North Math ONLY -
This blog assignment is due no later than January 28th!
Ms. Saarinen’s dad has always been a hockey fan and has decided to take the family to go visit the Hockey Hall of Fame in Toronto, Canada. Ms. Saarinen wasn’t sure she wanted to make the trip because as you know, she doesn’t like the cold weather. Ms. Saarinen asked her math students to help her find the average temperature in Toronto to help her prepare for the trip.
The average daily temperatures (in Fahrenheit) in Toronto for the previous two weeks are:
+6, -1, 0, -2, +4, -1, -1, -9, -6, -9, -12, -2, 0, and +3.
1. What is the range of the data?
2. What is the median temperature?
3. What is the mean temperature?
4. What is the mode temperature?
5. How would the mean change if the next day’s temperature of +7 was included in the data?
6. Suppose Ms. Saarinen was told that the average temperature in Toronto for one week in December was -2 degree Fahrenheit. She could read the temperatures for six of the temperatures on the newspaper, but the last temperature was smudged by someone’s greasy fingers. The six temperatures she could read were -7, +3, -5, 0, +4, and -1. What is the missing temperature?
Assignment - In your comment remember to include the following:
* your name (first name and last initial)
* your class
* the answer to the problem – there are SIX parts – be sure to include every part and number the solutions
* an explanation that includes the strategy you used to solve.
* is there another way to solve the problem?
* any additional thoughts you have about the problem(s)
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14 comments:
Sarah Ru. North
1.+6-(-12)= +18
2.-12,-9,-9,-6,-2,-2,-1,-1,-1,0,0,+ 3,+4,+6 The median is -1.
3.-12+(-9)= -21+(-9)= -30+(-6)= -36+(-2)= -38+(-2)= -40+(-1)=-41+(-1)=-42+(-1)= -43+3= -40+4= -36+6= -30/12= -2.5 The mean is -2.5.
4.The mode temperature is -1 because it appears 3 times.
5.-30+7= -23/13= -1.77 The mean would be -1.77
6.-7+3= -4+(-5)=-9+4= -5+(-1)= -6 -14/7= -2 -6+(-8)= -14/2+ -7 The missing number would be -8.
Noah H. North Math
1. The range of the data is 18. I got this number by finding the absolute value of the largest and smallest numbers. The absolute value of -12 is 12, and the AV of +6 is 6. 12 + 6 = 18.
2. The median temperature is -1.5. I got this number by putting the numbers in order from smallest to largest. This would be as follows, -12, -9, -9, -6, -2, -2, -1, -1, -1, 0, 0, 3, 4, and 6. Then I crossed out all of the numbers in order, leaving me with -2 and -1. To get a median, I have to find the number right in between these two, or -1.5.
3. The mean temperature is -2.5. I got this number by adding up every number, then dividing by how many numbers there were. Adding all of the negative numbers gives you -43, and adding all of the positives gives you 13. Adding the total of the positives and the negatives gives you -30. Then I divided -30 by 12, getting me a total of -2.5.
4. The mode temperature is -1. This was the 1 temperature that appeared in the data 3 times.
5. If the next day’s temperature of 7 was included in the data, then the negative total would remain the same, but the positive total would now be 20. Adding the positives to the negatives would total -23. Then you would divide this number by 13 (accounting for the new number), giving you a new mean of approx. -1.77
6. The missing temperature is +8. To find this temperature, you multiply -2 by 7 (since there were 7 numbers) to get -14. Then you subtract all of the given temperatures (to counteract the adding). This will get you -8, and since you had to start with 0, the missing variable is 8.
I used the “work backwards” strategy for #6, but for all of the others, I made a number list and/or remembered a strategy that I had used in previous problems. Both were very helpful in this problem. Another way to solve the problem would be to use or draw a table, or make an organized list. Both of these strategies came to mind when reading this problem.
In conclusion, this problem was too easy. Although this is the work we are doing now in class, it was not hard enough to give me any challenge, and I am sure that my fellow Advanced Math classmates will feel the same.
Mollie R
NORTH
1. The range is -6° F. I got this answer by subtracting the lowest number from the highest number. This is the only way to solve it. I wanted to know if there is another way of solving the range.
2. The median of the set of numbers is -1°F. I got this answer by putting the numbers in order from least to greatest and then I crossed out the end numbers until there was only one number left. This is also the only way to solve this. I was wondering if there was another way to also find the Median.
