Small group project: Make a group of 3–4 members. Do at least one of the following: (i) Track daily sleep time of all your family members for a week. Daily sleep time includes night sleep, naps, and any sleep during the day. (a) Represent this on strips. (b) Put together the data of all your group members. Calculate the average and median sleep time of children, adults, elderly. (c) Share your findings and observations. (ii) When do schools start and end? On a weekday, Manoj’s school starts at 9:30 am and ends at 4:30 pm, i.e., 7 hours which include class time and breaks. Collect information on the daily timings of different schools for Grade 8, including class time and break time (the schools can be anywhere in the country. You can ask your neighbours, relatives, parents and friends to find out). Analyse and present the data collected.

Understand the Question Project Objective: Collect data on daily school timings for Grade 8 from different schools, including start time, end time, total duration, class time, and break time, then analyze the data using Mean and Median. Key Formulas: Median: Arrange the data in ascending order. For an even number of observations (): Time Conversion: Convert minutes to fractional/decimal hours for calculations (e.g., , , ). Part (ii) When do schools start and end? On a weekday, Manoj’s school starts at 9:30 am and ends at 4:30 pm, i.e., 7 hours which include class time and breaks. Collect information on the daily timings of different schools for Grade 8, including class time and break time (the schools can be anywhere in the country. You can ask your neighbours, relatives, parents and friends to find out). Analyse and present the data collected. Step 1 · Data Collection Data collected from six different schools for Grade 8: Step 2 · Organise and Sort Data Convert times into 24-hour decimal hours from midnight and arrange in ascending order: School Start Times (in hours from midnight): Raw: Sorted: School End Times (in hours from midnight): Raw: Sorted: Total School Duration (in hours): Raw: Sorted: Class Time (in hours): Raw: Sorted: Break Time (in hours): Raw: Sorted: Step 3 · Calculate the Mean Mean School Start Time: Mean School End Time: Mean Total School Duration: Mean Class Time: Mean Break Time: Step 4 · Calculate the Median Since , the median is the average of the and values: Median School Start Time: Median School End Time: Median Total School Duration: Median Class Time: Median Break Time: Step 5 · Findings and Observations Start and End Timings: Most schools start between 8:00 AM and 9:00 AM (Mean 8:35 AM, Median 8:37 AM) and end between 2:15 PM and 4:30 PM (Mean 3:10 PM, Median 3:07 PM). Total Duration: The total duration is highly consistent around to (Mean , Median ). Class and Break Times: Class time is centered at (both Mean and Median), while break time averages between and . Conclusion: The mean and median values are extremely close across all parameters, indicating minimal skewness or extreme outliers in Grade 8 school schedules. Answer > (ii) The data analysis of six schools shows: Start Time: , End Time: , Total Duration: , Class Time: , Break Time: , Common Mistakes Decimal Time Conversion Error: Treating minutes as decimals directly (e.g., writing 8:30 as instead of , or 8:15 as instead of ). Forgetting to Sort Before Median: Finding the median from the unsorted raw order rather than arranging the data in ascending order first. Median for Even Number of Observations: Picking only one central value instead of averaging the two middle values ( and ).

Data Handling (Mean and Median) | A

Question 2

Small group project: Make a group of 3–4 members. Do at least one of the following:

(i) Track daily sleep time of all your family members for a week. Daily sleep time includes night sleep, naps, and any sleep during the day.

(a) Represent this on strips.

(b) Put together the data of all your group members. Calculate the average and median sleep time of children, adults, elderly.

(ii) When do schools start and end? On a weekday, Manoj’s school starts at 9:30 am and ends at 4:30 pm, i.e., 7 hours which include class time and breaks. Collect information on the daily timings of different schools for Grade 8, including class time and break time (the schools can be anywhere in the country. You can ask your neighbours, relatives, parents and friends to find out). Analyse and present the data collected.

