Standard Deviation, Mean and Median

Standard Deviation, Mean and Median

Defining Terms

  • Standard Deviation is a measure of dispersion that shows the average distance of each value from the mean in a data set.

  • Mean is a measure of central tendency calculated by adding all the values and dividing by the total number of values. Also known as the average.

  • Median is the middle value in an ordered set of data. If the dataset has an even number of observations, the median is the mean of the two middle values.

Calculating the Mean

  • Find the sum of all the values.

  • Then, count the number of values in the data set.

  • Finally, divide the sum by the count to get the mean.

Calculating the Median

  • Sort the data from lowest to highest.

  • If the dataset has an odd number of observations, the median is the middle number.

  • If the dataset has an even number, calculate the mean of the two middle numbers.

Understanding Standard Deviation

  • Calculate the mean of the dataset.

  • Subtract the mean from each data point, then square the result.

  • Find the mean of these squared differences.

  • Finally, take the square root of this average.

Comparing Mean, Median and Standard Deviation

  • The mean gives an average value, but can be skewed by outliers (very high or low values).

  • The median provides a more robust measure of central tendency when the dataset has pronounced outliers.

  • The standard deviation provides a measure of the spread of data around the mean, with a low standard deviation implying that data points are generally close to the mean.

Interpreting Standard Deviation

  • A lower standard deviation suggests that most of data is close to the mean, indicating consistency within the data set.

  • A higher standard deviation suggests a wide spread of values around the mean, indicating high variability within the data set.

Application of these Measures in Real-Life Context

  • These measures of central tendency and dispersion can be used in different fields such as statistics, finance, physics, and social sciences to make predictions, draw conclusions and make informed decisions.