Lists & Tables

Mastering data sets and iterative calculations with Desmos power commands.

📊 Trick #4: Statistical Visualization

The Move: Use L = [...] to handle large datasets instantly.

L = [10, 12, 12, 15, 20]

📝 SAT Problem

You have a data set: L = [10, 12, 12, 15, 20]. Find the mean and median.

(A) Mean = 12, Median = 13.8
(B) Mean = 13.8, Median = 12
(C) Mean = 13, Median = 12
(D) Mean = 14, Median = 12.5

Step 1: Define the List

Type L = [10, 12, 12, 15, 20].

Step 2: Type stats functions

Type mean(L) and median(L).

Desmos List Stats Solution

Mean = 13.8 and Median = 12.

✅ Final Answer:

Choice (B)

🧬 Trick #5: The List Filter

Scenario: "In the list above, how many integers are greater than 12?"

length(L[L > 12])

📝 SAT Problem

"In the list L = [10, 12, 12, 15, 20], how many integers are greater than 12?"

(A) 1
(B) 2
(C) 3
(D) 4

Step 1: The Logic Inside

Inside the brackets, Desmos checks L > 12 for every number. It asks: "Is 10 > 12? No. Is 15 > 12? Yes."

Step 2: The Filter

The brackets L[...] act like a gate. They keep only the numbers where the answer was "Yes".

  • ❌ 10 > 12? No. (Discarded)
  • ❌ 12 > 12? No. (Discarded)
  • ✅ 15 > 12? Yes! (Kept)
  • ✅ 20 > 12? Yes! (Kept)

The list becomes [15, 20].

Step 3: The Count

The length(...) function counts how many numbers survived the filter.

Desmos List Filter Solution

The calculator shows 2 because there are two numbers (15 and 20) greater than 12.

✅ Final Answer:

2 (Choice B)

📅 Using Tables for Coordinates

The Move: Use tables to plot multiple points and find patterns without manual sketching.

  1. Click + then Table.
  2. Enter $(x, y)$ pairs from the problem.
  3. Toggle the Points icon to see them on the graph.

∑ Trick #6: The Total Sum

The Move: Set L = [5, 5, 5, 10, 10].

total(L)

📝 SAT Problem

Calculate the total sum of the values: [2, 3, 5, 10].

(A) 15
(B) 20
(C) 25
(D) 30

Instant addition. Answer: 20.

✅ Final Answer:

20 (Choice B)

📏 Trick #7: Range Finder

Scenario: Find the range of a dataset.

max(L) - min(L)

📝 SAT Problem

Find the range of the dataset L = [5, 5, 5, 10, 10].

(A) 5
(B) 10
(C) 15
(D) 20

Step 1: Define the List

Type L = [5, 5, 5, 10, 10].

Step 2: Calculate Range

Type max(L) - min(L).

Desmos Range Finder Solution

Desmos calculates: 5

✅ Final Answer:

5 (Choice A)

🔃 Trick #8: Sorting

sort(L)

Instantly puts the list in ascending order. Helpful for manual median checks.

📊 Trick #3: Percentiles & Quartiles

The Move: Use quantile(L, p) to find the p-th percentile instantly.

quantile(L, 0.75)

📝 SAT Problem

Given the list L = [1, 2, 3, 4, 5], what is the value of the 3rd quartile (Q3)?

(A) 2
(B) 3
(C) 4
(D) 5

Step 1: The Concept

The "3rd Quartile" (Q3) is the same thing as the 75th Percentile.

It represents the value that is greater than 75% of the data points.

Step 2: The Command

In Desmos, we use quantile(List, Decimal).

  • For Q1 (25%), use 0.25.
  • For Q3 (75%), use 0.75.

So, type quantile(L, 0.75).

Desmos Quantile Solution

✅ Final Answer:

4 (Choice C)

📉 Trick #10: Mean Absolute Deviation

The Move: Use mad(L) to find the average distance from the mean.

mad(L)

📝 SAT Problem

Calculate the Mean Absolute Deviation of the set [2, 4, 6, 8].

(A) 1
(B) 2
(C) 2.24
(D) 4

Step 1: Define the List

Type L = [2, 4, 6, 8].

Step 2: Calculate MAD

Type mad(L).

Desmos Mean Absolute Deviation Solution

Desmos calculates: 2

✅ Final Answer:

2 (Choice B)

📊 Trick #11: Standard Deviation

The Move: Use stdevp(L) for population standard deviation (what SAT usually wants).

stdevp(L)

📝 SAT Problem

What is the standard deviation of the set [10, 10, 20, 20]?

(A) 2.5
(B) 5
(C) 10
(D) 15

Step 1: Define & Calculate

Type the list L = [10, 10, 20, 20]. Then type stdevp(L).

Desmos Standard Deviation

The result is 5.

✅ Final Answer:

5 (Choice B)

Use `stdevp` for population (SAT standard). Answer: 2.236.

✨ Trick #12: Unique Values

unique(L)

Removes duplicates. Great for counting how many *distinct* types exist.