Central Tendency (exam 1)

What is central tendency?

A measure that describes how scores cluster in a distribution. Where the data tends to cluster

What are the three measures of central tendency?

Mode, Median, Mean.

Define Mode.

The score that occurs most frequently.

What types of data can use Mode?

Nominal and ordinal data.

List one advantage and one disadvantage of Mode.

Advantage: Quick to find. Disadvantage: Unstable and does not reflect extreme scores.

Define Median.

The middle score, or the 50th percentile, preferred for skewed data.

Why use the Median instead of the Mean?

The Median is not affected by outliers.

How to find Median for odd number of values?

Identify the middle position using (n + 1) / 2.

How to find Median for even number of values?

Take the average of the two middle values.

Define Mean.

The arithmetic average, calculated by summing all scores and dividing by the number of scores.

When should you use the Mean?

When data are near normal and measured on interval or ratio scales.

Use the mean when your data forms a shape close to a normal bell curve and the numbers are things you can measure and do math with, like height, weight, or temperature.

What is the relationship among Mode, Median, and Mean in a normal distribution?

They all fall at or near the same value.

When should you use Mode?

When only a rough estimate is needed and the data are normal or nearly normal.

When should you use Median?

When data are ordinal, skewed, or when the middle score is needed.

When should you use Mean?

When all data points should be considered and further calculations like SD are needed.

Define Variability.

Measures how spread out the scores are in a distribution.

What are common measures of variability?

Range, Interquartile Range (IQR), Variance, Standard Deviation, Standard Error of the Mean.

Define Range.

The difference between the highest and lowest score.

What is a limitation of Range?

It only uses two scores and may be affected by outliers.

Define Interquartile Range (IQR).

The difference between the 75th percentile (Q3) and 25th percentile (Q1).

Why is IQR useful?

It focuses on the middle 50% of data and is not affected by extreme scores.

Define Variance.

The average squared difference between each score and the mean.

Why can Variance be hard to interpret?

It uses squared units, which are not intuitive.

Define Standard Deviation (SD).

The square root of the variance, representing average deviation in original units.

What is the formula for SD in a sample?

SD = sqrt(Σ(x - x̄)² / (N - 1)).

What is the formula for SD in a population?

SD = sqrt(Σ(x - x̄)² / N).

Define Coefficient of Variation (CoV).

CoV = (SD / Mean) × 100, allows comparison of variability between different units.

What is a boxplot used for?

To display variability, IQR, and identify outliers.

What percentage of data falls within ±1 SD in a normal curve?

Approximately 68%.

What does the Central Limit Theorem state?

As more random samples are added, their distribution approaches a normal curve.