Center, Shape, & Spread of Data - PSAT Math

Outliers are $<Q_1-1.5\text{IQR}$ or $>Q_3+1.5\text{IQR}$. Values beyond 1.5 IQRs from the quartiles.

The middle value after sorting the data. Sort first, then pick the one in the middle.

$\text{mean}=\frac{\text{sum of values}}{\text{number of values}}$. Divide the total by how many values there are.

The average of the two middle sorted values. No single middle value, so average the two center ones.

The median of the lower half (the $25$th percentile). Splits the bottom 25% from the rest.

The median of the upper half (the $75$th percentile). Splits the top 25% from the rest.

$5$. $\frac{2+4+4+10}{4}=\frac{20}{4}=5$

$8$. Already sorted; middle of 5 values is the 3rd.

$\frac{11}{2}$. Average of 5 and 6: $\frac{5+6}{2}=\frac{11}{2}$

$11$. $9-(-2)=11$

$8$. $20-12=8$

$1$. $Q_1-1.5(\text{IQR})=10-1.5(6)=10-9=1$

Mean. The tail pulls the mean toward higher values.

The interquartile range, $\text{IQR}$. Shows the spread of the middle 50% of data.

$Q_3-Q_1$. Third quartile minus first quartile.

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

The single middle value in the ordered list. With odd count, the middle value stands alone.

Average of the two middle values. With even count, average the two center values.

The value that occurs most frequently. The value with the highest frequency.

$\text{max}-\text{min}$. Subtract the smallest value from the largest.

$\text{min},\ Q_1,\ \text{median},\ Q_3,\ \text{max}$. Lists the key values that divide the data into quarters.

Typical distance of values from the mean. Measures how spread out data points are.

Median. Outliers affect mean more than median.

$IQR$. IQR ignores extreme values, unlike range.

Lower fence $=Q_1-1.5(IQR)$. Values below this are potential outliers.

Right-skewed (positively skewed). Tail extends right, pulling mean higher.

Left-skewed (negatively skewed). Tail extends left, pulling mean lower.

$5$. $(2+4+6+8)÷4=20÷4=5$.

$9$. Middle value of ordered list is $9$.