Quincy listed the amounts he earned doing yard work.
$42, $38, $26, $32, $40, $34, $28, $32
How would deleting the least amount affect the mean and the median of his data?
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To determine how deleting the least amount would affect the mean and median of Quincy's data, we first need to understand what mean and median represent.
The mean, also known as the average, is calculated by adding up all the values in a set of data and then dividing the sum by the total number of values. In this case, we add up all the amounts Quincy earned and divide by 8 (since there are 8 values).
The median is the middle value in a set of data when the values are arranged in ascending or descending order. If the set of data has an even number of values, the median is the average of the two middle values.
Now, let's calculate the mean and median for Quincy's original data:
Amounts: $42, $38, $26, $32, $40, $34, $28, $32
Mean = (42 + 38 + 26 + 32 + 40 + 34 + 28 + 32) / 8 = $32.75
To calculate the median, we need to arrange the values in ascending order:
$26, $28, $32, $32, $34, $38, $40, $42
Median = ($32 + $34) / 2 = $33
Now, let's delete the least amount, which is $26, and recalculate the mean and median with the updated data:
New amounts after deleting $26: $42, $38, $32, $40, $34, $28, $32
Mean = (42 + 38 + 32 + 40 + 34 + 28 + 32) / 7 = $35
To calculate the median, we arrange the values in ascending order:
$28, $32, $32, $34, $38, $40, $42
Median = $34
After deleting the least amount ($26) from Quincy's data, we can see that:
- The mean increases from $32.75 to $35.
- The median stays the same at $34.
In summary, deleting the least amount increases the mean but does not affect the median of Quincy's data.