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The image contains a set of questions based on the number of hours spent on remote learning by a group of students. Here's a breakdown of the questions along with the data provided:

**Given Data:**
Hours spent on remote learning:  
10, 15, 18, 12, 11, 7, 20, 10, 21, 19

**Questions:**
a. List the data in increasing order.  
b. Find the median (Q2) number of hours spent on remote learning.  
c. What does this indicate about the student's study habits?  
d. Calculate the D7 (7th decile) and P80 (80th percentile) of the survey.

---

Let's start answering these questions step-by-step.

### a. List the data in increasing order:
First, we need to arrange the given data in ascending order.

Sorted dataThe image contains a set of questions based on the number of hours spent on remote learning by a group of students. Here's a breakdown of the questions along with the data provided:

**Given Data:**
Hours spent on remote learning:  
10, 15, 18, 12, 11, 7, 20, 10, 21, 19

**Questions:**
a. List the data in increasing order.  
b. Find the median (Q2) number of hours spent on remote learning.  
c. What does this indicate about the student's study habits?  
d. Calculate the D7 (7th decile) and P80 (80th percentile) of the survey.

---

Let's start answering these questions step-by-step.

### a. List the data in increasing order:
First, we need to arrange the given data in ascending order.

Sorted   
7, 10, 10, 11, 12, 15, 18, 19, 20, 21

### b. Find the median (Q2) number of hours spent on remote learning:
To find the median (Q2), we need to locate the middle value in the sorted data. If the data set has an even number of values, the median is the average of the two middle values.

- Number of data points: 10 (even)
- Middle values: 12 and 15 (the 5th and 6th data points)

\[
\text{Median} = \frac{12 + 15}{2} = 13.5
\]

So, the median (Q2) is **13.5 hours**.

### c. What does this indicate about the student's study habits?
The median represents the central tendency of the data. A median of 13.5 hours suggests that half of the students spend more than 13.5 hours on remote learning in a week, while the other half spend less. This can indicate a moderate level of commitment to remote learning, where most students are likely spending a reasonable amount of time on their studies each week.

### d. Calculate for the D7 and P80:
- **D7 (7th Decile):** The 7th decile corresponds to the 70th percentile. To calculate this, we use the formula:
  \[
  D_7 = \left(\frac{7}{10}\right) \times (n+1)
  \]
  Where \(n\) is the number of data points.  
  \[
  D_7 = 0.7 \times 11 = 7.7
  \]
  The 7.7th value lies between the 7th and 8th data points, which are 18 and 19. Using linear interpolation:
  \[
  D_7 = 18 + 0.7(19 - 18) = 18.7
  \]
  So, **D7 = 18.7 hours**.

- **P80 (80th Percentile):** To calculate the 80th percentile:
  \[
  P_{80} = \left(\frac{80}{100}\right) \times (n+1)
  \]
  \[
  P_{80} = 0.8 \times 11 = 8.8
  \]
  The 8.8th value lies between the 8th and 9th data points, which are 19 and 20. Using linear interpolation:
  \[
  P_{80} = 19 + 0.8(20 - 19) = 19.8
  \]
  So, **P80 = 19.8 hours**.

---

Would you like more details or further explanations?  
Here are five related questions to expand your understanding:

1. How do we calculate the first quartile (Q1) for this data?
2. What is the interquartile range (IQR), and how can it be used to analyze data variability?
3. How do we calculate percentiles and deciles for grouped data?
4. What can the mode of this data set tell us about student behavior?
5. How would the calculations change if the data included outliers?

**Tip:** When calculating percentiles or deciles, ensure you use proper linear interpolation between the data points if the rank doesn't fall on a whole number.

Grade 10 Calungsod conducted a survey on the number of hours spent on remote learning in a week: 10, 15, 18, 12, 11, 7, 20, 10, 21, 19.

Explore how to calculate the median, 7th decile (D7), and 80th percentile (P80) based on a survey of hours spent on remote learning by Grade 10 students. Learn step-by-step how to arrange data, find central tendencies, and apply formulas for deciles and percentiles.

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