Math / Data & Statistics

QuestionA school principal wants to know what theme students prefer for the spring dance. There are 150 students in 6th grade, 200 students in 7th grade, and 187 students in 8th grade. Select all the representative samples that can help the principal draw conclusions about which themes the students prefer. The students in the 7th grade homerooms The same number of students from each grade whose names are randomly selected from a hat The members of student council Students who attended the winter dance 50 sixth graders, 67 seventh graders, and 62 eighth graders Assessment, Form A

Studdy Solution

STEP 1

What is this asking? Which groups of students would give the principal the best idea of what all students want for the spring dance theme? Watch out! Some groups might seem like a good idea at first, but they might not represent the whole student body fairly!

STEP 2

1. Representative Sample
2. Proportional Sample

STEP 3

A representative sample needs to include students from each grade level.
If we only ask 7th graders, we won't know what the 6th and 8th graders want!
The same goes for just asking homerooms or the student council.
Those groups might not represent everyone's preferences.
Students who went to the winter dance might have different preferences than those who didn't!

STEP 4

A truly representative sample also needs to be somewhat proportional to the size of each grade.
Let's look at the last option: $\text{50 sixth graders}$ , $\text{67 seventh graders}$ , and $\text{62 eighth graders}$ .

STEP 5

There are a total of $150 + 200 + 187 = 537$ students.

STEP 6

Let's calculate the proportion of each grade in the sample:
Sixth graders: $\frac{50}{150} \approx 0.33$
Seventh graders: $\frac{67}{200} \approx 0.34$
Eighth graders: $\frac{62}{187} \approx 0.33$

STEP 7

Since the proportions are roughly equal, this sample is representative of the entire student body!
Picking the same number of students from each grade randomly also works, as it ensures representation from all grades.

STEP 8

The best options are: picking the same number of students randomly from each grade, and the sample of $\text{50 sixth graders}$ , $\text{67 seventh graders}$ , and $\text{62 eighth graders}$ .

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Studdy Solution

STEP 1

What is this asking? Which groups of students would give the principal the best idea of what all students want for the spring dance theme? Watch out! Some groups might seem like a good idea at first, but they might not represent the whole student body fairly!

STEP 2

1. Representative Sample
2. Proportional Sample

STEP 3

STEP 4

A truly representative sample also needs to be somewhat proportional to the size of each grade.
Let's look at the last option: $\text{50 sixth graders}$ , $\text{67 seventh graders}$ , and $\text{62 eighth graders}$ .

STEP 5

There are a total of $150 + 200 + 187 = 537$ students.

STEP 6

Let's calculate the proportion of each grade in the sample:
Sixth graders: $\frac{50}{150} \approx 0.33$
Seventh graders: $\frac{67}{200} \approx 0.34$
Eighth graders: $\frac{62}{187} \approx 0.33$

STEP 7

Since the proportions are roughly equal, this sample is representative of the entire student body!
Picking the same number of students from each grade randomly also works, as it ensures representation from all grades.

STEP 8

The best options are: picking the same number of students randomly from each grade, and the sample of $\text{50 sixth graders}$ , $\text{67 seventh graders}$ , and $\text{62 eighth graders}$ .

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Studdy Solution

STEP 1

What is this asking? Which groups of students would give the principal the best idea of what *all* students want for the spring dance theme? Watch out! Some groups might seem like a good idea at first, but they might not represent the whole student body fairly!

STEP 2

1. Representative Sample2. Proportional Sample

STEP 3

STEP 4

STEP 5

There are a **total** of 150+200+187=537150 + 200 + 187 = 537150+200+187=537 students.

STEP 6

Let's calculate the **proportion** of each grade in the sample:Sixth graders: 50150≈0.33\frac{50}{150} \approx 0.3315050​≈0.33Seventh graders: 67200≈0.34\frac{67}{200} \approx 0.3420067​≈0.34Eighth graders: 62187≈0.33\frac{62}{187} \approx 0.3318762​≈0.33

STEP 7

Since the proportions are roughly equal, this sample is **representative** of the entire student body!Picking the same number of students from each grade randomly also works, as it ensures representation from all grades.

STEP 8

The best options are: picking the same number of students randomly from each grade, and the sample of 50 sixth graders\text{50 sixth graders}50 sixth graders, 67 seventh graders\text{67 seventh graders}67 seventh graders, and 62 eighth graders\text{62 eighth graders}62 eighth graders.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? Which groups of students would give the principal the best idea of what all students want for the spring dance theme? Watch out! Some groups might seem like a good idea at first, but they might not represent the whole student body fairly!

1. Representative Sample
2. Proportional Sample

There are a total of $150 + 200 + 187 = 537$ students.

Let's calculate the proportion of each grade in the sample:
Sixth graders: $\frac{50}{150} \approx 0.33$
Seventh graders: $\frac{67}{200} \approx 0.34$
Eighth graders: $\frac{62}{187} \approx 0.33$

Since the proportions are roughly equal, this sample is representative of the entire student body!
Picking the same number of students from each grade randomly also works, as it ensures representation from all grades.

The best options are: picking the same number of students randomly from each grade, and the sample of $\text{50 sixth graders}$ , $\text{67 seventh graders}$ , and $\text{62 eighth graders}$ .