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Practice sheet · Data Management Path · Lens 1: Math

Averages, odds & sines

Practice for The Math of Data: medians, range, percent change, rates, Venn diagrams, odds, counting and sine models with real 2024 Calgary and Edmonton weather (pp.8–16), plus A1–A2 (pp.17–18).
Warm-upCoreLevel Up
Name Date Time I spent
Remember

Median: order the values; with an even count, average the middle two. Range = highest − lowest. Percent change = (new − old) ÷ old × 100. Rate per 100,000 = count ÷ population × 100,000.

n(A ∪ B) = n(A) + n(B) − n(A ∩ B). P = favourable ÷ total; odds in favour = favourable : unfavourable. ₙPᵣ when order matters, ₙCᵣ when it doesn’t. Sine model: a = (max − min) ÷ 2, d = (max + min) ÷ 2.

Warm-up

One step

Real Alberta weather, 2024.
1

Median

Edmonton’s 2024 monthly precipitation (mm), in order: 2.0, 12.4, 13.1, 20.0, 20.3, 22.2, 28.0, 29.0, 32.0, 58.5, 67.0, 69.0. Find the median (p.8).

2

Range

In 2024, Edmonton’s highest daily maximum was 36.2 °C and its lowest daily minimum was −37.7 °C. Find the range (p.9).

3

Rate

A made-up town of 50,000 people had 15 cases of a cold-weather injury. What is the rate per 100,000 (p.11)?

4

Probability

In December 2024, Edmonton had a reported daily mean on 30 days, and 27 of them were below 0 °C. What is the probability (as a %) that one of those days was below zero (p.13)?

Core

Two or three steps

Say what each number can and can’t show.
5

Percent change

Calgary had 46.0 mm in July 2024, 86.4 mm in August and 74.0 mm in September. Find the percent change from July to August and from August to September, to the nearest percent (p.10).

6

Venn

In a made-up survey of 40 learners, 22 use a spreadsheet app, 18 use a drawing app and 9 use both. How many use only a spreadsheet app? How many use neither (p.12)?

Data Practice · Data Management Path · Unizon1/2
Data Management Path · Unizon · PracticeAverages, odds & sine curves
7

Odds

In November 2024, Calgary had a reported daily mean on 29 days, and 16 were below 0 °C. Find the probability to the nearest percent, and complete the odds in favour, 16 : ? (p.13).

8

PINs

How many 5-digit PINs are there (digits can repeat)? How many if all 5 digits must be different (p.14)?

9

Choices

A designer picks 3 colours from a palette of 7 for a chart (order doesn’t matter). How many ways? How many ways to pick 2 charts from 6 for a poster (p.14)?

10

Sine model

A made-up city’s monthly mean temperature peaks at 18.6 °C in July and bottoms out at −11.4 °C in January. Find the amplitude a and the midline d of a sine model (p.15).

Level Up

Equations

A1–A2 (pp.17–18).
11

Fahrenheit

Use C = (F − 32) ÷ 1.8 to change 77 °F to °C. Then use F = 1.8C + 32 to change −20 °C to °F (p.17).

12

Solve for C

A thermometer app shows 14 °F. Solve 1.8C + 32 = 14 for C (p.17).

13

Doubling data

A made-up photo library is S = 6 × 2t/2 GB after t years. When will it reach 96 GB (p.18)?

14

Backup growth

A made-up backup is S = 2 × 2t/3 TB after t years. When will it reach 64 TB (p.18)?

Make your own problem

Your turn to be the data detective

  1. Pick numbers from the dataset at the end of the book: a month, a city, a temperature or a precipitation total.
  2. Write a question that uses a median, a percent change, odds or a sine model.
  3. Solve it, and say what one year of data can’t tell you.

My problem, and my worked answer:

Data Practice · Data Management Path · Unizon2/2
Data Management Path · Unizon · PracticeAverages, odds & sine curves

Try every problem first, then check here. Wrong answers are useful: find the step where your work and the key split apart.

The key never prints with Print my work or Print blank. Open it to get its own Print the answer key button.

Answer key

Worked solutions. Weather numbers are real 2024 ECCC data from the book’s dataset; towns, surveys, PINs and file sizes are made up.

Warm-up
1
25.1 mm 12 values, so average the 6th and 7th: (22.2 + 28.0) ÷ 2 = 25.1 mm.
2
73.9 °C 36.2 − (−37.7) = 36.2 + 37.7 = 73.9 °C.
3
30 per 100,000 15 ÷ 50,000 × 100,000 = 30.
4
90% 27 ÷ 30 = 0.9 = 90%. That’s one month of one year, not a forecast.
Core
5
+88% · −14% (86.4 − 46.0) ÷ 46.0 × 100 ≈ +87.8%, so +88%. (74.0 − 86.4) ÷ 86.4 × 100 ≈ −14.4%, so −14%.
6
13 · 9 Only spreadsheet: 22 − 9 = 13. Either: 22 + 18 − 9 = 31. Neither: 40 − 31 = 9.
7
55% · 16 : 13 16 ÷ 29 ≈ 0.552, so 55%. Not below zero: 29 − 16 = 13, so the odds in favour are 16 : 13.
8
100,000 · 30,240 10⁵ = 100,000. All different: 10 × 9 × 8 × 7 × 6 = ₁₀P₅ = 30,240.
9
35 · 15 ₇C₃ = 7! ÷ (3! × 4!) = 35. ₆C₂ = 6! ÷ (2! × 4!) = 15.
10
a = 15 · d = 3.6 a = (18.6 − (−11.4)) ÷ 2 = 30 ÷ 2 = 15. d = (18.6 + (−11.4)) ÷ 2 = 7.2 ÷ 2 = 3.6 °C. Period 12, so b = 2π ÷ 12.
Level Up
11
25 °C · −4 °F (77 − 32) ÷ 1.8 = 45 ÷ 1.8 = 25 °C. 1.8 × (−20) + 32 = −36 + 32 = −4 °F.
12
−10 °C 1.8C = 14 − 32 = −18 → C = −18 ÷ 1.8 = −10.
13
8 years 96 ÷ 6 = 16 = 2⁴, so t/2 = 4 → t = 8.
14
15 years 64 ÷ 2 = 32 = 2⁵, so t/3 = 5 → t = 15.
Make your own: order values before a median, divide by the old value for percent change, fill the middle of a Venn diagram first, and remember one year of weather is weather, not climate.
Data Practice · Data Management Path · UnizonAnswer key