The boxplot below displays the average number of apple pies consumed in eating contests across a particular state. the higher outlier is from a professional, heavyweight contests, and the lower outlier is from a children's eating contest.

what effect will removing all outliers have on the mean and median of the data set?

neither the mean nor the median will change.
the mean will remain unchanged and the median will increase.
the mean will remain unchanged and the median will decrease.
the median will remain unchanged and the mean will increase.
the median will remain unchanged and the mean will decrease.

first, arrange the data set in increasing order:

23, 74, 75, 76, 76, 77, 79

the median is the middle value, 76.   now remove the outlier, 23:

74, 75, 76, 76, 77, 79

since there are now an even number of data points, there is no exact middle value.   so take the mean of the two values closest to the middle to get the median:

(76+76)/2 = 152/2 = 76

for this data set, the median remains unchanged when the outlier is removed.

see explanation

step-by-step explanation:

a

(6r + 7) + (13 + 7r) ( remove brackets and collect like terms )

= 6r + 7 + 13 + 7r

= 13r + 20

b

remove brackets and collect like terms

13 - r - 1 + r

= 12 - r

c

remove brackets and collect like terms

= - 8 - r + 2r - 4

= - 12 + r

d

remove brackets and collect like terms

= 7r - - - 6r

[-   - = - - = - ]

= r -

one peck is 9.309 quarts

9.309x 2