Normal Distribution and Z-Scores

These flashcards cover key concepts related to normal distribution, z scores, standard deviation, skewness, and kurtosis, essential for understanding statistical performance measures.

What are the typical characteristics of a normal curve?

A bell-shaped curve that is symmetrical, with most values clustering around the mean.

What is a z score?

A transformed score that indicates how many standard deviation units a raw score is above or below the mean.

How is the standard deviation (SD) related to the normal curve?

It measures how spread out the values are from the mean; a smaller SD means values are closer to the mean.

According to the Empirical Rule, what percentage of values fall within ±1 SD from the mean?

68% of values.

What percentage of scores fall within ±2 SDs according to the Empirical Rule?

95% of scores.

What is the z score calculation for a raw score of 85, given a mean of 80 and a standard deviation of 5?

The z score is 1.

What does it mean if a distribution is positively skewed?

Most values are clustered around the left tail, while the right tail is longer.

What does it mean if a distribution is negatively skewed?

Most values are concentrated on the right side tail of the distribution graph while the left tail of the distribution graph is longer.

What is kurtosis in relation to a normal distribution?

A measure of whether the data are heavy-tailed or light-tailed, which informs us about the peakedness of the distribution.

What is the meaning of z scores for determining performance in different subjects?

Z scores allow comparison of students' performance relative to their class averages and standard deviations.

What are the properties of z scores transformed from raw scores?

They preserve the shape of the original distribution, with a mean of 0 and a standard deviation of 1.

the normal curve is a _______ of population scores

Theoretical Distribution

the values are close to the mean

small SD

the values are more spread out

large SD

1 step above the mean

+1 SD

1 step below the mean

-1 SD

What percentage of scores fall within ±3 SDs according to the Empirical Rule?

99.7%

a measure of symmetry, or mire precisely the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the left and right of the center point

Skewness

Right Skewed

Positive Skewed

Left Skewed

Negative Skewed

The scores are tightly clustered around the mean.

The peak is tall and sharp.

There are more extreme outliers in the tails (very low or very high scores).

Leptokurtic

The scores are more spread out across the range.

There is less clustering around the mean.

The peak is low and broad.STAND

PlatykurticARDIZED

A ________ (also called a derived score or standard score) is a transformed score that indicates a test taker's position relative to the mean of a reference group, typically expressed in terms of standard deviation units.

Standardized Scres

A ______ is a transformed score that designates how many standard deviation units the corresponding raw score is above or below the mean.

Z-Scores

what process is called by which the raw score is altered

Score Transformation

The mean of the z scores always ____ (µ=0)

equals to 0

The standard deviation of z scores always _______

equals to 1