Statistics - Trivium Test Prep Online Courses

# 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.

$$mean\ (with\ outlier) = \frac{16\ +\ 19\ +\ 19\ +\ 25\ +\ 27\ +\ 29\ +\ 75}{7} = \frac{210}{7} = {30}$$

$$mean\ (without\ outlier) = \frac{16\ +\ 19\ +\ 19\ +\ 25\ +\ 27\ +\ 29}{6} = \frac{135}{6} = {22.5.}$$

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