Math / Data & Statistics

QuestionQuestion 15 of 30 (1 point) I Question Attempt: 1 of 1 $\equiv 1$ $=2$ 3 4 5 6 7 8 9
Following are final exam scores, arranged in increasing order, for students in an introductory statistics course. \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline 56 & 58 & 59 & 60 & 61 & 63 & 66 & 67 & 67 & 70 & 73 & 74 & 75 & 75 & 76 \\ \hline 82 & 85 & 86 & 86 & 90 & 91 & 91 & 92 & 92 & 93 & 96 & 96 & 97 & 97 & 98 \\ \hline \end{tabular}
Part: $0 / 2$
Part 1 of 2 (a) Find the first quartile of the scores.
The first quartile of the scores is $\square$ .

Studdy Solution

STEP 1

What is this asking? Find the score that separates the lowest 25% of final exam scores from the rest. Watch out! Don't forget that there are different ways to calculate quartiles, so make sure to use the method your teacher prefers!

STEP 2

1. Count the scores
2. Calculate the rank of the first quartile
3. Find the first quartile

STEP 3

Let's count how many scores we have!
We've got a whole bunch of exam scores laid out there, and it looks like there are $15$ scores in the first row and another $15$ in the second row.
So, we have a total of $15 + 15 = 30$ scores.
Woohoo!

STEP 4

Now, the first quartile is like the quarter-mark of the data.
It's the score that separates the bottom $25\%$ from the rest.
Since we have $30$ scores, we want to find the rank of the score that splits the data into $25\%$ and $75\%$ .
We can calculate this rank by multiplying the total number of scores by $0.25$ : $30 \cdot 0.25 = 7.5$ .

STEP 5

Since our calculated rank of $7.5$ isn't a whole number, we'll need to do a little bit of averaging.
The rank $7.5$ falls between the $7$ th and $8$ th scores.
Let's look back at our data: the $7$ th score is 66 and the $8$ th score is 67.

STEP 6

To find the first quartile, we'll take the average of these two scores: $\frac{66 + 67}{2} = \frac{133}{2} = 66.5$ .
So, our first quartile is $66.5$ !

STEP 7

The first quartile of the scores is $66.5$ .

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Studdy Solution

STEP 1

What is this asking? Find the score that separates the lowest 25% of final exam scores from the rest. Watch out! Don't forget that there are different ways to calculate quartiles, so make sure to use the method your teacher prefers!

STEP 2

1. Count the scores
2. Calculate the rank of the first quartile
3. Find the first quartile

STEP 3

Let's count how many scores we have!
We've got a whole bunch of exam scores laid out there, and it looks like there are $15$ scores in the first row and another $15$ in the second row.
So, we have a total of $15 + 15 = 30$ scores.
Woohoo!

STEP 4

STEP 5

Since our calculated rank of $7.5$ isn't a whole number, we'll need to do a little bit of averaging.
The rank $7.5$ falls between the $7$ th and $8$ th scores.
Let's look back at our data: the $7$ th score is 66 and the $8$ th score is 67.

STEP 6

To find the first quartile, we'll take the average of these two scores: $\frac{66 + 67}{2} = \frac{133}{2} = 66.5$ .
So, our first quartile is $66.5$ !

STEP 7

The first quartile of the scores is $66.5$ .

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Studdy Solution

STEP 1

What is this asking? Find the score that separates the lowest 25% of final exam scores from the rest. Watch out! Don't forget that there are different ways to calculate quartiles, so make sure to use the method your teacher prefers!

STEP 2

1. Count the scores2. Calculate the rank of the first quartile3. Find the first quartile

STEP 3

Let's **count** how many scores we have!We've got a whole bunch of exam scores laid out there, and it looks like there are 151515 scores in the first row and another 151515 in the second row.So, we have a **total** of 15+15=3015 + 15 = 3015+15=30 scores.Woohoo!

STEP 4

STEP 5

Since our calculated rank of 7.57.57.5 isn't a whole number, we'll need to do a little bit of averaging.The rank 7.57.57.5 falls between the 777th and 888th scores.Let's look back at our data: the 777th score is **66** and the 888th score is **67**.

STEP 6

To find the **first quartile**, we'll take the average of these two scores: 66+672=1332=66.5\frac{66 + 67}{2} = \frac{133}{2} = 66.5266+67​=2133​=66.5.So, our **first quartile** is 66.566.566.5!

STEP 7

The first quartile of the scores is 66.566.566.5.

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Studdy solves anything!

Start learning now

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

1. Count the scores
2. Calculate the rank of the first quartile
3. Find the first quartile

Let's count how many scores we have!
We've got a whole bunch of exam scores laid out there, and it looks like there are $15$ scores in the first row and another $15$ in the second row.
So, we have a total of $15 + 15 = 30$ scores.
Woohoo!

Since our calculated rank of $7.5$ isn't a whole number, we'll need to do a little bit of averaging.
The rank $7.5$ falls between the $7$ th and $8$ th scores.
Let's look back at our data: the $7$ th score is 66 and the $8$ th score is 67.

To find the first quartile, we'll take the average of these two scores: $\frac{66 + 67}{2} = \frac{133}{2} = 66.5$ .
So, our first quartile is $66.5$ !

The first quartile of the scores is $66.5$ .