3.The mean of the data is -2.14. I got this answer by adding all the numbers together and dividing it by 14, how many temperatures there were. I. rounded to the nearest hundredth. This is the only way to solve the mean. I was wondering if there was another way to solve it and why do people use the other ways more then this way.
4. The mode is -1. I looked at all the data and saw which number came most frequently and got my answer. This is the only way to solve it. I am wondering if you have two numbers that are the same in frequency if you get the average or do you put the two numbers down.
5. If a positive 6 was added, the mean would increase to -1.53. I added all the numbers together and then divided by 15. This is the only known way to do it.
6. The seventh number is -8. I solved this by multiplying 7 by -2 and got -14. I then added the six numbers together and got -6. Then, I subtracted -6 from -14 and got -8. I cannot think of another way to do this. I was wondering if there was an easier way to solver this.
Boris Apple
North Math
1-26-11
The range in temperatures is 18 degrees Fahrenheit. I got this by finding the difference between the lowest and highest number.
The median temperature is -1 degrees. I figured this out by putting the numbers in order from smallest to largest and then crossing them out: small large small etc.
The mean temperature is -2 degrees. I added all the numbers up and divided them by the amount there were.
The mode is -1 degrees. I got this by seeing which number occurred most often.
If -7 was added to the list, only the decimal would change but the whole number mean would stay at -2.
The missing number is -3.5. I got this by guessing and checking to find the right answer.
THE END
+6, -1, 0, -2, +4, -1, -1, -9, -6, -9, -12, -2, 0, and +3.
1. What is the range of the data?
To find the range, you subtract the smallest amount from the largest. in this set of temperatures, the smallest amount is-12. the largest is +6. so 6--12
(or) 6+12= 18. so the range is 18.
2. What is the median temperature?
to find the median, first you must put all the numbers in order, and then cross them out one by one to find the "last one standing" so, the set would look like this:
-12, -9, -9, -6, -2, -2, -1, -1, -1, 0, 0, +3, +4, +6. then like this:
-/12/, -/9/, -/9/, -/6/, -/2/, -/2/, (-1), -/1/, -/1/, 0 , 0, +/3/, +/4/, +/6/. as you can see, there is tow negative ones as the median. BUT WAIT!!! we need one number. so we add -1 + -1 and get -2 and then divide that by two. and get -1. and now were done.
3. What is the mean temperature?
To find the mean, you must add up all the numbers and then divide the sum by the amount of numbers you just added. so, the sum of the set of numbers is -30. and there are 14 numbers so -30/14 = -2.14
4. What is the mode temperature?
The mode is the most occurring number. in this set of numbers the most occurring number is -1. so the mode is -1
5. How would the mean change if the next day’s temperature of +7 was included in the data?
well, if +7 was added then the sum would be -23, not -30. so -23/14= -1.64. so it would increase by 0.5
6. Suppose Ms. Saarinen was told that the average temperature in Toronto for one week in December was -2 degree Fahrenheit. She could read the temperatures for six of the temperatures on the newspaper, but the last temperature was smudged by someone’s greasy fingers. The six temperatures she could read were -7, +3, -5, 0, +4, and -1. What is the missing temperature?
Well, the sum of the six numbers is -6 and 7X-2=
-14, so the next number would be -8
because -6 = -8 = -14. and negative 14/7 = -2!
ANOTHER great problem ms Saarinen! and it was easy to complete! i did it in like fifteen minutes!
TRUE STORY!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Hello Ms Saarinen! I’m Jackson Kneath and I think I have a solution for the tempter problem in Toronto. Cold weather like that can be very stressful and I believe you already have enough stress dealing with your north math group.
1. The range of an equation is the distance from the smallest number to the largest. In this case the lowest temperature in the collected data is negative twelve. The largest temperature is positive six. This is very simple all I need to is add the absolute values together. Negative twelve’s absolute value is twelve. Positive six’s absolute value is six. Now I just add six and twelve and get eighteen. You could also just count the number between the two numbers and you would still get eighteen.
2. To find the median in this set of data I have to take all of the data and line it up from smallest or lowest to biggest or highest. I have to then go on and cross out a number from each side until I get to a middle number. When I did this I got negative one. If I came across two of them at the end I would have to find the mean between the two, but I didn’t so my answer would be negative one.
