Calculation of mean, median, and mode for the given numerical sequence.

Let's carefully go through the problem and verify the solution step by step for mean, median, and mode of the sequence:

Given Sequence:

19, 12, 9, 5, 8, 5, 25, 8

---

Step 1: Mean

The mean is the average of all numbers.

$$
\text{Mean} = \frac{\sum x}{N}
$$

Where $ N = 8 $ (total numbers).

Add all values:

$$
19 + 12 + 9 + 5 + 8 + 5 + 25 + 8 =
$$

Break it down:

- 19 + 12 = 31
- 31 + 9 = 40
- 40 + 5 = 45
- 45 + 8 = 53
- 53 + 5 = 58
- 58 + 25 = 83
- 83 + 8 = 91

So,

$$
\text{Mean} = \frac{91}{8} = 11.375
$$

✔ Correct

---

Step 2: Median

To find the median, arrange the numbers in ascending order:

Original: 19, 12, 9, 5, 8, 5, 25, 8
Sorted: 5, 5, 8, 8, 9, 12, 19, 25

There are 8 numbers → even count.

For even $ N $, the median is the average of the $ \frac{N}{2} $th and $ \left(\frac{N}{2} + 1\right) $th terms.

So:

- $ \frac{8}{2} = 4 $th term → 8
- $ \frac{8}{2} + 1 = 5 $th term → 9

$$
\text{Median} = \frac{8 + 9}{2} = \frac{17}{2} = 8.5
$$

✔ Correct

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Step 3: Mode

The mode is the number that appears most frequently.

Look at the sorted list:
5, 5, 8, 8, 9, 12, 19, 25

- 5 → appears 2 times
- 8 → appears 2 times
- All others appear once

Since both 5 and 8 appear twice (and more than any other number), this data set has two modes.

➡️ This is called a bimodal distribution.

So, Mode = 5 and 8

But in some contexts, if no number repeats more than others, we say there is no mode, but here since two numbers tie for most frequent, they are both modes.

✔ So, Mode = 5 and 8 (bimodal)

---

Final Answer:

- Mean: 11.375
- Median: 8.5
- Mode: 5 and 8 (bimodal)

---

✔ Summary:

| Measure | Value |
|--------|---------------|
| Mean | 11.375 |
| Median | 8.5 |
| Mode | 5 and 8 |

> Note: The original solution provided only calculated mean and median. It did not include the mode, which is required by the question. So, to complete the answer, you must add the mode as shown above.

Let me know if you'd like a visual or table format!