Question 2

We will collect daily timings from different schools for Grade 8, then analyze this data by calculating the mean and median.

Step 1 — Data Collection

Our group has three members. We each collected information about school timings for Grade 8 from two different schools. We asked our relatives and friends to find this information. We recorded the school start time, end time, and then calculated the total school duration, class time, and break time for each school.

Here is the data we collected:

| School | Start Time | End Time | Total Duration (hours) | Class Time (hours) | Break Time (hours) | | :----- | :--------- | :------- | :--------------------- | :----------------- | :----------------- | | A | 8:00 AM | 2:30 PM | 6.5 | 5.5 | 1.0 | | B | 8:30 AM | 3:00 PM | 6.5 | 5.0 | 1.5 | | C | 9:00 AM | 3:30 PM | 6.5 | 5.25 | 1.25 | | D | 8:45 AM | 3:15 PM | 6.5 | 5.25 | 1.25 | | E | 9:30 AM | 4:30 PM | 7.0 | 5.5 | 1.5 | | F | 7:45 AM | 2:15 PM | 6.5 | 5.0 | 1.5 |

Step 2 — Organizing Data for Analysis

To calculate the mean and median, we first list the data for each category. We convert times to decimal hours for easier calculation. For example, 8:30 AM is $8.5$ hours, and 2:30 PM is $14.5$ hours.

• School Start Times (in hours from midnight): $8.0, 8.5, 9.0, 8.75, 9.5, 7.75$ Sorted: $7.75, 8.0, 8.5, 8.75, 9.0, 9.5$

• School End Times (in hours from midnight): $14.5, 15.0, 15.5, 15.25, 16.5, 14.25$ Sorted: $14.25, 14.5, 15.0, 15.25, 15.5, 16.5$

• Total School Duration (in hours): $6.5, 6.5, 6.5, 6.5, 7.0, 6.5$ Sorted: $6.5, 6.5, 6.5, 6.5, 6.5, 7.0$

• Class Time (in hours): $5.5, 5.0, 5.25, 5.25, 5.5, 5.0$ Sorted: $5.0, 5.0, 5.25, 5.25, 5.5, 5.5$

• Break Time (in hours): $1.0, 1.5, 1.25, 1.25, 1.5, 1.5$ Sorted: $1.0, 1.25, 1.25, 1.5, 1.5, 1.5$

Step 3 — Calculating the Mean

The mean is the average of all values in a data set. We find it by adding all values and dividing by the number of values.

• Mean School Start Time: $\text{Sum of start times} = 7.75 + 8.0 + 8.5 + 8.75 + 9.0 + 9.5$ $= 51.5 \text{ hours}$ $\text{Number of schools} = 6$ $\text{Mean start time} = \frac{51.5}{6}$

  $\boxed{8.58 \text{ hours (approx. 8:35 AM)}}$

• Mean School End Time: $\text{Sum of end times} = 14.25 + 14.5 + 15.0 + 15.25 + 15.5 + 16.5$ $= 91.0 \text{ hours}$ $\text{Mean end time} = \frac{91.0}{6}$

  $\boxed{15.17 \text{ hours (approx. 3:10 PM)}}$

• Mean Total School Duration: $\text{Sum of durations} = 6.5 + 6.5 + 6.5 + 6.5 + 7.0 + 6.5$ $= 39.5 \text{ hours}$ $\text{Mean duration} = \frac{39.5}{6}$

  $\boxed{6.58 \text{ hours}}$

• Mean Class Time: $\text{Sum of class times} = 5.0 + 5.0 + 5.25 + 5.25 + 5.5 + 5.5$ $= 31.5 \text{ hours}$ $\text{Mean class time} = \frac{31.5}{6}$

  $\boxed{5.25 \text{ hours}}$

• Mean Break Time: $\text{Sum of break times} = 1.0 + 1.25 + 1.25 + 1.5 + 1.5 + 1.5$ $= 8.0 \text{ hours}$ $\text{Mean break time} = \frac{8.0}{6}$

  $\boxed{1.33 \text{ hours}}$

Step 4 — Calculating the Median

The median is the middle value in a sorted data set. If there is an even number of values, the median is the average of the two middle values. We have 6 data points for each category, so we will average the 3rd and 4th values.

• Median School Start Time: Sorted data: $7.75, 8.0, \mathbf{8.5}, \mathbf{8.75}, 9.0, 9.5$ $\text{Median start time} = \frac{8.5 + 8.75}{2}$

  $\boxed{8.625 \text{ hours (approx. 8:37 AM)}}$

• Median School End Time: Sorted data: $14.25, 14.5, \mathbf{15.0}, \mathbf{15.25}, 15.5, 16.5$ $\text{Median end time} = \frac{15.0 + 15.25}{2}$

  $\boxed{15.125 \text{ hours (approx. 3:07 PM)}}$

• Median Total School Duration: Sorted data: $6.5, 6.5, \mathbf{6.5}, \mathbf{6.5}, 6.5, 7.0$ $\text{Median duration} = \frac{6.5 + 6.5}{2}$

  $\boxed{6.5 \text{ hours}}$

• Median Class Time: Sorted data: $5.0, 5.0, \mathbf{5.25}, \mathbf{5.25}, 5.5, 5.5$ $\text{Median class time} = \frac{5.25 + 5.25}{2}$

  $\boxed{5.25 \text{ hours}}$

• Median Break Time: Sorted data: $1.0, 1.25, \mathbf{1.25}, \mathbf{1.5}, 1.5, 1.5$ $\text{Median break time} = \frac{1.25 + 1.5}{2}$

  $\boxed{1.375 \text{ hours}}$

Step 5 — Findings and Observations

We have analyzed the school timings for Grade 8 students from six different schools.

• The average school start time is around 8:35 AM, and the median start time is around 8:37 AM. This shows most schools start between 8:00 AM and 9:00 AM.
• The average school end time is around 3:10 PM, and the median end time is around 3:07 PM. This means schools generally finish in the early afternoon.
• The average total school duration is about 6.58 hours, and the median duration is exactly 6.5 hours. This indicates that most schools have a similar total duration. Only one school (Manoj's school) had a longer duration of 7 hours.
• The average class time is 5.25 hours, which is also the median class time. This suggests a consistent amount of time dedicated to learning across schools.
• The average break time is about 1.33 hours, and the median break time is about 1.375 hours. This shows that students typically get between 1 hour and 1.5 hours of breaks during the school day.

Overall, we observe a good consistency in school timings for Grade 8 across the collected data. The mean and median values are quite close for all categories, which means there are no extreme outliers in our data set.

Answer

(ii) We collected daily timings for Grade 8 from six different schools. The data included start time, end time, total duration, class time, and break time. We calculated the mean and median for each category. The mean school start time was approximately 8:35 AM, and the median was 8:37 AM. The mean school end time was approximately 3:10 PM, and the median was 3:07 PM. The mean total school duration was 6.58 hours, with a median of 6.5 hours. Class time averaged 5.25 hours (median 5.25 hours), and break time averaged 1.33 hours (median 1.375 hours). Our findings show that most schools have similar timings and durations for Grade 8, with consistent class and break times.