The amount of time (minutes) a sample of students spent on online social media in a 4-hour window is organized in a frequency distribution with 7 class intervals. The class intervals are 0 to < 10, 10 to < 20, ..., 60 to < 70. The number of observations (frequencies) for the classes are 4, 9, 19, 18, 15, 9, and 4 respectively.
a. Complete the following frequency table for the distribution showing frequency, relative frequency, cumulative frequency, and cumulative relative frequencies.
Round to four decimal places when necessary
Class Interval	Frequency	Relative Frequency	Cumulative Frequency	Cumulative Relative Frequency
0 to < 10	
4
0.0513
4
0.0513
10 to < 20	
9
0.1154
13
0.1667
20 to < 30	
19
0.2436
32
0.4103
30 to < 40	
18
0.2308
50
0.641
40 to < 50	
15
0.1923
65
0.8333
50 to < 60	
9
0.1154
74
0.9487
60 to < 70	
4
0.0513
78
1
b. How many students spent between 40 and 60 minutes on social media?

Let's go through both parts of the problem.

### Part (a): Completing the Frequency Table

We are given the frequencies for each class interval, and we need to complete the relative frequency, cumulative frequency, and cumulative relative frequency columns.

#### Step-by-step process:

1. **Frequency Column**: The total number of observations is the sum of the frequencies.
   \[
   4 + 9 + 19 + 18 + 15 + 9 + 4 = 78
   \]
   So, the total sample size is 78.

2. **Relative Frequency**: For each class interval, divide the frequency by the total number of observations (78).
   \[
   \text{Relative Frequency} = \frac{\text{Frequency}}{78}
   \]
   Round these values to four decimal places.

3. **Cumulative Frequency**: Add the frequencies cumulatively as you go down the column.

4. **Cumulative Relative Frequency**: Add the relative frequencies cumulatively.

Now, let's fill in the table with the calculations:

\[
\begin{array}{|c|c|c|c|c|}
\hline
\text{Class Interval} & \text{Frequency} & \text{Relative Frequency} & \text{Cumulative Frequency} & \text{Cumulative Relative Frequency} \\
\hline
0 \, \text{to} \, < 10 & 4 & \frac{4}{78} = 0.0513 & 4 & 0.0513 \\
10 \, \text{to} \, < 20 & 9 & \frac{9}{78} = 0.1154 & 4 + 9 = 13 & 0.0513 + 0.1154 = 0.1667 \\
20 \, \text{to} \, < 30 & 19 & \frac{19}{78} = 0.2436 & 13 + 19 = 32 & 0.1667 + 0.2436 = 0.4103 \\
30 \, \text{to} \, < 40 & 18 & \frac{18}{78} = 0.2308 & 32 + 18 = 50 & 0.4103 + 0.2308 = 0.6410 \\
40 \, \text{to} \, < 50 & 15 & \frac{15}{78} = 0.1923 & 50 + 15 = 65 & 0.6410 + 0.1923 = 0.8333 \\
50 \, \text{to} \, < 60 & 9 & \frac{9}{78} = 0.1154 & 65 + 9 = 74 & 0.8333 + 0.1154 = 0.9487 \\
60 \, \text{to} \, < 70 & 4 & \frac{4}{78} = 0.0513 & 74 + 4 = 78 & 0.9487 + 0.0513 = 1.0000 \\
\hline
\end{array}
\]

### Part (b): Number of students who spent between 40 and 60 minutes on social media.

To find this, we need to look at the two class intervals from 40 to < 50 and 50 to < 60:

- Frequency for 40 to < 50 = 15
- Frequency for 50 to < 60 = 9

Thus, the total number of students who spent between 40 and 60 minutes on social media is:
\[
15 + 9 = 24 \, \text{students}.
\]

### Final Answer:

- **Part (a)**: The table is now complete.
- **Part (b)**: 24 students spent between 40 and 60 minutes on social media.

Would you like further details or have any questions?

---

Here are 5 relative questions you can explore:
1. What is the total time span covered by the class intervals?
2. How is cumulative relative frequency helpful in analyzing data trends?
3. What other visualization methods can be used to represent this data?
4. How would the results change if we divided the class intervals differently?
5. Can we estimate the average time spent using this frequency table?

**Tip**: When interpreting frequency distributions, cumulative frequencies help you see how data accumulates across intervals!

The amount of time (minutes) a sample of students spent on online social media in a 4-hour window is organized in a frequency distribution with 7 class intervals. The class intervals are 0 to < 10, 10 to < 20, ..., 60 to < 70. The number of observations (frequencies) for the classes are 4, 9, 19, 18, 15, 9, and 4 respectively. a. Complete the following frequency table for the distribution showing frequency, relative frequency, cumulative frequency, and cumulative relative frequencies. b. How many students spent between 40 and 60 minutes on social media?

Complete the frequency table for the time students spent on social media in a 4-hour window, including frequency, relative frequency, cumulative frequency, and cumulative relative frequency. Learn how many students spent between 40 and 60 minutes. This problem involves statistical concepts like frequency distribution and cumulative frequency, ideal for high school students (Grades 9-12).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation