Questions: Form 4 Homework Assignment #2 STATISTICS 1. The table below shows the grades of the top five students of form 4 F at a secondary school. Help the teacher work out the following information for her records. A. The mean mark for each student is corrected to one decimal place. B. The Median of the Averages. C. Which subject(s) could you find a grade representing a mode for the subject? If there is a mode, what is it? Students AG/SC ENGA MATH IT SS Hist INT/Sci RE Average --- --- --- --- --- --- --- --- --- --- AA 84 86 87 66 88 44 68 100 BZ 68 69 40 69 85 50 57 92 CC 73 71 36 72 92 42 83 99 DJ 77 86 74 78 69 92 80 100 ET 81 79 66 56 88 89 59 100 2. The table below shows the goals scored by a school's football team over a season of 20 games. Goals Scored Frequency --- --- 0 3 1 3 2 6 3 4 4 3 5 1 20 Use the table to find: A. The mean Goals scored by a school's football team B. The Median Goals scored by the team. C. The modal Goals scored by the team. 3. The table below shows the times taken by 144 runners at their local 5K park Run. A. Draw a histogram for the frequency distribution. (Use an appropriate scale of your own on the Vertical axis.) (Use a scale of 2 cm to represent 6 minutes on the horizontal axis) B. Use your chart drawn in part A to estimate the mode. (Appropriate markings must be shown on the chart to receive all marks.) Time (Mins) Frequency (F) --- --- 15-20 6 20-25 43 25-30 56 30-35 20 35-40 7 40-45 3 45-50 9 144 C. Add two new columns to the table and label them Midpoints and F X (i) Fill in the columns with the appropriate information. (ii) Hence or otherwise, find the mean minutes taken for the race.

Form 4 Homework Assignment #2 STATISTICS 1. The table below shows the grades of the top five students of form 4 F at a secondary school. Help the teacher work out the following information for her records. A. The mean mark for each student is corrected to one decimal place. B. The Median of the Averages. C. Which subject(s) could you find a grade representing a mode for the subject? If there is a mode, what is it? Students AG/SC ENGA MATH IT SS Hist INT/Sci RE Average --- --- --- --- --- --- --- --- --- --- AA 84 86 87 66 88 44 68 100 BZ 68 69 40 69 85 50 57 92 CC 73 71 36 72 92 42 83 99 DJ 77 86 74 78 69 92 80 100 ET 81 79 66 56 88 89 59 100 2. The table below shows the goals scored by a school's football team over a season of 20 games. Goals Scored Frequency --- --- 0 3 1 3 2 6 3 4 4 3 5 1 20 Use the table to find: A. The mean Goals scored by a school's football team B. The Median Goals scored by the team. C. The modal Goals scored by the team. 3. The table below shows the times taken by 144 runners at their local 5K park Run. A. Draw a histogram for the frequency distribution. (Use an appropriate scale of your own on the Vertical axis.) (Use a scale of 2 cm to represent 6 minutes on the horizontal axis) B. Use your chart drawn in part A to estimate the mode. (Appropriate markings must be shown on the chart to receive all marks.) Time (Mins) Frequency (F) --- --- 15-20 6 20-25 43 25-30 56 30-35 20 35-40 7 40-45 3 45-50 9 144 C. Add two new columns to the table and label them Midpoints and F X (i) Fill in the columns with the appropriate information. (ii) Hence or otherwise, find the mean minutes taken for the race.
Transcript text: Form 4 Homework Assignment #2 STATISTICS 1. The table below shows the grades of the top five students of form 4 F at a secondary school. Help the teacher work out the following information for her records. A. The mean mark for each student is corrected to one decimal place. B. The Median of the Averages. C. Which subject(s) could you find a grade representing a mode for the subject? If there is a mode, what is it? \begin{tabular}{|c|l|l|l|l|l|l|l|l|l|} \hline \multirow{3}{*}{ Students } & \multicolumn{8}{|c|}{ SUBJECTS } & Average \\ \cline { 2 - 10 } & \begin{tabular}{l} AG \\ SC \end{tabular} & ENGA & MATH & IT & SS & Hist & \begin{tabular}{l} INT \\ Sci \end{tabular} & RE & \\ \hline AA & 84 & 86 & 87 & 66 & 88 & 44 & 68 & 100 & \\ \hline BZ & 68 & 69 & 40 & 69 & 85 & 50 & 57 & 92 & \\ \hline CC & 73 & 71 & 36 & 72 & 92 & 42 & 83 & 99 & \\ \hline DJ & 77 & 86 & 74 & 78 & 69 & 92 & 80 & 100 & \\ \hline ET & 81 & 79 & 66 & 56 & 88 & 89 & 59 & 100 & \\ \hline \end{tabular} 2. The table below shows the goals scored by a school's football team over a season of 20 games. \begin{tabular}{|r|r|} \hline Goals Scored & Frequency \\ \hline 0 & 3 \\ \hline 1 & 3 \\ \hline 2 & 6 \\ \hline 3 & 4 \\ \hline 4 & 3 \\ \hline 5 & 1 \\ \hline & 20 \\ \hline & \\ \hline \end{tabular} Use the table to find: A. The mean Goals scored by a school's football team B. The Median Goals scored by the team. C. The modal Goals scored by the team. 3. The table below shows the times taken by 144 runners at their local 5 K park Run. A. Draw a histogram for the frequency distribution. (Use an appropriate scale of your own on the Vertical axis.) (Use a scale of 2 cm to represent 6 minutes on the horizontal axis) B. Use your chart drawn in part A to estimate the mode. (Appropriate markings must be shown on the chart to receive all marks.) \begin{tabular}{|l|r|} \hline Time (Mins) & Frequency (F) \\ \hline $15-20$ & 6 \\ \hline $20-25$ & 43 \\ \hline $25-30$ & 56 \\ \hline $30-35$ & 20 \\ \hline $35-40$ & 7 \\ \hline $40-45$ & 3 \\ \hline $45-50$ & 9 \\ \hline & 144 \\ \hline \end{tabular} C. Add two new columns to the table and label them Midpoints and $\boldsymbol{F} \boldsymbol{X}$ (i) Fill in the columns with the appropriate information. (ii) Hence or otherwise, find the mean minutes taken for the race.
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Solution

