In one three day weekend, the daily high temperature had a median value of 73. The mean temperature was 74.33 and the range of temperatures was 14. What were the three weekend daily high temperatures?
solve (x + 73 + x+14)/3 = 74.33
To find the three weekend daily high temperatures, we can use the information given and some mathematical equations.
1. We know that the mean temperature is 74.33. The mean is calculated by adding up all the temperatures and dividing by the number of temperatures. Let's say the three temperatures are A, B, and C. So, we can write the equation as:
(A + B + C) / 3 = 74.33
2. We also know that the range of temperatures is 14. The range is the difference between the highest and lowest temperatures. So, we can write the equation as:
max(A, B, C) - min(A, B, C) = 14
3. Finally, the median temperature is 73, which means it is the middle value when the temperatures are arranged in ascending order. So, we can say that the three temperatures when arranged in ascending order, will be either (A, 73, C) or (A, B, 73).
Now, let's solve these equations simultaneously:
From equation 1:
(A + B + C) / 3 = 74.33
(A + B + C) = 74.33 * 3
(A + B + C) = 223
From equation 2:
max(A, B, C) - min(A, B, C) = 14
Let's assume that A <= B <= C
C - A = 14
From the given median value, we can conclude:
C = 73 or A = 73
Case 1 - C = 73:
Substituting this in the previous equation, we get:
73 - A = 14
A = 73 - 14
A = 59
Substituting both A and C values in equation 1:
59 + B + 73 = 223
B + 132 = 223
B = 223 - 132
B = 91
So, when C = 73, the three temperatures are 59, 91, and 73.
Case 2 - A = 73:
Substituting this in the previous equation, we get:
C - 73 = 14
C = 73 + 14
C = 87
Substituting both A and C values in equation 1:
73 + B + 87 = 223
B + 160 = 223
B = 223 - 160
B = 63
So, when A = 73, the three temperatures are 73, 63, and 87.
Therefore, the three weekend daily high temperatures can be either 59, 91, and 73 or 73, 63, and 87.
To find the three daily high temperatures, we need to use the information given about the median, mean, and range of temperatures.
1. Let's start by finding the middle value or the median temperature. Since the median is given as 73, we know that one of the temperatures is 73.
2. The mean temperature is given as 74.33. The mean is calculated by summing up all the temperatures and dividing by the number of temperatures. So, if we multiply the mean temperature (74.33) by the number of temperatures (which is 3), we get the total sum of all the temperatures. In this case, that would be 74.33 * 3 = 223.
3. The range of temperatures is given as 14. The range is the difference between the highest and lowest temperatures. Therefore, if we subtract the range from the highest value (which is unknown), we should get the lowest value. So, we have highest temperature - range = lowest temperature. This gives us an equation: highest temperature - 14 = lowest temperature.
4. Now, we can solve for the highest and lowest temperatures using the information we have. Let's denote the unknown highest temperature as "x." Using the equation from the previous step, we can rewrite it as: x - 14 = lowest temperature.
5. We know that the median temperature is 73, so the lowest temperature cannot be higher than 73. Therefore, the lowest temperature is either 73 or greater.
6. Substituting the lowest temperature (73) into the equation from step 4, we get x - 14 = 73. By adding 14 to both sides of the equation, we find that x = 87.
7. Now we know that the highest temperature is 87, and the lowest temperature is 73.
So, the three weekend daily high temperatures are 73, 74.33, and 87.