3. To find the mean in an equation you have to add up all of the data. I got negative thirty. Then you have to divide that by the number of data you have. There was fourteen pieces of data in my problem. I had to divide negative thirty by fourteen. I came up with 2.142. It goes on a lot longer but I will cut it to 2.14.
4. The mode in this situation would be negative one because there are three negative ones in the set of data. To find the mode all you have to do is find the number that comes up most frequently. If there are more than one number that come up the most you just have two modes and there are none that come up more than one then there are no modes. Finding the mode is very simple.
5. If the next temperature was seven degrees then the mean would be negative twenty seven degrees. All I did was take negative twenty-seven and divide that by fifteen. I got 1.53333 so I will just cut it to 1.53.
6. The last number would have to be negative eight because you need the mean to be negative two and when you add up all of the data with the negative eight it comes to negative fourteen. Then you divide that by the number of pieces of data, which is seven, and negative fourteen divided by seven equals negative two.
JACKSON KNEATH
Michaela G. North- Math
-Problem 1: The range for the Cold Integers is –6 degrees F. I used the strategy of first ordering the numbers from least to greatest. Then, I grabbed the lowest and greatest number and subtracted the lowest number from the greatest number. Since it was a negative and positive number that I was dealing with, I just did 6+-12 to get the answer of –6. I didn’t do subtraction because it would be difficult trying to do that. So that’s how I got the answer of –6 degrees F.
-Problem 2: The median of the Cold Integers is –1. I got –1 because I used the strategy of getting the numbers and ordering them from least to greatest. After, I worked my way inwards towards the middle, crossing out the numbers on my way towards the middle. For example, I would have –12, 6,9. So I would cross out the 9 and then the –12 to leave me with the number 3 as my median. That’s how I got –1 degrees F as my answer.
-Problem 3: The mean to the Cold Integers is –2.142857 and repeating degrees F. My strategy was to add up all the numbers and my answer that I got was –30. Then, since there’s a total of 14 numbers, I did 14/-30 and I got –2.142857 and repeating degrees F as my answer.
-Problem 4: The mode for the Cold Integers is –1 degrees F. I got this answer by using the strategy to put the numbers in order from least to greatest. Next, I looked at all the numbers and looked for the number(s) that occurred the most frequent. So when I did this, I saw that –1 occurred three times and all the others would either occur once or twice, so I knew that –1 degrees F was my answer.
-Problem 5: if you were to add an extra 7 for the degrees F for the next day, it would effect the mean because now you have 15 numbers to divide by and the new answer for the adding of all numbers will come to an answer of –23. So when you do 15/-23, you will get the answer of –1.53 and repeating for the 3 degrees F. Also, as you can see, the mean has gotten smaller ever since we have added just one extra number. Another strategy you could’ve done was just grab your answer from the first mean of when you just added the numbers and then minus 7 from it since it was a positive 7. Then, you could’ve divided your answer by 15.
-Problem 6: The missing number is 4 degrees F. I got this answer by adding up all the 6 numbers that the newspaper gave Ms. Saarinen. The total I got for that was –6. Since we are looking for one number and it needs to equal –2, I did 6-2 to get and answer of 4. Then, I had to decide if it was going to be positive or negative. So I did –6+-4 and got the answer of –10, so I knew that was wrong, which means that it has to be a positive which it is because it =-2 degrees F.
1.The range of the Fahrenheit temperatures +6, -1, 0, -2, +4, -1, -1, -9, -6, -9, -12, -2, 0, and +3 is -18 degrees Fahrenheit.
I got this as my answer by doing (-12-+6). In order to complete this subtraction problem, you have to use the method of Keep, Change, Change. So, I then got (-12) +-6 which would be -18. There is no other solution to the problem.
2.The median temperature of these temperatures is -1 degrees Fahrenheit.
To get this as my answer, I first put the numbers in order from least to greatest: -12,-9,-9,-6,-2,-2,-1,-1,-1,0,0,3,4,6. Then I crossed out each number from one end to the other, (-12 and 6, -9 and 4 and so on) Then I finally got to the middle which came out to be -1. There is no other solution to the problem.
3.The mean temperature is -2.14 degrees Fahrenheit.
I got this as my answer by adding up all the number which came up to -30. Then I divided -30 by how many numbers there are which is 14. When you divide -30 by 14, you get -2.14285714. I then rounded this to 2.14. There is no other solution to the problem.
