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00XP

Key errors & ambiguities

Every answer in this course was recomputed by code. In 6 places the recomputed value disagrees with Chung's printed key. Both are shown below. The app grades the recomputed value, and each card explains why the key is off, which rule settles it, and what to do on the exam.

Each one is a trap from your cheat sheet: select = combination unless roles or order are named; quartile halves exclude the median; percent OF a group means that group is the denominator; cumulative frequency ends at n; and a fraction is reduced by dividing top and bottom by the same number.

Unit 10 · Probability with combinations

HW 2.6 #7 — three dice, sum of 7

When 3 dice are rolled, find the probability of getting a sum of 7.

Chung's key

3/72

Recomputed (graded)

5/72 (= 15/216 ≈ 0.069)

Why they differ

There are 15 ordered rolls that add to 7: 1-1-5 (3 orders), 1-2-4 (6 orders), 1-3-3 (3 orders), 2-2-3 (3 orders), out of 6³ = 216. 15/216 reduces to 5/72 by dividing BOTH numbers by 3. The typed key 3/72 divides the top by 5 and the bottom by 3, which changes the value (3/72 = 9/216, as if only 9 rolls worked); Chung's own handwritten solution circles 5/72.

The rule that decides it

Reduce a fraction by dividing the top and the bottom by the SAME number.

Lesson for you

On the exam, list each combo, count its orders (all different → 6, one pair → 3), add them, put the total over 216, and reduce with one common factor. If your answer is 5/72, trust it.

Unit 9 · Permutations vs combinations

HW 2.5 #5 — select 3 coins from 6

How many ways can a person select 3 coins from a box consisting of a penny, a nickel, a dime, a quarter, a half-dollar, and a one-dollar coin?

Chung's key

120

Recomputed (graded)

20 (= C(6, 3))

Why they differ

The key's 120 is P(6, 3) = 6·5·4, which counts ordered picks (penny-then-dime differs from dime-then-penny). The question only says "select 3 coins" — no positions, titles or order — so swapping two chosen coins gives the same handful. That is a combination: C(6, 3) = 120 ÷ 3! = 20. Every other "select" problem in the same key (#6, #11, #15) is treated as a combination, so 120 is inconsistent with the key itself.

The rule that decides it

Swap test: if swapping two picks gives the same outcome, use C(n, r); "select / choose" with no roles = combination.

Lesson for you

On the exam, "select", "choose", "committee", "group", "hand" → nCr unless the problem names roles, places, order or different tasks. If you get the P answer, divide by r! to get the C answer.

Unit 5 · Sample spaces & probability

HW 2.1 #16 — percent of High-School-degree holders who attended

The General Social Survey asked this question “Have you attended religious services in the last week?” Here are the responses for those whose highest degree was high school or above

High SchoolCommunity CollegeBachelor'sGraduate
Attended Services4006214676
Did not attend services880101232105

What percent of those with a High School degree attended services last week?

Chung's key

20%

Recomputed (graded)

31% (= 400/1280 = 31.25%)

Why they differ

The question asks for a percent OF those with a High School degree, so that group (400 attended + 880 did not = 1280) is the whole. The key's 20% is 400/2002, which uses everyone surveyed as the base — that answers "what percent of all people surveyed are HS-degree holders who attended", a different question. This is the same "and" vs "given" decision as exam Q17 vs Q21.

The rule that decides it

"Percent of a group" / "given" → that group's total is the denominator; plain "and" → the grand total.

Lesson for you

Underline the words after "of those…" or "given that…" — that row or column total goes on the bottom. Only use the grand total when no group is named (Q17: male AND no = 251/1520).

Unit 4 · Five-number summary & box plots

HW 1.4 #6 — five-number summary of 14.6, 19.8, 16.3, 15.5, 18.2

For problems 4 – 6: Identify the five-number summary and find the interquartile range.

14.6, 19.8, 16.3, 15.5, 18.2

Chung's key

14.6, 15.5, 16.3, 18.2, 19.8; 2.7

Recomputed (graded)

14.6, 15.05, 16.3, 19, 19.8

Why they differ

Sorted: 14.6, 15.5, 16.3, 18.2, 19.8, so n = 5 and the median is 16.3. Chung's rule (and the TI-84's 1-Var Stats) leaves the median out: lower half 14.6, 15.5 → Q1 = 15.05; upper half 18.2, 19.8 → Q3 = 19. The key's Q1 = 15.5 and Q3 = 18.2 come from putting 16.3 into both halves. The same key uses the median-excluded rule on #2, #3c and #4, so #6 contradicts the key itself.

The rule that decides it

Quartiles: when n is odd, the median is in NEITHER half.

Lesson for you

This is your trouble spot. Sort, cross out the median, then take the middle of each half — or check with stat → CALC → 1-Var Stats on the Evo. If your Q1/Q3 match the calculator, they are right.

Unit 4 · Five-number summary & box plots

HW 1.4 #6 — IQR of the same data

For problems 4 – 6: Identify the five-number summary and find the interquartile range.

14.6, 19.8, 16.3, 15.5, 18.2

Chung's key

14.6, 15.5, 16.3, 18.2, 19.8; 2.7

Recomputed (graded)

3.95 (= 19 − 15.05)

Why they differ

The IQR is Q3 − Q1, so it inherits whatever quartiles you used. With Chung's median-excluded quartiles, IQR = 19 − 15.05 = 3.95. The key's 2.7 = 18.2 − 15.5 comes from the median-included quartiles above. A wrong quartile also moves the outlier limits (Q1 − 1.5·IQR, Q3 + 1.5·IQR), so this one error spreads to outlier questions.

