CBSE Class 9 Answered

There are a number of measures of central tendency

• Arithmetic mean (or simply, mean) – the sum of all measurements divided by the number of observations in the data set
• Median – the middle value that separates the higher half from the lower half of the data set. The median and the mode are the only measures of central tendency that can be used for ordinal data, in which values are ranked relative to each other but are not measured absolutely.
• Mode – the most frequent value in the data set. This is the only central tendency measure that can be used with nominal data, which have purely qualitative category assignments.
• Geometric mean – the nth root of the product of the data values, where there are n of these. This measure is valid only for data that are measured absolutely on a strictly positive scale.
• Harmonic mean – the reciprocal of the arithmetic mean of the reciprocals of the data values. This measure too is valid only for data that are measured absolutely on a strictly positive scale.
• Weighted mean – an arithmetic mean that incorporates weighting to certain data elements
• Truncated mean – the arithmetic mean of data values after a certain number or proportion of the highest and lowest data values have been discarded.
  • Interquartile mean (a type of truncated mean)
• Midrange – the arithmetic mean of the maximum and minimum values of a data set.
• Midhinge – the arithmetic mean of the two quartiles.
• Trimean – the weighted arithmetic mean of the median and two quartiles.
• Winsorized mean – an arithmetic mean in which extreme values are replaced by values closer to the median.