Math / Data & Statistics

QuestionSimon plans to make gloves. One morning, Simon decided to carry out a survey to find the mean hand span of people in Wales.
He decided to sample systematically. He decided to sample from the first 240 people who pass him in the street during the morning.
He wanted to take 20 people's hand span measurements. Explain how Simon could use systematic sampling to obtain 20 measurements.

Studdy Solution

STEP 1

What is this asking? How can Simon pick 20 people out of 240 in a structured way? Watch out! Don't just pick 20 people randomly; there's a specific method called systematic sampling!

STEP 2

1. Calculate the sampling interval.
2. Determine the starting point.
3. Select the sample.

STEP 3

To figure out how many people Simon should skip between measurements, we divide the total number of people he'll see by the number of measurements he wants to take.
This is called the sampling interval.
It's like dividing a cake into equal slices!

STEP 4

So, Simon will see $240$ people and wants $20$ measurements.
The sampling interval is: $240 \div 20 = 12$

STEP 5

Simon needs to pick a random starting point within his sampling interval.
This makes sure everyone has a fair chance of being selected.
It's like spinning a wheel to pick a lucky number!

STEP 6

Since our sampling interval is $12$ , Simon should pick a random number between $1$ and $12$ .
Let's say he picks the number 7.

STEP 7

Now, Simon starts with the 7th person and measures their hand span.
Then, he adds the sampling interval of $12$ to find the next person.
It's like taking steps of a certain size!

STEP 8

The second person will be the $7 + 12 = 19$ th person.
The third person will be the $19 + 12 = 31$ st person, and so on.

STEP 9

Simon keeps adding $12$ to the previous number until he gets $20$ measurements.
This is systematic sampling in action!

STEP 10

Simon should select a random starting point between $1$ and $12$ .
Let's say he picks 7.
Then, he measures the hand span of every $12$ th person starting with the 7th** person.
So, he'll measure the 7th, 19th, 31st, and so on, until he has 20 measurements.

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Studdy Solution

STEP 1

What is this asking? How can Simon pick 20 people out of 240 in a structured way? Watch out! Don't just pick 20 people randomly; there's a specific method called systematic sampling!

STEP 2

1. Calculate the sampling interval.
2. Determine the starting point.
3. Select the sample.

STEP 3

To figure out how many people Simon should skip between measurements, we divide the total number of people he'll see by the number of measurements he wants to take.
This is called the sampling interval.
It's like dividing a cake into equal slices!

STEP 4

So, Simon will see $240$ people and wants $20$ measurements.
The sampling interval is: $240 \div 20 = 12$

STEP 5

Simon needs to pick a random starting point within his sampling interval.
This makes sure everyone has a fair chance of being selected.
It's like spinning a wheel to pick a lucky number!

STEP 6

Since our sampling interval is $12$ , Simon should pick a random number between $1$ and $12$ .
Let's say he picks the number 7.

STEP 7

Now, Simon starts with the 7th person and measures their hand span.
Then, he adds the sampling interval of $12$ to find the next person.
It's like taking steps of a certain size!

STEP 8

The second person will be the $7 + 12 = 19$ th person.
The third person will be the $19 + 12 = 31$ st person, and so on.

STEP 9

Simon keeps adding $12$ to the previous number until he gets $20$ measurements.
This is systematic sampling in action!

STEP 10

Simon should select a random starting point between $1$ and $12$ .
Let's say he picks 7.
Then, he measures the hand span of every $12$ th person starting with the 7th** person.
So, he'll measure the 7th, 19th, 31st, and so on, until he has 20 measurements.

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Studdy Solution

STEP 1

What is this asking? How can Simon pick 20 people out of 240 in a structured way? Watch out! Don't just pick 20 people randomly; there's a specific method called systematic sampling!

STEP 2

1. Calculate the sampling interval.2. Determine the starting point.3. Select the sample.

STEP 3

To figure out how many people Simon should skip between measurements, we **divide** the **total number of people** he'll see by the **number of measurements** he wants to take.This is called the **sampling interval**.It's like dividing a cake into equal slices!

STEP 4

So, Simon will see 240240240 people and wants 202020 measurements.The **sampling interval** is: 240÷20=12 240 \div 20 = 12 240÷20=12

STEP 5

Simon needs to pick a random starting point within his **sampling interval**.This makes sure everyone has a fair chance of being selected.It's like spinning a wheel to pick a lucky number!

STEP 6

Since our **sampling interval** is 121212, Simon should pick a random number between 111 and 121212.Let's say he picks the number **7**.

STEP 7

Now, Simon starts with the **7th** person and measures their hand span.Then, he adds the **sampling interval** of 121212 to find the next person.It's like taking steps of a certain size!

STEP 8

The second person will be the 7+12=197 + 12 = 197+12=19**th person.The third person will be the 19+12=3119 + 12 = 3119+12=31**st person, and so on.

STEP 9

Simon keeps adding 121212 to the previous number until he gets 202020 measurements.This is systematic sampling in action!

STEP 10

Simon should select a random starting point between 111 and 121212.Let's say he picks **7**.Then, he measures the hand span of every 121212**th person starting with the **7th** person.So, he'll measure the 7th, 19th, 31st, and so on, until he has 20 measurements.

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1. Calculate the sampling interval.
2. Determine the starting point.
3. Select the sample.

To figure out how many people Simon should skip between measurements, we divide the total number of people he'll see by the number of measurements he wants to take.
This is called the sampling interval.
It's like dividing a cake into equal slices!

So, Simon will see $240$ people and wants $20$ measurements.
The sampling interval is: $240 \div 20 = 12$

Simon needs to pick a random starting point within his sampling interval.
This makes sure everyone has a fair chance of being selected.
It's like spinning a wheel to pick a lucky number!

Since our sampling interval is $12$ , Simon should pick a random number between $1$ and $12$ .
Let's say he picks the number 7.

Now, Simon starts with the 7th person and measures their hand span.
Then, he adds the sampling interval of $12$ to find the next person.
It's like taking steps of a certain size!

The second person will be the $7 + 12 = 19$ th person.
The third person will be the $19 + 12 = 31$ st person, and so on.

Simon keeps adding $12$ to the previous number until he gets $20$ measurements.
This is systematic sampling in action!

Simon should select a random starting point between $1$ and $12$ .
Let's say he picks 7.
Then, he measures the hand span of every $12$ th person starting with the 7th** person.
So, he'll measure the 7th, 19th, 31st, and so on, until he has 20 measurements.