Statistics Test Prep

What is IQR?

The interquartile range is a measure of statistical dispersion representing the spread of the middle 50% of a data set

What is the IQR formula?

IQR= Q3 - Q1

IQR Steps

1. Order data (low—>high)

2. Find N

3. Q= N x 0.25

4. Q= N x 0.75

5. Find positions

6. Average if needed

7. IQR= Q3 - Q1

What is Q1?

25th percentile (bottom 25%)

What is Q3?

75th percentile (top 25%)

Range

The simplest measure of variability, calculated as the difference between the highest and lowest values in dataset.

How do you find the range?

Highest # - Lowest # = RANGE

Population vs Sample

Population = whole group

Sample = part of the group

Subtracting a negative rule

Subtracting a negative= adding

Example: 18-(-10)=28

Sign rules with negatives

• -(-)= add

• +(-)= subtract

• -(+)= subtract

Which number is smaller? (negatives)

More negative= smaller

Example number line:

-10, -3, -2, 0, 5

Further LEFT= smaller

Finding range with negative numbers

    1. Find highest

    2. Find lowest (most negative)

    3. Subtract:

• Range = highest − lowest

• subtracting a negative = ADD

Observed / Possible Differences (IQV)

• Measures how many differences exist

• 0 = no differences (low variation)

• 1 = many differences (high variation)

Example:

All same group:

• A = 100%

• B = 0%

• C = 0%

👉 No differences
👉 IQV ≈ 0 (LOW variation)

Example:

All same group:

A = 100%

B = 0%

C = 0%

👉 No differences

👉 IQV ≈ 0 (LOW variation)

what makes IQV high?

• data is evenly spread across categories

• Values are similar in size

• Result is close to 1

What is the mean? How do you find it?

Mean = average
Steps:

1. Add all numbers

2. Divide by how many numbers there are

What does it mean to “square” a number?

Square = multiply the number by itself
Examples:
3² = 3 × 3 = 9
(−5)² = (−5)(−5) = 25

• Squaring ALWAYS makes numbers positive

Rules for multiplying negatives

Positive × Positive = Positive
Negative × Negative = Positive
Positive × Negative = Negative

What is a square root?

Square root = number that multiplies by itself to get the original

Examples:
√16 = 4 (because 4×4 = 16)
√25 = 5

Steps to find variance

1. Find mean

2. Subtract mean (deviations)

3. Square each deviation

4. Add

5. Divide by (n − 1)

• Final answer = variance

Steps to find standard deviation

Do ALL variance steps, then:
•Take square root at the end

Variance vs Standard Deviation

Variance = before square root
Standard deviation = after square root

•Variance = squared units
•SD = original units

What does a bigger standard deviation mean?

Bigger SD = data is more spread out

What does a smaller standard deviation mean?

Smaller SD = data is closer to the mean

Standard deviation steps

1. Find the Mean

2. Subtract all #s by mean

3. Square all #s

4. Add results

5. Divide previous # by (n−1)

6. Square root