6. The temperatures at Peponi Weather Station were recorded for 30 days as follows: $$ 29,22,23,26,35,38,45,42,30,20,34 $$, $$ 33,31,28,36,27,38,44,34,31,39,43 $$, $$ 40,25,35,37,30,29,28,26 $$. (a) Using a class width of 5 , make a frequency table of the this data. (b) Find the mean and median of the data.

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Let's address each part of the problem step by step.

---

### **Part (a): Frequency Table with Class Width of 5**

**Step 1: Identify the Range of Data**
- **Minimum Temperature**: 20°C
- **Maximum Temperature**: 45°C

**Step 2: Determine the Class Intervals**
Using a **class width of 5**, the classes will be:
1. **20 - 24**
2. **25 - 29**
3. **30 - 34**
4. **35 - 39**
5. **40 - 44**
6. **45 - 49**

**Step 3: Tally the Frequencies**
Let's sort and count the number of temperatures falling into each class.

| Temperature Data | Class Interval |
|------------------|-----------------|
| 20               | 20 - 24         |
| 22, 23           | 20 - 24         |
| 25               | 25 - 29         |
| 26, 26, 27       | 25 - 29         |
| 28, 28, 29, 29    | 25 - 29         |
| 30, 30           | 30 - 34         |
| 31, 31           | 30 - 34         |
| 33               | 30 - 34         |
| 34, 34           | 30 - 34         |
| 35, 35           | 35 - 39         |
| 36               | 35 - 39         |
| 37               | 35 - 39         |
| 38, 38           | 35 - 39         |
| 39               | 35 - 39         |
| 40               | 40 - 44         |
| 42               | 40 - 44         |
| 43               | 40 - 44         |
| 44               | 40 - 44         |
| 45               | 45 - 49         |

**Frequency Table:**

| **Class Interval (°C)** | **Frequency** |
|-------------------------|---------------|
| 20 - 24                 | 3             |
| 25 - 29                 | 8             |
| 30 - 34                 | 7             |
| 35 - 39                 | 7             |
| 40 - 44                 | 4             |
| 45 - 49                 | 1             |
| **Total**               | **30**        |

---

### **Part (b): Calculating the Mean and Median**

**Step 1: Calculating the Mean**

The **mean** is the average of all temperature values.

$$
\text{Mean} = \frac{\text{Sum of all temperatures}}{\text{Number of days}}
$$

First, sum all the temperatures:

$$
29 + 22 + 23 + 26 + 35 + 38 + 45 + 42 + 30 + 20 + 34 + 33 + 31 + 28 + 36 + 27 + 38 + 44 + 34 + 31 + 39 + 43 + 40 + 25 + 35 + 37 + 30 + 29 + 28 + 26 = 978
$$

Then, divide by the number of days (30):

$$
\text{Mean} = \frac{978}{30} = 32.6 \, °C
$$

**Step 2: Determining the Median**

The **median** is the middle value when the data is ordered. Since there are an even number of observations (30), the median is the average of the 15th and 16th values.

**Ordered Data:**

20, 22, 23, 25, 26, 26, 27, 28, 28, 29, 29, 30, 30, 31, **31**, **33**, 34, 34, 35, 35, 36, 37, 38, 38, 39, 40, 42, 43, 44, 45

- **15th value**: 31
- **16th value**: 33

$$
\text{Median} = \frac{31 + 33}{2} = 32 \, °C
$$

---

### **Final Answers**

**(a) Frequency Table:**

| **Temperature Range (°C)** | **Frequency** |
|----------------------------|---------------|
| 20 – 24                    | 3             |
| 25 – 29                    | 8             |
| 30 – 34                    | 7             |
| 35 – 39                    | 7             |
| 40 – 44                    | 4             |
| 45 – 49                    | 1             |

**(b) Calculations:**

- **Mean Temperature**: **32.6°C**
- **Median Temperature**: **32°C**
**Frequency Table:** | **Temperature Range (°C)** | **Frequency** | |----------------------------|---------------| | 20 – 24 | 3 | | 25 – 29 | 8 | | 30 – 34 | 7 | | 35 – 39 | 7 | | 40 – 44 | 4 | | 45 – 49 | 1 | **Mean Temperature:** 32.6°C **Median Temperature:** 32°C

The temperatures at Peponi Weather
Station were recorded for 30 days as
follows:
,
,
.
(a) Using a class width of 5 , make a
frequency table of the this data.
(b) Find the mean and median of the data.

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Temperature Range (°C)	Frequency
20 – 24	3
25 – 29	8
30 – 34	7
35 – 39	7
40 – 44	4
45 – 49	1

The temperatures at Peponi Weather Station were recorded for 30 days as follows: , , . (a) Using a class width of 5 , make a frequency table of the this data. (b) Find the mean and median of the data.