Understand Measures of Center and Variation - 6th Grade Math

$5$. $\frac{2+4+6+8}{4}=\frac{20}{4}=5$

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

$20-9=11$. Maximum is $20$, minimum is $9$.

Range. This formula calculates spread, not center.

A single number that summarizes all values in the data set. It represents the entire dataset with one typical value.

Variation. Measures of variation quantify how dispersed the data values are.

Center. Measures of center give one representative value for the whole dataset.

Greatest value minus least value. Range measures the total spread from minimum to maximum.

Mean. The mean is where data would balance if placed on a number line.

Range. Range spans from the minimum to maximum data value.

Mean. Outliers pull the mean toward them but don't shift the median as much.

Median. The median's position-based calculation resists outlier influence.

$4$. $(2+4+4+6) ÷ 4 = 16 ÷ 4 = 4$.

$5$. With $5$ values, the median is the $3$rd value in order.

$5$. With $4$ values, median $= (4+6) ÷ 2 = 5$.

$5$. The value $5$ appears $3$ times, more than any other value.

$8$. Range $= 18 - 10 = 8$.

$(3,9)$. Median of $1,2,3,4,10$ is $3$; range $= 10-1 = 9$.

Mean, median, and mode. These are the three ways to find a typical or central value.

Sum of values divided by the number of values. The mean is the arithmetic average of all data values.

The middle value after the data are ordered. For odd counts, it's the exact middle; for even, average the two middle values.

$\text{range}=\text{maximum}-\text{minimum}$. Difference between highest and lowest values.

Median. Middle position resists outlier influence.

The mean of the two middle values. Average the two center values when count is even.