Question

A local dog show features 8 Portuguese water dogs. The weights of the dogs are 38, 40, 42, 46,

45, 39, 42, 40. What are the mean and median weights of the Portuguese water dogs in the dog
show?

Answer 1

A local dog show features 8 Portuguese water dogs. The weights of the dogs are 38, 40, 42, 46,

45, 39, 42, 40. What are the mean and median weights of the Portuguese water dogs in the dog

show?

Explanation:

Answer 2

`\boxed{ \bold{ \sf{Mean \: = 41.5}}}`

`\boxed{ \bold{ \sf{Median = \: 41}}}`

Explanation:

Given weights of the dogs :

38 , 40 , 42 , 46 , 45 , 39 , 42 , 40

Find the sum of the whole data:

sum of all items ( Σx ) = 38 + 40 + 42 + 46 + 45 + 39 + 42 + 40 = 332

Number of items ( n ) = 8

To find mean, divide the sum by the total number of data.

Finding the mean weights:

`\boxed{ \sf{Mean = \: ( Σx)/(n)}}`

⇒
`\sf{ (332)/(8) }`

⇒
`\sf{41.5}`

Mean weights = 41.5

-----------------------------------------------------------------------

Finding the median

To find the median, arrange the given data in ascending order.

Given data : 38, 40 , 42 , 46 , 45 , 39 , 42 , 40

Arranging the data in ascending order :

38 , 39 , 40 , 40 , 42 , 42 , 45 , 46

Total number of observation ( n ) = 8

Finding the position of median

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

⇒
`\sf{( (8 + 1)/(2) ) ^(th) item}`

⇒
`\sf{( (9)/(2) ) ^(th) item}`

⇒
`\sf{ {4.5}^(th) item}`

4.5 th item is the average of 4 th and 5th items .

Here, 4 th item = 40

5 th item = 42

Finding the median

`\boxed{ \sf{Median = ( \frac{{4}^(th) \: item + {5}^(th) item}{2}) }}`

⇒
`\sf{ (40 + 42)/(2) }`

⇒
`\sf{ (82)/(2) }`

⇒
`\sf{41 }`

Hope I helped!

Best regards!!