3.6: Chapter 3 - Key Terms and Symbols
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- 58260
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Key Terms
Interquartile range (IQR): the difference between the third quartile (Q3) and the first quartile (Q1). It measures the spread of the middle 50% of the data.
Mean: the arithmetic average of the numbers. This is the center that most people call the average, though all three – mean, median, and mode – really are averages.
Median: the data value in the middle of a sorted list of data. To find it, you put the data in order and then determine which data value is in the middle of the data set.
Midrange: the sum of the least and the greatest value in the data set, divided by 2.
Mode: the data value that occurs the most frequently in the data. To find it, you count how often each data value occurs, and then determine which data value occurs most often.
Percentile: a measure of ranking. It represents a location measurement of a data value to the rest of the values. Many standardized tests give the results as a percentile. Doctors also use percentiles to track a child’s growth.
kth percentile: the data value that has k% of the data at or below that value.
Quartiles: values that divide a data set into four equal parts, each containing 25% of the data. They help describe the spread and center of the data.
First quartile: the value that marks the 25th percentile of a data set. It separates the lowest 25% of the data from the rest and is the median of the lower half of the data.
Second quartile: the median of the data set. It marks the 50th percentile, meaning half of the data values are less than or equal to Q2, and the other half are greater.
Third quartile: the value at the 75th percentile of a data set. It separates the lowest 75% of the data from the highest 25% and is the median of the upper half of the data.
Sample variance: a statistical measure that shows how spread out the values in a sample are from the sample mean. It estimates the variability or dispersion within a sample data set.
Standard deviation: a measure of how spread out or dispersed the values in a data set are from the mean (average). It tells you, on average, how much the data values differ from the means.
Z-score: measures how far a data point is from the average (mean) of a data set, measured in standard deviations. It helps compare values from different distributions by showing if a number is above or below the average and by how much. Z-scores help standardize values so they can be compared, even if they come from different groups or scales.
Symbols
\( \bar{x} \) - sample mean
\( \mu \) - population mean
\(x_M\) - midpoint
\( \text{MD} \) - median
\( \text{MR} \) - midrange
\( \text{Mode} \) - mode
\( P_k \) - k-th percentile
\( Q_1 \) - first quartile
\( Q_2 \) - second quartile (median)
\( Q_3 \) - third quartile
\( R \) - range
\( s \) - sample standard deviation
\( s^2 \) - sample variance
\( \sigma \) - population standard deviation
\( \sigma^2 \) - population variance
\(w\) - weight
\( z \) - z-score
Authors
"3.6: Chapter 3 - Key Terms and Symbols" by Toros Berberyan, Tracy Nguyen, and Alfie Swan is licensed under CC BY 4.0