An art collector had 666 paintings and then bought a new painting for \$100{,}000$100,000dollar sign, 100, comma, 000. The value of the \blueD{\text{original $6$ paintings}}original 6 paintingsstart color #11accd, start text, o, r, i, g, i, n, a, l, space, 6, space, p, a, i, n, t, i, n, g, s, end text, end color #11accd and the \purpleC{\text{new painting}}new paintingstart color #aa87ff, start text, n, e, w, space, p, a, i, n, t, i, n, g, end text, end color #aa87ff are shown in the following dot plot. A dot plot has a horizontal axis labeled, Value, in thousands of dollars, marked from 30 to 100, in increments of 2. Dots are plotted above values as follows: 30, 2; 32, 1; 34, 1; 36, 1; 40, 1; 100, 1. The dot above 100 is shaded purple. How will buying the \purpleC{\text{new painting}}new paintingstart color #aa87ff, start text, n, e, w, space, p, a, i, n, t, i, n, g, end text, end color #aa87ff affect the mean and median?
Answers
Given : An art collector had 6 Paintings & then bought a new painting for $100,000
To find : Change in Mean & Median
Solution:
Original 6 Painting
Cost numbers f Total Cost cf
30 ,000 $ 2 60,000 $ 2
32 ,000 $ 1 32,000 $ 3
34 ,000 $ 1 34,000 $ 4
36 ,000 $ 1 36,000 $ 5
40 ,000 $ 1 40,000 $ 6
Total 6 202,000 $
Mean = 202,000/6 = 33,666.67 $
30,000 , 30,000 , 32,000 , 34,000 , 36,000 , 40,000
Median (32,000 + 34,000) = 33,000 $
7th Painting at 100,000 $
Total Amount = 202,000 + 100,000 = 302,000$
New Mean = 302,000/7 = 43,142.86 $
30,000 , 30,000 , 32,000 , 34,000 , 36,000 , 40,000 , 100,000
New Median = 34,000 $
Increase in Mean = 43142.86 - 33,666.67 = 9,476.19 $
Increase in Median = 34,000 - 33,000 = 1,000 $
Increase in Mean = 9,476.19 $
Increase in Median = 1,000 $
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Answer:
Both The mean and the median will increase, but the mean will increase more then the median.
Step-by-step explanation:
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