Answer: The median changed the most.
Old median = 79.5
new median = 86.5
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Step-by-step explanation:
To find the mean, we add up the values and divide by 12 since there are 12 numbers in this list.
mean = (add up the values)/(number of values)
mean = (58+61+71+77+91+100+105+102+95+82+66+57)/12
mean = 80.41667 approximately
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To get the median, we need to sort the numbers from smallest to largest
57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105
There are n = 12 items in this set.
Because n = 12 is an even number, the median is between slots n/2 = 12/2 = 6 and 7
- The value in slot 6 is 77
- The value in slot 7 is 82
The midpoint of those values is (77+82)/2 = 79.5 which is the median.
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The range is the difference between the min and max
range = max - min = 105 - 57 = 48
The IQR will involve splitting the sorted set into two halves
L = lower half = stuff below the median
L = {57, 58, 61, 66, 71, 77}
U = upper half = stuff above the median
U = {82, 91, 95, 100, 102, 105}
The median of set L is (61+66)/2 = 63.5 which is the value of Q1.
The median of set U is (95+100)/2 = 97.5 which is the value of Q3
IQR = interquartile range
IQR = Q3 - Q1
IQR = 97.5 - 63.5
IQR = 34
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Here is a summary of what we calculated
- Mean = 80.41667 approximately
- Median = 79.5
- Range = 48
- IQR = 34
If we were to replace the "71" with "93", and redo the calculations, then we'll get these results:
- mean = 82.25
- median = 86.5
- range = 48
- IQR = 34
The range and IQR stay the same, but the mean and median values are different.
Let's see which of those two values changed the most.
- Mean: The jump from 80.41667 to 82.25 is +1.83333 (since 82.25-80.41667 = 1.83333)
- Median: The jump from 79.5 to 86.5 is +7 (since 86.5-79.5 = 7)
The median has changed the most because the +7 is larger than +1.83333