Normal Curve Flashcards

Questions and Answers

What are the characteristics of a normal curve? (Select all that apply)

Frequency gradually tapers off towards the ends of the curve (correct)

Mean, median, mode are all equal (correct)

Curve is bell-shaped & symmetrical (correct)

Highest frequency is at the ends of the curve

What is the proportion of area under the normal curve by SD/Z-score?

Know how to calculate.

What is a Z-score?

A transformed score that designates how many standard deviations the raw score is above or below the mean.

How do you calculate a Z-score?

For sample data: (Xi - Mean) / SDsample; For population: (Xi - Mean) / SDpop. Signup and view all the answers

How do you read the Z-table for a fraction?

Use the table to find the percentile rank; add 0.5 if above mean. Signup and view all the answers

How can you change a Z-score to a raw score?

X = Z(SD) + Mean. Signup and view all the answers

Why do we care about Z-scores?

They allow easy comparison across distributions and focus on relative differences. Signup and view all the answers

How is standard deviation different from range?

Standard deviation measures dispersion relative to the mean; range only gives the difference between highest and lowest scores. Signup and view all the answers

Study Notes

Normal Curve Characteristics

Bell-shaped and symmetrical distribution.
Mean, median, and mode are identical.
Highest frequency occurs at the center of the curve.
Frequency diminishes gradually towards the tails.

Proportion of Area under the Normal Curve

Knowledge of calculating area under the curve using standard deviations (SD) or Z-scores is essential.

Z-score Definition

A Z-score transforms raw scores into standardized scores.
It indicates the number of standard deviations a score is above or below the mean.

Calculating a Z-score

For sample data: ( Z = \frac{X_i - \bar{X}}{SD_{sample}} )
For population data: ( Z = \frac{X_i - \mu}{SD_{pop}} )
Sample mean is denoted as ( \bar{X} ) and population mean as ( \mu ).
Population standard deviation is represented by the Greek letter sigma (σ).

Reading the Z-table for Fractional Z-scores

Example: For a Z-score of 0.47, determine percentile rank.
Percentile rank calculation: 50% (mean) + 18.08% (from Z-table) = 68.08%.
If the Z-score is above the mean, add 0.5 to the percentile rank.

Converting Z-scores to Raw Scores

Use the formula: ( X = (Z \times SD) + \text{Mean} )
Z-scores can also help determine percentile rank.

Importance of Z-scores

Facilitate comparisons across different distributions.
Highlight relative differences, useful in correlations (e.g., height vs. weight).

Standard Deviation vs. Range

Standard deviation measures score dispersion relative to the mean, indicating score variability.
Range merely indicates the difference between the highest and lowest scores without offering insights into relative dispersion across variables.

Description

Explore the key characteristics of the normal curve with these flashcards. Learn about the properties such as symmetry, central tendency, and area under the curve. This quiz will also introduce you to Z-scores and their calculation in relation to standard deviations.