4.The mode temperature is -1 degrees Fahrenheit.
I got this as my answer by looking at all the temperatures that were recorded. Since the mode temperature is the number that shows up the most. I noticed that -1 occurs 3 three times, and none of the other numbers do. There is no other solution to the problem.
5.If next day’s temperature was +7, the mean would change. The new mean would be -1.53 degrees Fahrenheit.
I got this as my answer because I added +7 to the total sum of all the temperatures I had got before. (-30) +7= 23. Then I divided 23 by 15 because that’s how many days would be recorded. After dividing, I got -1.53333333. I round it which got to my mean of -1.53 degrees Fahrenheit.
6.The missing temperature is -8 degrees Fahrenheit. There is no other solution to the problem.
To figure this problem out I first added up the numbers I already had. This came out to -6. Then I used guess and check. When I got to -8, I knew that if you added that to -6, you would get -14. To make sure this could be correct; I divided -14 by 7 and got -2. So, I knew this was my answer. There is no other solution to the problem.
Brittany S. North Math
1.The range of the Fahrenheit temperatures +6, -1, 0, -2, +4, -1, -1, -9, -6, -9, -12, -2, 0, and +3 is -18 degrees Fahrenheit.
I got this as my answer by doing (-12-+6). In order to complete this subtraction problem, you have to use the method of Keep, Change, Change. So, I then got (-12) +-6 which would be -18. There is no other solution to the problem.
2.The median temperature of these temperatures is -1 degrees Fahrenheit.
To get this as my answer, I first put the numbers in order from least to greatest: -12,-9,-9,-6,-2,-2,-1,-1,-1,0,0,3,4,6. Then I crossed out each number from one end to the other, (-12 and 6, -9 and 4 and so on) Then I finally got to the middle which came out to be -1. There is no other solution to the problem.
3.The mean temperature is -2.14 degrees Fahrenheit.
I got this as my answer by adding up all the number which came up to -30. Then I divided -30 by how many numbers there are which is 14. When you divide -30 by 14, you get -2.14285714. I then rounded this to 2.14. There is no other solution to the problem.
4.The mode temperature is -1 degrees Fahrenheit.
I got this as my answer by looking at all the temperatures that were recorded. Since the mode temperature is the number that shows up the most. I noticed that -1 occurs 3 three times, and none of the other numbers do. There is no other solution to the problem.
5.If next day’s temperature was +7, the mean would change. The new mean would be -1.53 degrees Fahrenheit.
I got this as my answer because I added +7 to the total sum of all the temperatures I had got before. (-30) +7= 23. Then I divided 23 by 15 because that’s how many days would be recorded. After dividing, I got -1.53333333. I round it which got to my mean of -1.53 degrees Fahrenheit. There is no other solution to the problem.
6.The missing temperature is -8 degrees Fahrenheit. There is no other solution to the problem.
To figure this problem out I first added up the numbers I already had. This came out to -6. Then I used guess and check. When I got to -8, I knew that if you added that to -6, you would get -14. To make sure this could be correct; I divided -14 by 7 and got -2. So, I knew this was my answer. There is no other solution to the problem.
Patrick M.
1/28/12
North
The answer for problem number one where you find the range by subtracting the lowest number from the largest is 18. The equation used is 6- -12 but by using the keep change, change it becomes 6+12 which equals 18. The answer for problem two is -1. Because if you line up the numbers from highest to lowest and take away one of the highest and one of the lowest you will eventually end up with one number and that number is -1. The mean for problem three is -2.14. If you add every number you get -30. Then you divide by fourteen and you get -2.14. The mode for problem four is -1. Because if you look at all the data then you’ll see that the number that appears most is -1. It comes up three times. For the mean of problem five is -1.53. IF you take all the data and put 7 into it then you add it all together to get -23 then you divide by 15 and get -1.53. The answer for the final question is -8. If you take -2 and multiply it by the number of numbers collected, in this case seven then you get -14. Then you add all the data together and you get -6 so you add -8 and that gives you a total of -14. These problem were hard and really mad you think but if you took your time and checked your math then you would get the answers.
