Question

Matthew collected data about the ages of the actors in two different community theater groups. He drew a box plot for one of the sets of data and made a table of the other set of data.Ages of Actors is the Southside Players

Answer 1

For the  Northside players, the median is 36, the range is 32 and the IQR is 18. For the southside Players :  the median is 26, the range is 12 and the IQR is 12.

What is median?

The median is regarded as the middle number among a series of  sorted numbers  that are placed in ascending or descending order.

Note that from the image attached, the northside ages are 22, 25, 28, 29, 29, 36, 36, 41, 49, 49, 54.

The median northside ages therefore is 36

For Range = Highest number - Lowest number

54-22 = 32

IQR = Q₃ - Q₁

Note that first quartile Q1 is said to be the median of the n lowest values and third quartile Q3 is the median of the n highest values.

Lowest value is 22 + 25/2 = 28.5.

Highest value is 49 + 44/ 2=  46.5.

Therefore,  IQR = Q₃ - Q₁

46.5 - 28.5 =

IQR = 36

Note, for Southside Players;

If the Ages of Actors is the Southside Players are 20 22 24 26 28 30 32 34.

Then the median is =  26

Range is = 34-22 = 12

IQR = Q₃ - Q₁

Lowest = 20 + 22/ 2 = 21

Highest is 32 + 34 / 2 = 33

33 - 21

IQR  = 12

Therefore, for the  Northside players, the median is 36, the range is 32 and the IQR is 18. For the southside Players :  the median is 26, the range is 12 and the IQR is 12.

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