7-82. Ms. Poppy has finished grading her students’ tests. The scores were , and 82 . Homework Help
d. Find the quartiles.
d.

Ask by Boone Johnston. in the United States

Mar 26,2025

Question

7-82. Ms. Poppy has finished grading her students’ tests. The scores were , and 82 . Homework Help
d. Find the quartiles.
d.

Ask by Boone Johnston. in the United States

Mar 26,2025

UpStudy AI · Accepted Answer

**Step 1. List and sort the scores.**

The scores given are:  
$$ 62, 65, 93, 51, 55, 76, 79, 85, 55, 72, 78, 83, 91, 82 $$.

First, sort them in ascending order:  
$$ 51, 55, 55, 62, 65, 72, 76, 78, 79, 82, 83, 85, 91, 93 $$.

---

**Step 2. Find the median.**

There are $$ 14 $$ scores (an even number), so the median is the average of the $$ 7^{\text{th}} $$ and $$ 8^{\text{th}} $$ scores.

- The $$ 7^{\text{th}} $$ score is $$ 76 $$.
- The $$ 8^{\text{th}} $$ score is $$ 78 $$.

Thus, the median is:  
$$
\text{Median} = \frac{76 + 78}{2} = \frac{154}{2} = 77.
$$

---

**Step 3. Find the quartiles.**

Divide the sorted data into two halves.

- **Lower half:** The first $$ 7 $$ scores:  
  $$ 51, 55, 55, 62, 65, 72, 76 $$.

- **Upper half:** The last $$ 7 $$ scores:  
  $$ 78, 79, 82, 83, 85, 91, 93 $$.

*Find $$ Q_1 $$ (first quartile):*  
Since there are $$ 7 $$ numbers in the lower half, $$ Q_1 $$ is the median of these numbers, which is the $$ 4^{\text{th}} $$ score:  
$$
Q_1 = 62.
$$

*Find $$ Q_3 $$ (third quartile):*  
Similarly, $$ Q_3 $$ is the median of the upper half, which is the $$ 4^{\text{th}} $$ score:  
$$
Q_3 = 83.
$$

Thus, the quartiles are:  
$$
Q_1 = 62, \quad Q_2 = 77 \ (\text{median}), \quad Q_3 = 83.
$$

---

**Step 4. Find the Interquartile Range (IQR).**

The IQR is given by the difference between $$ Q_3 $$ and $$ Q_1 $$:
$$
\text{IQR} = Q_3 - Q_1 = 83 - 62 = 21.
$$

---

**Final Answers:**

- **Median:** $$ 77 $$
- **IQR:** $$ 21 $$
- **Quartiles:** $$ Q_1 = 62, \quad Q_2 = 77, \quad Q_3 = 83 $$
Median: 77 IQR: 21 Quartiles: Q₁ = 62, Q₂ = 77, Q₃ = 83

7-82. Ms. Poppy has finished grading her students’ tests. The scores were , and 82 . Homework Help
d. Find the quartiles.
d.

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7-82. Ms. Poppy has finished grading her students’ tests. The scores were , and 82 . Homework Help d. Find the quartiles. d.

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