Geneva Casalegno North Math
1. The answer to number one is 18 degrees Fahrenheit. I solved this problem by subtracting the minimum from the maximum. The minimum is -12 and the maximum is 6. 6-(-12) =18. 2. The answer to number two is -1degrees Fahrenheit. I solved this problem by putting all the numbers in order from smallest to largest. Then I crossed out one number from the top and bottom until I had two numbers. They were both -1 so the median temperature was -1. Another way to solve this problem would be to count all the numbers (14) and divide by two (7). If the total amount of numbers was odd then round the decimal up after dividing by two and find that number after putting all the numbers in order from least to greatest. If the total amount of numbers was even, then whatever number you got by dividing by two and the next higher number you would average to get the median. 3. The answer to number three is -2.14degrees Fahrenheit. I got my answer by adding up all the numbers (-30) and dividing by the amount of numbers in the set of data (14). 4. The answer to number four is -1 degrees Fahrenheit. I got my answer by putting all the numbers in order from least to greatest. Then I decide what number there are the most of. 5. The new mean would be -1.53 degrees Fahrenheit which is a difference of -.61 degrees Fahrenheit. I got my answer by adding up all the numbers (-23) and dividing by the amount of numbers there were in that set of data (15). To find how much different that number was from the original mean, I subtracted it (1.53) from the original mean (-2.14) to get my answer of -.61 degrees. 6. The missing temperature would be -8 degrees Fahrenheit. I found this answer by first adding up all the numbers to get -6. Then I multiplied -2 times 7 to get -14. I did that because there were 7 numbers in the set of data and -2 was the answer if you divided the numbers by 7. If you reverse that (multiply -2 times 7), you get the total amount the numbers add up to. Then I subtracted -6 from -14 to get the missing number (-8). I agree with Ms.Saarinen. The weather is really cold so I wouldn’t want to make the trip:).
Sarah Ricks
North Math
1. To get the range, I added -12 to 6, with an answer of -6 F.
2. To get the median, I first ordered all of the temperatures in order from least to greatest. Then I crossed off each one, from least to greatest to least again, until I got an answer of -1.
3. To get the mean, I first added all of the positive temperatures together, and then the negative temperatures. I added the total of the positives with the negatives, with a total of -30. I divided -30 by 16, the amount of temperature data, and got -1.875 F.
4. The mode, or most common number in the set of data was -1.
5. If the next day’s temperature was 7, then the new mean would be -6 F. All I did was add 7 to -30, with an answer of -27. Then I divided -27 by 17 and got -6 F.
6. If the average temperature in Toronto for one week was -2, with a data set of -7, 3, -5, 0, 4, and -1, then the last number in the set of data has to be -9 F. First, I added all of data together and got -6. Because the mean was -2, and there were 7 numbers in all in the data set, I multiplied -2 by 7 and got -14. Then I added -14 to -6 and got -20, and then added 7 to -20 to get -13. Then, using guess-and-check, I divided -13 by 7, then 6, and so on until -13/9=-2, so my answer was -9.
Alec D. North
1. 18 degrees
2.-1 degree
3.-2.14 degrees
4.-1 degree
5. It would increase by 1 degree.
6.-4 degrees
This is the only way to solve this problem.
Alan A
North math
1. The range of the data is -6. For this answer you simply have to subtract the highest number by the lowest number. There is no other way to solve this problem.
2. The median of the numbers is -0.5. For this answer you have to line up the numbers from highest to lowest value. Then you cross out a number until you are left with one or two numbers in the middle. If it is one number that number is the median if there are two numbers then the number in between the two is the median. As far as I know there is no other way to solve this problem.
3. The mean of the numbers is -2. I got this answer by adding up all of the numbers, which came up as -28. Then I divided that number by the number of numbers (14). There is, as I know no other way to solve this problem.
4. The mode of the numbers is -1. The mode of a group of numbers is the number that accurse the most. Since -1 occurred 3 times it appeared more Then any other number so I new it was the mode. There is no other way to solve this problem.
5. The mean would change from -2 to -1.4. This would happen because you are adding to the set of numbers as well as how many numbers there are. I got this answer by adding seven to the total of the 14 numbers then divided -21 by 15. There is no other way to answer this problem.
6. The missing number is -8. This problem I solved by first adding up all of the numbers, which added up to -6. I already new that the answer had to be divisible by seven because there was 7 numbers. Then I noticed the -2 as the total average so I knew that the total had to be -14. So I added -8 to the total of -6 and got -14. Then divided by 7 to get -2. I think there are more ways to solve this problem but cannot think of any thing else. I enjoyed these problems mostly because they were easier then a P.O.W.
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