thought they were smart enough to determine which of them was downriver from the other. If they could answer that simple question within three tries, they could win $1,000,000.

GordonH and Glacier were blind folded and dumped off at the banks of the Fraser River some 163 km apart. Glacier was stationed just south of Quesnel and GordonH just south of Lillooet. Both were given fancy equipment to measure the volume of the river and cell phones for communicating. Both of these geniuses got to work, and concluded that Glacier was downriver from GordonH. Queen K laughed, and said, "sorry guys, try again!" They were blind folded again the next day, and placed at different spots along the river, and conducted the same experiment, and came to the same wrong conclusion. They had only one more chance, so they tested and retested the profile of the river such that they could get an accurate flow rate measurement. And yet again, they got the question wrong, missing out of the one million dollar prize.

Why?

[Queen K]

Because it's two men and not two women?

[Glacier]

Because it's two men and not two women?

Ha ha, but wrong... Here's a graph of the stream flows to help solve the riddle. Other Castanutters also measured the flow rates at various spots along the river. Kgcayenne took Hope, neilsimon took Prince George, LANDM took Shelly, looking4one took Hansard, Lady tehMa took McBride, and Bsuds took Red Pass on the way toward Jasper. We all got together and produce the graph below with our data. If you look closely there's something wrong with either GordieH or Glace... or is there?

[Glacier]

Let's put it another way for you guys with another example. The water flowing out of Shuswap like is coming out at 197 m^3/s while the water going in is flowing at a rate of 260 m^3/s. Why is there more flowing in than out?