Mean, Median, Mode

Mean

The balance point or the average value of a data set.

How to Calculate the Mean

Add all data values together and divide the sum by the total count of numbers in the data set.

Median

The exact middle value when data points are arranged in order.

How to Find the Median

1. Arrange the numbers in order from least to greatest. 2. If the count is odd, choose the middle number. 3. If the count is even, add the two middle values together and divide by 2.

Mode

The number or numbers that appear most frequently in a data set.

Range

The total distance covered between the highest and lowest points of the data set.

Quartiles

Values that divide an ordered data set into four equal parts (quarters).

Interquartile Range (IQR)

The distance between the first and third quartiles, representing the spread of the middle 50% of the data.

Mean Absolute Deviation (MAD)

The average distance between each individual data point and the calculated mean of the data set.

Outlier

An extreme value within a data set that is significantly higher or lower than the rest of the observations.

First Quartile (Q1)

The median of the lower half of the data (halfway to the main median).

Third Quartile (Q3)

The median of the upper half of the data (halfway from the main median to the maximum).

Step 1 of Outlier Formula

Calculate the Interquartile Range (IQR = Q3 - Q1).

Step 2 of Outlier Formula

Multiply the IQR by the standard scaling constant of 1.5.

Step 3 of Outlier Formula

Establish the Lower Limit: Q1 - (1.5 x IQR).

Step 4 of Outlier Formula

Establish the Upper Limit: Q3 + (1.5 x IQR).

Line Plot

Displays individual data frequency along a standard continuous number line using dots or X marks.

Histogram

Graphs continuous quantitative data sorted into equal-sized ranges called intervals along the X-axis.

Box Plot

A graphic summary of a data set mapped across its Five-Number Summary boundaries.

Peaks

Distinct cluster high points or crest positions showing maximum frequency zones.

Gaps

Empty sections along the axis showing where absolutely no observations occurred.

Clusters

Tight groupings where numerous data entries occur close together.

Symmetric Distribution

A balanced distribution shape where the left half looks like a mirror reflection of the right half.

Skewed Right (Positive Skew)

The bulk of the data values clump on the left side, and a long tail pulls the mean toward the right.

Skewed Left (Negative Skew)

The bulk of the data values clump on the right side, with a long tail extending toward lower values.