Question
Download Solution PDFWhat is the mean deviation from the mean of the numbers 10, 9, 21, 16, 24 ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Mean deviation about the mean = \(\frac{{\mathop \sum \nolimits_{{\rm{i}} = 1}^{{\rm{i}} = {\rm{n}}} \left| {{{\rm{x}}_{\rm{i}}}-{\rm{\;\bar x}}} \right|}}{{\rm{n}}}\), Where \({\rm{\bar x}}\) is mean.
Calculation:
Given numbers are 10, 9, 21, 16, 24
Total numbers = 5
\({\rm{Mean}} = {\rm{\bar x}} = \;\frac{{10 + 9 + 21 + 16 + 24}}{5} = \frac{{80}}{5} = 16\)
We know that mean deviation about the mean = \(\frac{{\mathop \sum \nolimits_{{\rm{i}} = 1}^{{\rm{i}} = {\rm{n}}} \left| {{{\rm{x}}_{\rm{i}}}-{\rm{\;\bar x}}} \right|}}{{\rm{n}}}\)
Mean deviation from the mean = \(\frac{{\left| {10-{\rm{\;}}16} \right| + \left| {9-{\rm{\;}}16} \right| + \left| {21-{\rm{\;}}16} \right| + \left| {16{\rm{\;}}-{\rm{\;}}16} \right| + \left| {24-{\rm{\;}}16} \right|\;}}{5}\)
\(= \frac{{6 + 7 + 5 + 0 + 8}}{5} = \frac{{26}}{5} = 5.2\)Last updated on May 30, 2025
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