Statistics
Statistics (Basic)
Statistics is the study of data. Analyzing data requires using measures of central tendency (mean, median, and mode) to identify trends or patterns.
The mean is the average; it is determined by adding all values and then dividing by the total number of values.
Find the average of the data set: {16, 19, 19, 25, 27, 29, 75}
mean =
\(\frac{16\ +\ 19\ +\ 19\ +\ 25\ +\ 27\ +\ 29\ +\ 75}{7} = \frac{210}{7} = {30}\)
The median is the number in the middle when the data set is arranged in order from least to greatest.
Find the median of the data set: {16, 19, 19, 25, 27, 29, 75}
median = 25
When a data set contains an even number of values, finding the median requires averaging the two middle values.
Find the median of the data set: {75, 80, 82, 100}
median = \(\frac{80\ +\ 82}{2}\)
= 81
The mode is the most frequent outcome in a data set. If several values appear an equally frequent number of times, both values are considered the mode. If every value in a data set appears only once, the data set has no mode.
Find the mode: {16, 19, 19, 25, 27, 29, 75}
mode = 19
Mode is most common. Median is in the middle (like a median in the road). Mean is average.
Other useful indicators include range and outliers. The range is the difference between the highest and the lowest values in a data set.
Find the range: {16, 19, 19, 25, 27, 29, 75}
range = 75 − 16 = 59
Outliers, or data points that are much different from other data points, should be noted as they can skew the central tendency. In the data set {16, 19, 19, 25, 27, 29, 75}, the value 75 is far outside the other values and raises the value of the mean. Without the outlier, the mean is much closer to the other data points.
\(mean\ (with\ outlier) = \frac{16\ +\ 19\ +\ 19\ +\ 25\ +\ 27\ +\ 29\ +\ 75}{7} = \frac{210}{7} = {30}\)
\(mean\ (without\ outlier) = \frac{16\ +\ 19\ +\ 19\ +\ 25\ +\ 27\ +\ 29}{6} = \frac{135}{6} = {22.5.}\)