Question

What is the median of the data shown heights of the members of me.smith class

Answer 1

`\boxed{ \bold{ \huge{ \boxed{ \sf{72}}}}}`

Explanation:

Given data : 68 , 69 , 71 , 71 , 71 , 73 , 74 , 75 , 75 , 78

N ( total number of observation ) = 10

Finding the position of median

`\boxed{ \sf{median = { ((n + 1)/(2) )}^(th \: item) }}`

`\dashrightarrow{ \sf{median = { ((10 + 1)/(2) )}^(th \: item)}}`

`\dashrightarrow{ \sf{median = {( (11)/(2)) }^(th \: item)} }`

`\dashrightarrow{ \sf{ median = {5.5}^(th \: item)}}`

`\sf{ {5.5}^(th) }` item is the average of 5 th and 6 th items.

Now, Finding the median

`\dashrightarrow{ \sf{median = \frac{ {5}^(th)item + {6}^(th) item}{2} }}`

`\dashrightarrow{ \sf{ (71 + 73)/(2) }}`

`\dashrightarrow{ \sf{ (144)/(2) }}`

`\dashrightarrow{ \sf{72}}`

Hope I helped!

Best regards! :D