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Lesson Example Discussion Quiz: Class Homework

Step-1

Title: Probability

Grade: 1400-a Lesson: S4-L3

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Suppose you have a dataset of students' ages and their corresponding heights. The table below shows the number of students in different age groups and their average heights: Calculate the weighted average height of the students in this dataset ?
2	Step	The weighted average height takes into account the number of students in each age group To calculate it, we multiply the average height of each age group by the number of students in that group, sum those products, and then divide by the total number of students.
3	Step	From the table you provided, we can calculate the weighted average height as follows: Multiply the average height of each age group by the number of students in that group, → \$(135 "cm" times 15 "students") = 2025 "cm"\$ → \$(145 "cm" times 20 "students") = 2900 "cm"\$ → \$(160 "cm" times 25 "students") = 4000 "cm"\$
4	Step	Sum the products	2025 cm + 2900 cm + 4000 cm = 8925 cm
5	Step	The total number of students	15 students + 20 students + 25 students = 60 students
6	Formula:	Weighted average height = \$("Sum of weighted terms")/("Total number of terms")\$
7	Step	The weighted average height is	\$(8925 "cm") / (60 "students")\$ = 148.75 cm
8	Step	Therefore, the weighted average height of the students in this dataset is approximately 148.75 cm.
9	Choice.A	This is the correct answer. It considers the number of students in each age group (weighting) when calculating the average height	148.75cm
10	Choice.B	This option is significantly lower than what we’d expect for the weighted average height. The average heights in the table (135cm, 145cm, 160cm) are already baseline averages for each age group. The weighted average considers the number of students, and because there are likely to be more students with heights closer to the initial averages, the overall weighted average wouldn’t be this low	123.50cm
11	Choice.C	This value is too low. Even the youngest age group (10-12) would likely have an average height significantly higher than 83.25cm. The weighted average would be a combination of all three age groups and wouldn’t be this low	83.25cm
12	Choice.D	This value is simply too low to be a realistic average height for any age group listed in the table (typically students in these ranges would be much taller than 60cm). It’s likely a result of a miscalculation or a misunderstanding of the scale used for height (e.g., centimeters vs meters)	60.00cm
13	Answer	Option	A
14	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Suppose you have a dataset of students' ages and their corresponding heights. The table below shows the number of students in different age groups and their average heights:
Calculate the weighted average height of the students in this dataset ?

Step

The weighted average height takes into account the number of students in each age group
To calculate it, we multiply the average height of each age group by the number of students in that group, sum those products, and then divide by the total number of students.

Step

From the table you provided, we can calculate the weighted average height as follows:
Multiply the average height of each age group by the number of students in that group,
→ \$(135 "cm" times 15 "students") = 2025 "cm"\$
→ \$(145 "cm" times 20 "students") = 2900 "cm"\$
→ \$(160 "cm" times 25 "students") = 4000 "cm"\$

Step

Sum the products

2025 cm + 2900 cm + 4000 cm = 8925 cm

Step

The total number of students

15 students + 20 students + 25 students = 60 students

Formula:

Weighted average height = \$("Sum of weighted terms")/("Total number of terms")\$

Step

The weighted average height is

\$(8925 "cm") / (60 "students")\$ = 148.75 cm

Step

Therefore, the weighted average height of the students in this dataset is approximately 148.75 cm.

Choice.A

This is the correct answer. It considers the number of students in each age group (weighting) when calculating the average height

148.75cm

Choice.B

This option is significantly lower than what we’d expect for the weighted average height. The average heights in the table (135cm, 145cm, 160cm) are already baseline averages for each age group. The weighted average considers the number of students, and because there are likely to be more students with heights closer to the initial averages, the overall weighted average wouldn’t be this low

123.50cm

Choice.C

This value is too low. Even the youngest age group (10-12) would likely have an average height significantly higher than 83.25cm. The weighted average would be a combination of all three age groups and wouldn’t be this low

83.25cm

Choice.D

This value is simply too low to be a realistic average height for any age group listed in the table (typically students in these ranges would be much taller than 60cm). It’s likely a result of a miscalculation or a misunderstanding of the scale used for height (e.g., centimeters vs meters)

60.00cm

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?