Math 1153 - 10 September 2026 - Sections 2.4

Overview

Mike Jacobsen introduces Section 2.4 on measuring the center of quantitative data, explaining the sample mean and median and showing how to calculate them with a TI-84. Using 20 restaurant-tip percentages, he finds a mean of 27.315% and a median of 21%, then connects the gap to right skew and outliers while troubleshooting calculator setup and model-specific behavior.

Key takeaways

The sample mean is computed as Σyᵢ/n; for the 20 restaurant-tip observations, the TI-84 returned a mean of 27.315% and a median of 21%.
The tip distribution is unimodal and right-skewed, with a main cluster below 40% and an upper-end outlier at 105%; the right tail pulls the mean above the median.
The median is the 50th percentile: with 20 observations and a median of 21%, 10 tables tipped less and 10 tipped more.
On a TI-84, enter observations in L1, choose STAT → Calculate → 1-Var Stats, leave Frequency List blank, and inspect X̄ for the mean and MD for the median.
For TI-84 versions that show only a 1-Var Stats prompt, insert L1 with 2nd + 1; on the TI-84 EVO, pressing ZOOM may be needed to trigger the calculation.
When a distribution is strongly skewed, the median is typically more resistant and representative of the main cluster than the mean, which moves in the direction of the skew.

Chapters

0:00 Quiz Deadline, Exam Scheduling, and Week-Five Plans

Quiz 1 is considered on time if submitted any time on September 10, despite the Canvas deadline showing 1:00.
Mike Jacobsen plans to post Exam 1 sections and review problems on Friday; quizzes and homework are intended as exam preparation.
Students will receive individual Canvas instructions Sunday evening for scheduling Exam 1, which may be taken Monday through Thursday.
There is no class on the exam Monday, giving students a breather and allowing them to take the exam during the usual class period.

7:08 Mean, Median, and the Sample-Mean Formula

Center describes a typical observation in a quantitative dataset; the histogram example suggests a typical synovial-fluid pH near 7.2–7.3.
The sample mean, written y-bar in the course text, is the sum of all observations divided by sample size n.
The summation symbol Σ means to add observations y₁ through yₙ; for data 3, 5, and 7, the sample mean is 5.
Use the median, the 50th percentile, when strong skew makes the mean a less representative description of center.

11:06 Restaurant Tips: Right Skew, Unimodality, and Outliers

The example contains 20 quantitative restaurant-tip percentages, constructed to match summary statistics from a real labor-market study of restaurant servers.
Ten of the 20 tables tipped between 0% and 20%, forming the dataset’s single main peak and making the distribution unimodal.
The distribution is skewed to the right, with unusual observations at 55.2% and 105%; the 105% tip is an upper-end outlier.
When describing a distribution’s shape, report modality, skew direction, and any outlier with its approximate location.

17:17 TI-84 Setup: Restoring the Statistics List Editor

Press STAT and then ENTER to open the list editor, which should display L1, L2, and L3.
If L1 is missing or the editor starts at a later list such as L5, use STAT, select option 5 (SetUpEditor), press ENTER twice, then reopen the editor.
Restoring L1 matters because the one-variable statistics command defaults to that list.
The class will enter this example’s data in L1; later work may use both L1 and L2.

22:09 Clearing Old Data from TI-84 Lists

Existing values can be removed one at a time with DELETE, but clearing an entire list is faster for a long dataset.
Highlight the list name, such as L1, press CLEAR, and then ENTER to erase its contents.
Do not press CLEAR while highlighting the list column itself; clear the list by selecting its L1 heading.
Check that the list is empty before entering the restaurant-tip observations.

25:18 Navigating Lists and Troubleshooting the TI-84 Editor

The list editor scrolls horizontally between L1, L2, and later lists, and vertically through observations.
If L1 is not visible, restore the editor with STAT → SetUpEditor or use the left-arrow key to scroll back.
Mike Jacobsen encourages students to share calculator model details or photos of errors so he can troubleshoot TI-84 and other brands.
Practicing with the same calculator intended for quizzes and exams helps make the keystrokes familiar.

31:37 Entering 20 Tip Percentages and Verifying the Sample Size

Enter each restaurant-tip percentage into L1 carefully; column-by-column entry and checking off values help prevent transcription mistakes.
A small input error, such as entering 27.8 instead of 27.9, can change the result and cause an online homework answer to be marked incorrect.
The 20-table context requires exactly 20 observations: the next cell should be L1(21), while the final entered value should appear at L1(20).
Check the observation count to catch a skipped or duplicated value before calculating statistics.

38:26 Running One-Variable Statistics on L1

After data entry, press STAT again and use the right arrow to move from Edit to Calculate.
Select option 1, 1-Var Stats, which computes summary statistics for one quantitative variable.
Confirm the list is L1 and leave the frequency-list field blank before pressing ENTER to run the calculation.
If the menu instead shows Z Test, move back to the statistics menu tab before selecting 1-Var Stats.

41:35 TI-84 Menu Differences and Entering L1 Manually

Some TI-84 Plus versions show a simplified 1-Var Stats prompt without visible List and Frequency List fields.
For that interface, press 2nd and then 1 to insert L1 manually, then press ENTER to calculate.
The TI-84 Plus interface changed across versions, so identical model names may not produce identical prompts.
If the output differs from the class example, verify that the same 20 values were entered in L1.

50:37 Troubleshooting the TI-84 EVO Calculation Screen

A student using a TI-84 EVO reported that 1-Var Stats remained on the Calculate screen instead of advancing to the results.
Mike Jacobsen did not initially know the fix and planned to investigate the new model’s behavior.
A later class report found that pressing the ZOOM key prompted the EVO to compute the statistics.
Testing the calculator used for homework and quizzes also prepares students to use that same device during exams.

55:57 Reading the TI-84 Output: Mean and Median

The calculator labels the sample mean X̄, while the course text uses y-bar; both symbols refer to the sample mean.
For the 20 tip percentages, the sample mean is 27.315%.
Scroll down through the output to find MD, the calculator’s label for the sample median, which is 21%.
The output also reports sample size n = 20, minimum 0%, and maximum 105%, alongside quartiles.

1:00:49 Interpreting the 27.315% Mean and 21% Median

The median of 21% is the 50th percentile: 10 tables tipped less and 10 tipped more.
The median lies near the distribution’s main cluster, while the right-skewed tail pulls the mean up to 27.315%.
For strongly right-skewed measures such as incomes or housing prices, the median often better represents a typical value than the mean.
The mean follows the direction of skew, and increasingly extreme outliers can move it farther from the center of the main data cluster.

1:04:19 Choosing a Center Measure and Preparing for Quiz 2

For roughly symmetric data, the mean and median are generally closer; with noticeable skew, the median is usually the more resistant measure of center.
The class will compare symmetric, left-skewed, and right-skewed distributions in the next discussion of choosing a center statistic.
Mike Jacobsen recommends practicing the TI-84 workflow in homework and Quiz 2, due September 17.
Students can contact him about calculator problems, including unfamiliar TI-84 models, while preparing for Exam 1.

Summary, takeaways, and chapters were generated by AI from the video's transcript and may contain errors. The video belongs to its creator, Mike Jacobsen.