Understand Data Distribution Characteristics - 6th Grade Math

The value that occurs most often. A data set can have multiple modes or no mode.

$\text{range}=\text{max}-\text{min}$. Measures the total spread from smallest to largest value.

Median. Outliers don't affect the median's position in ordered data.

Mean. Outliers pull the mean toward extreme values.

$\frac{15}{2}$. $(4+6+8+12)/4 = 30/4 = 15/2$.

$\frac{9}{2}$. Average the 2nd and 3rd values: $(3+6)/2 = 9/2$.

$7$. The middle value in 5 ordered values is the 3rd one.

$7$. $10 - 3 = 7$ using the range formula.

Most values are high with a long tail toward lower values. Left skew means the tail extends toward lower values.

Most values are low with a long tail toward higher values. The tail points in the direction of the skew.

Left and right sides look like mirror images around the center. In symmetric distributions, mean and median are equal.

A question that anticipates variability in its data answers. Expects different answers from different individuals or measurements.

How data values are spread out and how often each value occurs. Shows the pattern of how data values occur across the range.

A typical or representative value for the data set. The center summarizes where most data values cluster.

How far apart the data values are from each other. Spread measures the variability or dispersion of the data.

The mean. The mean is calculated by summing all values and dividing by count.

The pattern of the data (clusters, peaks, gaps, symmetry, skew). Shape reveals patterns like symmetry or clustering in the data.

$\text{mean}=\frac{x_1+x_2+\cdots+x_n}{n}$. Sum all values and divide by the number of values.

Mean and median. Both mean and median measure center; range measures spread.

$\text{mean}=\frac{x_1+x_2+\cdots+x_n}{n}$. Add all values and divide by the count.

Median. Outliers pull the mean but don't affect the median's position.

Left and right sides are roughly mirror images around the center. In symmetric distributions, data balances equally on both sides.

One side has a longer tail than the other side. Skewed means data bunches on one side with a tail stretching out.

$5$. With 5 values, the 3rd position holds the median.