How to find the median

The median is the value that’s exactly in the middle of a data set when it is ordered. It’s a measure of central tendency that separates the lowest 50% from the highest 50% of values.

The steps for finding the median differ depending on whether you have an odd or an even number of data points. If there are two numbers in the middle of a data set, their mean is the median.

The median is usually used with quantitative data (where the values are numerical), but you can sometimes also find the median for an ordinal data set (where the values are ranked categories).

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How to find the mode

The mode or modal value of a data set is the most frequently occurring value. It’s a measure of central tendency that tells you the most popular choice or most common characteristic of your sample.

When reporting descriptive statistics, measures of central tendency help you find the middle or the average of your data set. The three most common measures of central tendency are the mode, median, and mean.

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How to find the interquartile range

In descriptive statistics, the interquartile range tells you the spread of the middle half of your distribution.

Quartiles segment any distribution that’s ordered from low to high into four equal parts. The interquartile range (IQR) contains the second and third quartiles, or the middle half of your data set.

Quartiles and the IQR

Whereas the range gives you the spread of the whole data set, the interquartile range gives you the range of the middle half of a data set.

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Understanding and calculating standard deviation

The standard deviation is the average amount of variability in your dataset. It tells you, on average, how far each value lies from the mean.

A high standard deviation means that values are generally far from the mean, while a low standard deviation indicates that values are clustered close to the mean.

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How to find the range of a data set

In statistics, the range is the spread of your data from the lowest to the highest value in the distribution. It is a commonly used measure of variability.

Along with measures of central tendency, measures of variability give you descriptive statistics for summarizing your data set.

The range is calculated by subtracting the lowest value from the highest value. While a large range means high variability, a small range means low variability in a distribution.

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Measures of variability

Variability describes how far apart data points lie from each other and from the center of a distribution. Along with measures of central tendency, measures of variability give you descriptive statistics that summarize your data.

Variability is also referred to as spread, scatter or dispersion. It is most commonly measured with the following:

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An introduction to inferential statistics

While descriptive statistics summarize the characteristics of a data set, inferential statistics help you come to conclusions and make predictions based on your data.

When you have collected data from a sample, you can use inferential statistics to understand the larger population from which the sample is taken.

Inferential statistics have two main uses:

  • making estimates about populations (for example, the mean SAT score of all 11th graders in the US).
  • testing hypotheses to draw conclusions about populations (for example, the relationship between SAT scores and family income).

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What is a ratio scale of measurement?

A ratio scale is a quantitative scale where there is a true zero and equal intervals between neighboring points. Unlike on an interval scale, a zero on a ratio scale means there is a total absence of the variable you are measuring.

Length, area, and population are examples of ratio scales.

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