Calculating compression ratio and space saved

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Quick Questions

Shade in the A or B circle for each question.

1. A 10 MB video is compressed to 2 MB. What is the compression ratio?

A 5 to 1 (10 / 2)

B 2 to 1 (compressed / original)

2. Which formula gives the compression ratio?

A compressed size / original size

B original size / compressed size

3. A 50 KB file is compressed to 10 KB. What percentage of space was saved?

A 20%

B 80%

4. Which formula gives the percentage saved?

A (original - compressed) / original x 100

B (original - compressed) / compressed x 100

5. A 200 MB file is compressed to 50 MB. Which statement is correct?

A The ratio is 4 to 1 and 75% was saved

B The ratio is 4 to 1 and 25% was saved

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1ratio = original / compressed		A10 / 2 = 5
2saved = (original - compressed) / original * 100		BThe sizes are the wrong way around. The ratio should be original divided by compressed, so 10 MB down to 2 MB gives 5, not 0.2.
3A 10 MB file compressed to 2 MB has a compression ratio of 5 to 1		CWorks out the percentage of space saved by compression
4Technique A shrinks 50 MB to 10 MB and technique B shrinks 50 MB to 25 MB, so A saves more space		DThe percentage saved is divided by the compressed size (2). It must be divided by the original size (10), giving 80%, not 400%.
5ratio = compressed / original		EWorks out the compression ratio by dividing the original size by the compressed size
6saved = (10 - 2) / 2 * 100		F(50 - 10) / 50 * 100 = 80 and (50 - 25) / 50 * 100 = 50

Definitions

compression ratio = original size / compressed size

Fill in the Blanks

Complete each line of code by filling in the missing parts.

ratio ← original / __________

saved ← (original - compressed) / ________ percent ← saved * 100

original ← 10 compressed ← 2 saved ← (original _ compressed) / original

saved ← 8 / 10 percent ← saved * ___

ratioA ← 12 / 4 ratioB ← 12 / 3 IF ratioA _ ratioB THEN OUTPUT "B"

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A orig ← 10

B comp ← 2

C diff ← orig - comp

D pct ← diff / comp * 100

Question 2

A ratio ← 2 / 10

B pct ← (10 - 2) / 10 * 100

C DISPLAY ratio, pct

Question 3

A orig ← 50

B comp ← 10

C saved ← orig + comp

D pct ← saved / orig * 100

Question 4

A ratioA ← 60 / 20

B ratioB ← 30 / 60

C IF ratioA > ratioB THEN

D DISPLAY 'A is better'

Question 5

A ratio ← 10 / 2

B saved ← 10 - 2

C pct ← saved / 10

D DISPLAY pct

Answer Key

Calculating compression ratio and space saved

Section A: Quick Questions

A — 5 to 1 (10 / 2)

B — original size / compressed size

B — 80%

A — (original - compressed) / original x 100

A — The ratio is 4 to 1 and 75% was saved

Section B: Match the Pairs

ratio = original / compressed → Works out the compression ratio by dividing the original size by the compressed size

saved = (original - compressed) / original * 100 → Works out the percentage of space saved by compression

A 10 MB file compressed to 2 MB has a compression ratio of 5 to 1 → 10 / 2 = 5

Technique A shrinks 50 MB to 10 MB and technique B shrinks 50 MB to 25 MB, so A saves more space → (50 - 10) / 50 * 100 = 80 and (50 - 25) / 50 * 100 = 50

ratio = compressed / original → The sizes are the wrong way around. The ratio should be original divided by compressed, so 10 MB down to 2 MB gives 5, not 0.2.

saved = (10 - 2) / 2 * 100 → The percentage saved is divided by the compressed size (2). It must be divided by the original size (10), giving 80%, not 400%.

Section C: Definitions

compression ratio = original size / compressed size — Original size divided by compressed size. Percentage saved = (original - compressed) / original x 100. Example: 10 MB down to 2 MB is a ratio of 5 to 1, saving 80%.

Section D: Fill in the Blanks

ratio ← original / compressed

saved ← (original - compressed) / original
percent ← saved * 100

original ← 10
compressed ← 2
saved ← (original - compressed) / original

saved ← 8 / 10
percent ← saved * 100

ratioA ← 12 / 4
ratioB ← 12 / 3
IF ratioA < ratioB THEN OUTPUT "B"

Section E: Spot the Error

D — Percentage saved is divided by the ORIGINAL size, not the compressed size. It should be pct ← diff / orig * 100, which gives 80.

A — Compression ratio is original size divided by compressed size. It should be ratio ← 10 / 2, which gives 5 (a ratio of 5 to 1).

C — The space saved is the original size MINUS the compressed size, not plus. It should be saved ← orig - comp, which gives 40.

B — Both ratios must be original divided by compressed. Technique B should be ratioB ← 60 / 30 (a ratio of 2), so it can be compared fairly with A (a ratio of 3).

C — The division gives a fraction (0.8). It must be multiplied by 100 to become a percentage. It should be pct ← saved / 10 * 100, which gives 80.