Question Number 111533 by Aina Samuel Temidayo last updated on 04/Sep/20
$$\mathrm{The}\:\mathrm{mean},\mathrm{median}\:\mathrm{and}\:\mathrm{mode}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{data}\:\mathrm{values}\:\mathrm{90},\mathrm{54},\mathrm{x},\mathrm{123},\mathrm{62},\mathrm{78},\mathrm{58},\mathrm{81} \\ $$$$\mathrm{are}\:\mathrm{all}\:\mathrm{equal}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}? \\ $$
Commented by Rasheed.Sindhi last updated on 04/Sep/20
$$\mathrm{78} \\ $$
Commented by Aina Samuel Temidayo last updated on 04/Sep/20
$$\mathrm{Your}\:\mathrm{solution}\:\mathrm{please}? \\ $$
Answered by Rasheed.Sindhi last updated on 05/Sep/20
$${If}\:{x}\:{has}\:{a}\:{value}\:{other}\:{than} \\ $$$$\mathrm{90},\mathrm{54},\mathrm{123},\mathrm{62},\mathrm{78},\mathrm{58},\mathrm{81}\:{then}\:{the} \\ $$$${mode}\:{doesn}'{t}\:{exist}. \\ $$$${But}\:{as}\:{the}\:{mode}\:{exists}\:{so} \\ $$$${x}\in\left\{\mathrm{90},\mathrm{54},\mathrm{123},\mathrm{62},\mathrm{78},\mathrm{58},\mathrm{81}\right\} \\ $$$${And}\:{also}\:{mode}\:{is}\:\:{x}\left(\because\:{it}\:{exist}\right. \\ $$$$\left.{twice}\:{and}\:{all}\:{others}\:{once}\:{only}\right) \\ $$$${Now} \\ $$$$\:\:\:\:\:\:\:{mean}={mode} \\ $$$$\frac{\mathrm{90}+\mathrm{54}+{x}+\mathrm{123}+\mathrm{62}+\mathrm{78}+\mathrm{58}+\mathrm{81}}{\mathrm{8}}={x} \\ $$$$\mathrm{546}+{x}=\mathrm{8}{x} \\ $$$$\:{x}=\mathrm{78} \\ $$$${Fortunately}\:{it}'{s}\:{also}\:{median} \\ $$$$\mathrm{123},\mathrm{90},\mathrm{81},\mathrm{78},\mathrm{78},\mathrm{62},\mathrm{58},\mathrm{54} \\ $$$${Middle}\:{position}\:{numbers}:\:\mathrm{78},\mathrm{78} \\ $$$${So},\:\:\:\:\:\:\:{median}=\frac{\mathrm{78}+\mathrm{78}}{\mathrm{2}}=\mathrm{78} \\ $$$${Finally}, \\ $$$$\:\:{x}=\:{mean}={mode}={median}=\mathrm{78} \\ $$
Commented by Aina Samuel Temidayo last updated on 05/Sep/20
$$\mathrm{Thanks}. \\ $$