Solution

Understand the Question

Project Objective: Collect data on daily school timings for Grade 8 from different schools, including start time, end time, total duration, class time, and break time, then analyze the data using Mean and Median.
Key Formulas:
- $\text{Mean} = \dfrac{\text{Sum of all observations}}{\text{Total number of observations}}$
- Median: Arrange the data in ascending order. For an even number of observations ( $n = 6$ ): $\text{Median} = \dfrac{\left(\frac{n}{2}\right)^{\text{th}} \text{value} + \left(\frac{n}{2} + 1\right)^{\text{th}} \text{value}}{2} = \dfrac{3^{\text{rd}} \text{value} + 4^{\text{th}} \text{value}}{2}$
Time Conversion: Convert minutes to fractional/decimal hours for calculations (e.g., $15\text{ min} = 0.25\text{ h}$ , $30\text{ min} = 0.5\text{ h}$ , $45\text{ min} = 0.75\text{ h}$ ).

Step 1 · Data Collection

Data collected from six different schools for Grade 8:

\begin{array}{|c|c|c|c|c|c|} \hline \text{School} & \text{Start Time} & \text{End Time} & \text{Total Duration (hours)} & \text{Class Time (hours)} & \text{Break Time (hours)} \\ \hline \text{A} & \text{8:00 AM} & \text{2:30 PM} & 6.5 & 5.5 & 1.0 \\ \hline \text{B} & \text{8:30 AM} & \text{3:00 PM} & 6.5 & 5.0 & 1.5 \\ \hline \text{C} & \text{9:00 AM} & \text{3:30 PM} & 6.5 & 5.25 & 1.25 \\ \hline \text{D} & \text{8:45 AM} & \text{3:15 PM} & 6.5 & 5.25 & 1.25 \\ \hline \text{E} & \text{9:30 AM} & \text{4:30 PM} & 7.0 & 5.5 & 1.5 \\ \hline \text{F} & \text{7:45 AM} & \text{2:15 PM} & 6.5 & 5.0 & 1.5 \\ \hline \end{array}

Step 2 · Organise and Sort Data

Convert times into 24-hour decimal hours from midnight and arrange in ascending order:

School Start Times (in hours from midnight):
- Raw: $8.0, 8.5, 9.0, 8.75, 9.5, 7.75$
- Sorted: $7.75, 8.0, 8.5, 8.75, 9.0, 9.5$
School End Times (in hours from midnight):
- Raw: $14.5, 15.0, 15.5, 15.25, 16.5, 14.25$
- Sorted: $14.25, 14.5, 15.0, 15.25, 15.5, 16.5$
Total School Duration (in hours):
- Raw: $6.5, 6.5, 6.5, 6.5, 7.0, 6.5$
- Sorted: $6.5, 6.5, 6.5, 6.5, 6.5, 7.0$
Class Time (in hours):
- Raw: $5.5, 5.0, 5.25, 5.25, 5.5, 5.0$
- Sorted: $5.0, 5.0, 5.25, 5.25, 5.5, 5.5$
Break Time (in hours):
- Raw: $1.0, 1.5, 1.25, 1.25, 1.5, 1.5$
- Sorted: $1.0, 1.25, 1.25, 1.5, 1.5, 1.5$

Step 3 · Calculate the Mean

Mean School Start Time:

\begin{aligned} \text{Sum of start times} &= 7.75 + 8.0 + 8.5 + 8.75 + 9.0 + 9.5 = 51.5 \text{ hours} \\[0.6em] \text{Mean start time} &= \dfrac{51.5}{6} \approx 8.58 \text{ hours} \approx \text{8:35 AM} \end{aligned}

Mean School End Time:

\begin{aligned} \text{Sum of end times} &= 14.25 + 14.5 + 15.0 + 15.25 + 15.5 + 16.5 = 91.0 \text{ hours} \\[0.6em] \text{Mean end time} &= \dfrac{91.0}{6} \approx 15.17 \text{ hours} \approx \text{3:10 PM} \end{aligned}

