The range is $25 - $11 = $14.
The interquartile range is $8.
The mean absolute deviation is $3.9.
Range
The range is the difference between the highest and lowest values in the data set.
In this case, the highest value is $25 and the lowest value is $11, so the range is $25 - $11 = $14.
Interquartile range
The interquartile range (IQR) is a measure of the spread of the middle half of the data set.
To calculate the IQR, we first need to order the data from least to greatest:
$11, $12, $15, $16, $20, $20, $25
The median of the data set is the middle value, which is $16. The IQR is then calculated as the difference between the third quartile (Q3) and the first quartile (Q1):
Q3 - Q1 = $20 - $12 = $8
Therefore, the interquartile range is $8.
Mean absolute deviation
The mean absolute deviation (MAD) is a measure of the average distance between each data point and the mean.
To calculate the MAD, we first need to calculate the mean of the data set:
mean = ($11 + $12 + $15 + $16 + $20 + $20 + $25) / 7 = $17
Next, we calculate the absolute deviation of each data point from the mean:
|$11 - $17| = $6
|$12 - $17| = $5
|$15 - $17| = $2
|$16 - $17| = $1
|$20 - $17| = $3
|$20 - $17| = $3
|$25 - $17| = $8
Finally, we calculate the mean of the absolute deviations:
MAD = ($6 + $5 + $2 + $1 + $3 + $3 + $8) / 7 = $3.9
Therefore, the mean absolute deviation is $3.9.
Interpretation-The range tells us that the admission prices vary by no more than $14.
The interquartile range tells us that the middle half of the prices vary by no more than $8.
The mean absolute deviation tells us that the admission prices differ from the mean price by an average of $3.9.