Wiki Page, Math 13 - Perez Sandbox : ANSWER(S): Module 4 – Histograms (4 of 4 discussion 3)

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2026-01-17T21:14:51-08:00

Here is the problem for your reference:

Students researching backpack weights gathered data from 45 elementary school children in the 3rd and 5th grades. The variable is “percent of body weight carried in the school backpack.” So a child who weighs 60 pounds and carries 9 pounds has a variable value of 15% (9 ÷ 60 = 0.15 = 15%). The American Chiropractic Association (ACA) recommends that children carry no more than 10% of their body weight.

Questions to answer:

When we analyze backpack weight as a percentage of body weight, how do 3rd and 5th graders compare? Are children in this study following the ACA recommendation?

Frequency of backpack weights

% of body weight carried in backpack

Third
graders

Fifth
graders

0-5% | 1 | 1
5-10% | 6 | 6
10-15% | 11 | 4
15-20% | 3 | 7
20-25% | 0 | 1
25-30% | 0 | 2
30-35% | 0 | 1
Totals | 21 | 22

Note: Left-hand end-points are included in each bin. So the 2nd bin contains students carrying 5% of their body weight.

Sample answer

Our observations:

3rd graders:

The typical range is 10% to 15% of body weight. About half (11 out of 21) of the 3rd graders fall into this range.

The overall range is about 0 to 20%.

Shape appears slightly skewed to the left.

67% (14 out of 21) of the 3rd graders are not following the ACA recommendations. These students are carrying more than 10% of their body weight.

5th graders:

There is a lot of variability with an overall range of about 0 to 35%.

Typical values also appear to vary widely between about 5% and 20%; 77% of the 5th graders fall within this range.

The distribution has a slight right skew with the upper 18% of the data (4 out of 22 = 18%) spread out between 20% and 35%. None of the 3rd graders carried this much.

68% (15 out of 22) of the 5th graders are not following the ACA recommendations. These students are carrying more than 10% of their body weight.

Sample Paragraphs:

(Note: There are many, many other good paragraphs. Also, you may have an entirely different thesis that is supported by the data. This is just a sample.)

In this study, students calculated backpack weight as a percentage of body weight for a sample of elementary school children. They compared 3rd graders to 5th graders.

They discovered that there is a lot of overlap in the distributions, due mainly to the large amount of variability among 5th graders. Third graders carried between about 0 and 20% of their body weight while fifth graders carried between 0 and 35% of their body weight.

Despite this overlap, there is some evidence that 3rd graders tend to carry a smaller percentage of their body weight and this measurement is more consistent for 3rd graders. Typical 3rd graders carried 10-15% of their body weight. Typical 5th graders varied more, carrying between about 5% and 20% of their weight with 4 students out of the 22 (18%, about one in five) carrying more than this. None of the 3rd graders carried more than 20% of their body weight.

The ACA recommends that students carry no more than 10% of their body weight in their school backpack. Roughly the same percentage of students (about 67-68%) in each grade did not meet the ACA recommendations.

Tips for evaluating your answer and providing feedback to your peers:

1. Do you have a thesis that compares the two groups?

2. Is the context of the data clear to the reader (individuals, variable with units)?

3. Did you synthesize your observations into paragraphs that compare the groups in ways that support your thesis, as opposed to just listing your observations?

4. Did you incorporate concepts we have studied: shape, center, spread, relative frequencies (percentages)?

5. Did you use the benchmark recommendation by the ACA to compare the two groups?

6. Note that the variable here is a percentage. Don’t confuse the variable “percent of body weight carried” with the relative frequency, which is the percentage of children within each interval. Did you avoid this confusion?