Mean Total School Duration:

\begin{aligned} \text{Sum of durations} &= 6.5 + 6.5 + 6.5 + 6.5 + 7.0 + 6.5 = 39.5 \text{ hours} \\[0.6em] \text{Mean duration} &= \dfrac{39.5}{6} \approx 6.58 \text{ hours} \end{aligned}

Mean Class Time:

\begin{aligned} \text{Sum of class times} &= 5.0 + 5.0 + 5.25 + 5.25 + 5.5 + 5.5 = 31.5 \text{ hours} \\[0.6em] \text{Mean class time} &= \dfrac{31.5}{6} = 5.25 \text{ hours} \end{aligned}

Mean Break Time:

\begin{aligned} \text{Sum of break times} &= 1.0 + 1.25 + 1.25 + 1.5 + 1.5 + 1.5 = 8.0 \text{ hours} \\[0.6em] \text{Mean break time} &= \dfrac{8.0}{6} \approx 1.33 \text{ hours} \end{aligned}

Step 4 · Calculate the Median

Diagram 1

Since $n = 6$ , the median is the average of the $3^{\text{rd}}$ and $4^{\text{th}}$ values:

Median School Start Time: $\text{Median start time} = \dfrac{8.5 + 8.75}{2} = 8.625 \text{ hours} \approx \text{8:37 AM}$
Median School End Time: $\text{Median end time} = \dfrac{15.0 + 15.25}{2} = 15.125 \text{ hours} \approx \text{3:07 PM}$
Median Total School Duration: $\text{Median duration} = \dfrac{6.5 + 6.5}{2} = 6.5 \text{ hours}$
Median Class Time: $\text{Median class time} = \dfrac{5.25 + 5.25}{2} = 5.25 \text{ hours}$
Median Break Time: $\text{Median break time} = \dfrac{1.25 + 1.5}{2} = 1.375 \text{ hours}$

Step 5 · Findings and Observations

Start and End Timings: Most schools start between 8:00 AM and 9:00 AM (Mean $\approx$ 8:35 AM, Median $\approx$ 8:37 AM) and end between 2:15 PM and 4:30 PM (Mean $\approx$ 3:10 PM, Median $\approx$ 3:07 PM).
Total Duration: The total duration is highly consistent around $6.5\text{ hours}$ to $7.0\text{ hours}$ (Mean $= 6.58\text{ hours}$ , Median $= 6.5\text{ hours}$ ).
Class and Break Times: Class time is centered at $5.25\text{ hours}$ (both Mean and Median), while break time averages between $1.33\text{ hours}$ and $1.38\text{ hours}$ .
Conclusion: The mean and median values are extremely close across all parameters, indicating minimal skewness or extreme outliers in Grade 8 school schedules.

Answer

(ii) The data analysis of six schools shows:

Start Time: $\text{Mean} \approx \text{8:35 AM}$ , $\text{Median} \approx \text{8:37 AM}$
End Time: $\text{Mean} \approx \text{3:10 PM}$ , $\text{Median} \approx \text{3:07 PM}$
Total Duration: $\text{Mean} = 6.58\text{ h}$ , $\text{Median} = 6.5\text{ h}$
Class Time: $\text{Mean} = 5.25\text{ h}$ , $\text{Median} = 5.25\text{ h}$
Break Time: $\text{Mean} \approx 1.33\text{ h}$ , $\text{Median} = 1.375\text{ h}$

Common Mistakes

Decimal Time Conversion Error: Treating minutes as decimals directly (e.g., writing 8:30 as $8.3\text{ hours}$ instead of $8.5\text{ hours}$ , or 8:15 as $8.15\text{ hours}$ instead of $8.25\text{ hours}$ ).
Forgetting to Sort Before Median: Finding the median from the unsorted raw order rather than arranging the data in ascending order first.
Median for Even Number of Observations: Picking only one central value instead of averaging the two middle values ( $\frac{n}{2}^{\text{th}}$ and $(\frac{n}{2}+1)^{\text{th}}$ ).

Question 2

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