The rule that decides it

IQR = Q3 − Q1 using median-excluded quartiles; outlier limits use 1.5 × that IQR.

Lesson for you

Get Q1 and Q3 right first; the IQR and the outlier limits follow automatically. Exam Q11–Q12: IQR 20, limits −10 and 70 → 71 is the outlier.

Unit 2 · Histograms, polygons, ogives

HW 1.2 #4c — ogive for the blood-glucose data

The frequency distribution shows the blood glucose levels (in milligrams per deciliter) for 50 patients at a medical facility. Construct a histogram, frequency polygon, and ogive for the data. What range of glucose levels did most patients fall into?

Blood Glucose LevelsFrequency
59.5 – 64.52
64.5 – 69.51
69.5 – 74.55
74.5 – 79.512
79.5 – 84.518
84.5 – 89.56
89.5 – 94.55
94.5 – 99.51

Construct an ogive for the data.

Chung's key

[Figure: Ogive (cumulative frequency graph) titled "Blood Glucose Levels". Vertical axis labeled "Cumulative frequency" with a "y" at the arrowhead, ticks at 0, 10, 20, 30, 40, 50. Horizontal axis labeled "Level" with an "x" at the arrowhead, ticks at the class boundaries 59.5, 64.5, 69.5, 74.5, 79.5, 84.5, 89.5, 94.5, 99.5. Blue line with dots; y-values read from the scan: (59.5, 0); (64.5, 1[?]) dot sits just above 0; (69.5, 2[?]) dot sits slightly higher than the 64.5 dot; (74.5, 6[?]); (79.5, 17[?]); (84.5, 35); (89.5, 40[?]) dot sits at or just above 40; (94.5, 45); (99.5, 45[?]) dot level with or barely above the 94.5 dot. The curve is S-shaped, rising steeply between 74.5 and 84.5 and flattening after 94.5.]

Recomputed (graded)

cumulative frequencies 0, 2, 3, 8, 20, 38, 44, 49, 50 at boundaries 59.5, 64.5, …, 99.5

Why they differ

The key's own frequency table (2, 1, 5, 12, 18, 6, 5, 1; total 50) fixes the running totals: 2, 3, 8, 20, 38, 44, 49, 50. The drawn ogive on the key page sits about 1–5 units low at every boundary (≈ 1, 2, 6, 17, 35, 40, 45, 45) and never reaches 50, even though an ogive must end at n. The x-values (upper boundaries) in the key are correct; it is a drawing error, not a data error.

The rule that decides it

An ogive plots cumulative frequency at each upper boundary, starts at 0 and must end exactly at n.

Lesson for you

When you draw or read an ogive, check the last point equals n. If a graph says otherwise, trust the table and your running totals.

Can't be checked from the source (8)

These have no complete printed key to compare against, or their numbers were filled in live in class and are blank in the notes. Where a value can be computed it is used; the blank ones are never graded.

  • 1.1 · Class notes #1

    The notes only show the sorted-L1 screenshot and the frequency of 1 (5); computed frequency of 1 = 5 agrees. The other five frequencies have no key in the notes.

  • 1.1 · Class notes #5

    Only the first row is worked in the notes; computed first class 7 – 12 → 6.5 – 11.5 agrees (R = 29, W = 29/6 = 4.83 → 5). The remaining rows and all frequencies have no key.

  • 2.1 · Class notes #7a

    The survey table and sample size are blanks in Class-notes (filled in live); no numbers exist to compute. Listed in unverifiable.

  • 2.1 · Class notes #7b

    The survey table and sample size are blanks in Class-notes (filled in live); no numbers exist to compute. Listed in unverifiable.

  • 2.1 · Class notes #7c

    The survey table and sample size are blanks in Class-notes (filled in live); no numbers exist to compute. Listed in unverifiable.

  • 2.1 · Class notes #7d

    The survey table and sample size are blanks in Class-notes (filled in live); no numbers exist to compute. Listed in unverifiable.

  • 1.2 · Homework #3

    Graph item. Compared: the key's eight x-values (20.5 … 83.5) equal the computed boundaries exactly; the key's y-values are transcribed as approximate scan readings (≈5, ≈15, ≈28, ≈38, ≈42, ≈45, ≈46) and each coincides with the computed cumulative frequency (5, 15, 28, 38, 42, 45, 46). Not called a match because the key values are read off a drawing whose y-axis is ticked only every 10, not printed.

  • 1.2 · Homework #4

    Graph item. Compared: the key's midpoint column (62, 67, 72, 77, 82, 87, 92, 97) equals the computed midpoints exactly, and the left anchor drawn at about 57 equals the computed 62 − 5 = 57. The key's plotted heights are scan readings marked [?] (2, 1, 4, 11, 17, 5, 4, 0) that sit roughly one unit below the printed frequencies (2, 1, 5, 12, 18, 6, 5, 1); readings that differ from the table: x = 72: drawn ≈4, table f = 5; x = 77: drawn ≈11, table f = 12; x = 82: drawn ≈17, table f = 18; x = 87: drawn ≈5, table f = 6; x = 92: drawn ≈4, table f = 5; x = 97: drawn ≈0, table f = 1 — the last dot is drawn on (or within half a unit of) the axis at 97 although f = 1. The drawing cannot be compared exactly; the computation follows the printed table, which the key itself prints beside the figure.