6. Kurt recorded the daily temperature highs for a science project.

Daily Temperature Highs in [tex]${ }^{\circ} F$[/tex]

a. On how many days did he record the temperature?

b. What were the mean and median temperatures?

[tex]\[
\begin{array}{l}
27, 28, 28, 28, 29, 29, 30, 31 \\
\text{Median} = \frac{28 + 29}{2} = \frac{57}{2} = 28.5 \\
\text{Mean} = \frac{261}{9} = 29
\end{array}
\][/tex]

c. The temperature high on another day was included with the data. The new mean temperature changed to [tex]$30^{\circ} F$[/tex]. What was this temperature?

d. Find the new median temperature.



Answer :

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.

---

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.