Sure! Let's solve each part of the question step-by-step.
### Part (a)
On how many days did he record the temperature?
Kurt recorded the daily temperature highs for a total of 8 days.
### Part (b)
What were the mean and median temperatures?
1. Mean Temperature:
We have the temperatures: [27, 28, 28, 28, 29, 29, 30, 31].
To find the mean, we sum up all the temperatures and then divide by the number of days.
The sum of the temperatures is 27 + 28 + 28 + 28 + 29 + 29 + 30 + 31 = 230.
Mean = Sum of temperatures / Number of days = 230 / 8 = 28.75
2. Median Temperature:
The median is the middle value in a sorted list.
Since there are 8 values, the median will be the average of the 4th and 5th values (when sorted):
Sorted list: [27, 28, 28, 28, 29, 29, 30, 31].
Median = (28 + 29) / 2 = 28.5.
### Part (c)
The temperature high on another day was included with the data. The new mean temperature changed to 30\(^{\circ}\)F. What was this temperature?
When another day's temperature high is included, the new mean temperature is 30\(^{\circ}\)F for 9 days (8 original days + 1 new day).
We know the original sum of temperatures: 230
Let \( x \) be the new temperature recorded.
New mean = (Sum of old temperatures + new temperature) / New number of days.
30 = (230 + x) / 9.
So, we solve for \( x \):
230 + x = 270
x = 270 - 230
x = 40
So, the temperature recorded on the new day was 40\(^{\circ}\)F.
### Part (d)
Find the new median temperature.
Now, including the new temperature, we have the temperatures: [27, 28, 28, 28, 29, 29, 30, 31, 40].
Sorted list: [27, 28, 28, 28, 29, 29, 30, 31, 40].
Since there are 9 values, the median will be the middle value (the 5th value in the sorted list):
New median temperature = 29°F.
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Summarizing the answers:
a. Kurt recorded the temperature for 8 days.
b. The mean temperature was 28.75°F and the median temperature was 28.5°F.
c. The new recorded temperature was 40°F after including another day.
d. The new median temperature is 29°F.