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Solution Steps

Step 1: Calculate the mean mark for each student

The mean mark for each student is calculated by summing their marks and dividing by the number of subjects.

For AA: \[ \text{Mean} = \frac{84 + 86 + 87 + 66 + 88 + 44 + 68 + 100}{8} = \frac{623}{8} = 77.875 \approx 77.9 \]

For BZ: \[ \text{Mean} = \frac{68 + 69 + 40 + 69 + 85 + 50 + 57 + 92}{8} = \frac{530}{8} = 66.25 \approx 66.3 \]

For CC: \[ \text{Mean} = \frac{73 + 71 + 36 + 72 + 92 + 42 + 83 + 99}{8} = \frac{568}{8} = 71 \approx 71.0 \]

Step 2: Calculate the median of the averages

The averages for the students are: \[ 77.9, 66.3, 71.0, 84.5, 77.3 \] Sorting these values: \[ 66.3, 71.0, 77.3, 77.9, 84.5 \] The median is the middle value: \[ \text{Median} = 77.3 \]

Step 3: Determine the mode for each subject

We need to find the mode for each subject by checking the frequency of each grade.

For AG: \[ \text{Grades: } 84, 68, 73, 77, 81 \quad (\text{No mode}) \]

For ENGA: \[ \text{Grades: } 86, 69, 71, 86, 79 \quad (\text{Mode: } 86) \]

For MATH: \[ \text{Grades: } 87, 40, 36, 74, 66 \quad (\text{No mode}) \]

Final Answer

Step 1: Calculate the mean mark for each student

For AA: \[ \text{Mean} = 77.9 \]

For BZ: \[ \text{Mean} = 66.3 \]

For CC: \[ \text{Mean} = 71.0 \]

Step 2: Calculate the median of the averages

\[ \text{Median} = 77.3 \]

Step 3: Determine the mode for each subject

For ENGA: \[ \text{Mode: } 86 \]

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