Basic Statistics & Consecutive Numbers - Cheat Sheet
Your last-minute revision companion for mastering statistics formulas and consecutive number problems before your exam.
Basic Statistics Formulas
Formulas
Average/Mean = Sum of all terms / Number of terms
Meaning
Sum = total of all values, Number = count of values
Watch out
Don't confuse sum with count - make sure you're dividing by the correct number of terms
When to use
When asked to find the average or mean of a set of numbers
Missing term = Sum of original terms - Sum of remaining terms
Meaning
Original sum = average × total count, Remaining sum = sum of known values
Watch out
Calculate the total sum first using average × count before subtracting
When to use
When one value is missing from a group with known average
Sum of all terms = Average × Number of terms
Meaning
Average = given mean, Number = total count of values
Watch out
Make sure you use the correct count including any new additions
When to use
When you know the average and need to find the total sum
Weighted Average = Sum of weighted terms / Total number of terms
Meaning
Weighted terms = value × frequency, Total number = sum of all frequencies
Watch out
Multiply each average by its group size before adding, don't just average the averages
When to use
When different groups have different sizes or weights
Important facts
- Average can be decimal even if all original numbers are whole numbers
- When one person joins/leaves a group, both the sum and count change
- Weighted average is closer to the average of the larger group
- If all values are the same, the average equals that value
- Adding the same number to all terms doesn't change their average
Key definitions
Average (Mean)
Example
Average of 10, 20, 30 = (10+20+30)/3 = 20
The sum of all values divided by the number of values
Weighted Average
Example
26 boys (40kg avg) + 14 girls (35kg avg) = weighted average of class
Average where some values count more than others based on frequency or importance
Sum of Terms
Example
If average of 5 numbers is 20, sum = 5 × 20 = 100
Total when all values in a data set are added together
Diagrams to know
- Formula relationship diagram showing connections between average, sum, and count
- Step-by-step process for solving missing term problems
Unit Conversion
Formulas
New Unit = Original Value × (New Unit / Original Unit)
Meaning
Original Value = given measurement, Conversion Factor = ratio of units
Watch out
Make sure units cancel out correctly - wrong fraction gives wrong answer
When to use
Converting between different units of measurement
Common values
Value
7 days
Symbol
week
Quantity
Days per week
Value
12 inches
Symbol
ft
Quantity
Inches per foot
Value
3 feet
Symbol
yd
Quantity
Feet per yard
Value
16 ounces
Symbol
lb
Quantity
Ounces per pound
Value
8 pints
Symbol
gal
Quantity
Pints per gallon
Important facts
- 1 week = 7 days
- 1 foot = 12 inches
- 1 yard = 3 feet
- 1 pound = 16 ounces
- 1 gallon = 8 pints
- 1 mile = 1.6 kilometers
- 1 inch = 25.4 millimeters
Key definitions
Unit Conversion
Example
644 days = 644 ÷ 7 = 92 weeks
Process of changing a measurement from one unit to another equivalent unit
Conversion Factor
Example
1 foot/12 inches or 1 yard/3 feet
A fraction equal to 1 that relates two different units
Diagrams to know
- Common unit conversion chart
- Step-by-step conversion process
Fraction Word Problems
Formulas
Whole = 1 - (Sum of other fractions)
Meaning
Whole = complete unit (1), Other fractions = parts already accounted for
Watch out
Convert all fractions to common denominator before adding or subtracting
When to use
Finding remaining fraction when some parts are given
Rate = 1 ÷ Time to complete
Meaning
Rate = fraction completed per unit time, Time = total time needed
Watch out
Don't confuse time with rate - rate is always 1/time
When to use
Finding what fraction of work is done in given time
Part = Fraction × Whole
Meaning
Part = portion you want to find, Fraction = given ratio, Whole = total amount
Watch out
Make sure you identify what represents the 'whole' correctly
When to use
Finding actual amount when fraction of total is given
Important facts
- All fractions in a problem must add up to 1 (the whole)
- When finding missing part, subtract known parts from 1
- Rate problems: if job takes x hours, rate is 1/x per hour
- Fraction × Whole = Part, so Whole = Part ÷ Fraction
- When two parts have ratio a:b, longer part = total × a/(a+b)
Key definitions
Fraction of Whole
Example
3/8 of tank is filled means 3 parts out of 8 total parts
Part of a complete unit expressed as numerator over denominator
Rate Problem
Example
If tank fills in 2¼ hours, rate = 1/(9/4) = 4/9 per hour
Problem involving how much work is completed per unit time
Diagrams to know
- Fraction bar diagrams showing parts of whole
- Rate and work relationship diagrams
Must remember
- Average = Sum ÷ Count (most basic and important formula)
- To find missing term: Calculate total sum first, then subtract known values
- Weighted average formula: (Group1×Size1 + Group2×Size2) ÷ (Size1+Size2)
- 1 week = 7 days, 1 foot = 12 inches, 1 yard = 3 feet, 1 pound = 16 ounces
- Unit conversion: multiply by conversion factor as fraction
- All fractions in a whole must sum to 1
- Rate = 1 ÷ (time to complete), so if job takes 2¼ hours, rate is 4/9 per hour
- Part = Fraction × Whole, so Whole = Part ÷ Fraction
- When joining/leaving groups, both sum and count change
- Always convert fractions to common denominator before adding/subtracting
Last minute tips
- For average problems, always check if someone joins/leaves the group - this changes both sum and count
- In weighted average, multiply each group's average by its size before adding
- For conversion problems, set up fraction so original units cancel out
- When finding missing fraction, subtract all known fractions from 1
- Read fraction problems twice to identify what represents the 'whole'
Comparison tables
Average vs Weighted Average
| Aspect | Simple Average | Weighted Average |
|---|---|---|
| Formula | Sum ÷ Count | (Sum of weighted terms) ÷ Total count |
| When to use | All values equal importance | Groups have different sizes |
| Example | Test scores: 80, 90, 70 | 26 boys (40kg) + 14 girls (35kg) |
Finding Missing Values
| Known | Unknown | Formula to Use | |
|---|---|---|---|
| Average + Count | Average, Count | Sum | Sum = Average × Count |
| Average + Some terms | Average, Some values | Missing term | Missing = Total sum - Known sum |
| Sum + Count | Sum, Count | Average | Average = Sum ÷ Count |
Diagrams
Statistics & Numbers Concept Map
Overview of all major concepts showing relationships between different types of problems
Average Problem Solving Process
Step-by-step decision process for solving different types of average problems
Unit Conversion Method
Systematic approach to unit conversion problems ensuring correct setup