---
title: "STAT 540 Homework 6"
subtitle: "Section 001, Fall 2026  |  **Due: Wednesday, October 21, 2026 (before class)**  |  Total Points: 80"
author: "Your Name"
date: Oct 14, 2026
date-format: "[Assigned] MMM D, YYYY"
format:
  html:
    theme: cosmo
    toc: true
    toc-depth: 2
    code-fold: false
    highlight-style: github
  pdf:
    toc: true
execute:
  echo: true
  warning: false
---

::: {.callout-important title="📅 Due: Wednesday, October 21, 2026 — before class"}
Compile your homework as a webpage (**html**). Then open it in a browser and
print it to a **.pdf** file. Upload this pdf file **and** your Quarto
(`*.qmd`) file to Blackboard. Please use the Python Quarto homework template
(`python_hw_template.qmd`) to write your homework solutions.
**Work on the homework independently.**
:::

## Instructions

This is the Python counterpart of Homework 1. Everything you need comes from
Lectures 1–2 and the *Python Data Science Handbook* (Chapter 2, "Introduction
to NumPy").

- Write your Python code (commands) for each task **and present your results
  clearly** — a code cell that runs but prints nothing earns no credit.
- Answer the "Is it a …?" questions **with evidence**: run a function whose
  output settles the question, then state your conclusion in a sentence.
- Start every code cell from the setup cell below; later parts reuse objects
  created in earlier parts.
- Where a question asks you to find a function "on your own", say in one
  sentence how you found it (`help()`, `dir()`, the docs, the textbook).

```{python}
#| label: setup
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

# Use this generator (and this seed) everywhere so your numbers are reproducible.
rng = np.random.default_rng(540)
```

---

## Problem 1. NumPy arrays and their types (20 points)

Write your Python code for the following tasks and present your results clearly.

### 1(a) — 2 points

Generate an array `x` with 30 random numbers from the uniform distribution on
$(0,1)$, i.e. $U(0,1)$. Show the first 5 values of `x` you get.
*Hint:* `rng.uniform`

```{python}
# YOUR CODE HERE
```

### 1(b) — 3 points

Use built-in NumPy functions (find them on your own if you don't know them
yet) to calculate the **sample mean**, **median**, and **standard deviation**
of `x`.

*Note:* `np.std()` divides by $n$ by default, while the sample standard
deviation divides by $n-1$. Report the sample standard deviation and state
which argument you used to get it (?np.std).

```{python}
# YOUR CODE HERE
```

### 1(c) — 3 points

Run the command `y = (x > 0.5)`. Is `y` a numerical array? Confirm or
disprove it by executing some appropriate Python/NumPy functions, then write
one sentence explaining what you found.

```{python}
# YOUR CODE HERE
```

### 1(d) — 5 points

Run the command `z = np.column_stack((x, y))`. Is `z` a NumPy array or a
pandas DataFrame? Is the second column of `z` a Boolean column or a numerical
column? Show the output of `pd.DataFrame(z).describe()` and explain what
happened to `y` when it was stacked with `x`.

```{python}
# YOUR CODE HERE
```

### 1(e) — 3 points

What method or function can be used to change `y` into an array of
**strings**? Demonstrate it and print the `dtype` of the result.

```{python}
# YOUR CODE HERE
```

### 1(f) — 4 points

Run the command `xx = np.diag(x)`. Is `xx` a one-dimensional array or a
two-dimensional matrix? Find the "length" of `xx` by running both `len(xx)`
and `xx.size`. Why do the two answers differ?

```{python}
# YOUR CODE HERE
```

---

## Problem 2. Lists, tuples and dictionaries (30 points)

### 2(a) — 6 points

Create a **list** `scores` holding the five numbers 88, 72, 95, 61, 79, and a
**tuple** `limits` holding the two numbers 60 and 90. Print both, and print
the `type()` of each.

```{python}
# YOUR CODE HERE
```


### 2(b) — 8 points

Create a **dictionary** `grades` that maps each of the five student names
`"Ana"`, `"Ben"`, `"Cleo"`, `"Dev"`, `"Eli"` to the corresponding score in
`scores`. Print Cleo's score by using her name as the key.
*Hint:* `zip`

```{python}
# YOUR CODE HERE
```

### 2(c) — 8 points

Using `scores`, print (i) the last element with **negative indexing**,
(ii) the first three elements with **slicing**, and (iii) every other element
starting from the second, using **step slicing**.

```{python}
# YOUR CODE HERE
```

### 2(d) — 8 points

Run `scores * 2` and `np.array(scores) * 2`. The two results are different —
show both and explain in one or two sentences why.

```{python}
# YOUR CODE HERE
```

---

## Problem 3. Functions, conditionals and plotting (30 points)

### 3(a) — 12 points

Write a function `summary_stats(a)` that takes a NumPy array and **returns a
dictionary** with keys `"n"`, `"mean"`, `"sd"`, `"min"`, and `"max"`. Apply it
to `x` from Problem 1 and print the dictionary.

```{python}
def summary_stats(a):
    # YOUR CODE HERE
    pass

# YOUR CODE HERE
```

### 3(b) — 8 points

Write a function `letter_grade(score)` that returns

- `"A"` if the score is 90 or above,
- `"B"` if the score is at least 80 but below 90,
- `"C"` if the score is at least 70 but below 80,
- `"F"` otherwise.

Apply it to every value in `scores` from Problem 2 and print each student's
name with their letter grade.

```{python}
def letter_grade(score):
    # YOUR CODE HERE
    pass

# YOUR CODE HERE
```

### 3(c) — 10 points

Make a **histogram** of `x` with 10 bins. Add a vertical dashed line at the
sample mean, a title, and axis labels. *Hint:* `ax.hist`, `ax.axvline`

```{python}
fig, ax = plt.subplots(figsize=(7, 4))

# YOUR CODE HERE

plt.tight_layout()
plt.show()
```

---

## Before you submit

- [ ] Every code cell runs from top to bottom without errors
- [ ] Every part prints its result — no silent cells
- [ ] The "Is it a …?" questions each have a one-sentence written answer
- [ ] Your plot has a title and axis labels
- [ ] You rendered with `quarto render hw6.qmd`, printed the html
      to pdf, and are uploading **both** the pdf and the `.qmd`

**Due: Wednesday, October 21, 2026, before class.**