The heights, in feet, of the trees for sale at two nurseries are shown below.

Yard Works: 7, 9, 7, 12, 5
The Grow Station: 9, 11, 6, 12, 7

Which statements are true regarding the measures of center and variability of these data sets? Select three choices.
The mean of the tree heights at Yard Works is less than the mean of the tree heights at The Grow Station.
The median of the tree heights at Yard Works is greater than the median of the tree heights at The Grow Station.
The range of the tree heights at Yard Works is greater than the range of the tree heights at The Grow Station.
The mean absolute deviation of the tree heights at Yard Works is greater than the mean absolute deviation of the tree heights at The Grow Station.
The mean absolute deviation of the tree heights at Yard Works is equal to the mean absolute deviation of the tree heights at The Grow Station.

The correct statements are (1), (3) and (5).

Step-by-step explanation:

The mean () of a data set is the average value that represents the entire data set.

The median (m) is a measure of central tendency. To obtain the m, we assemble the data in ascending order. If the data is odd, the m is the mid-value. If the data is even, the m is the arithmetic mean of the two mid-values.

The range of the data set is the difference between the highest and lowest value.

The mean absolute deviation (MAD) of a data set is the average distance amid each value and the mean. The MAD provides us with an idea about the deviation in the data set.

(1)

The heights, in feet, of the trees for sale at Yard Works is:

A = {5, 7, 7, 9, 12}

Compute mean of A as follows:

The mean is 8.

Compute the median of A as follows:

The data consists of odd number of values.

So, the median is the mid-value, i.e. the 3rd observation.

The median is 7.

Compute the range  for A as follows:

The range is 7.

Compute the value of MAD for A as follows:

The value of MAD for A is 2.

(2)

The heights, in feet, of the trees for sale at The Grow Station is:

B = {6, 7, 9, 11, 12}

Compute mean of B as follows:

The mean is 9.

Compute the median of A as follows:

The data consists of odd number of values.

So, the median is the mid-value, i.e. the 3rd observation.

The median is 9.

Compute the range  for A as follows:

The range is 6.

Compute the value of MAD for A as follows:

The value of MAD for A is 2.

Thus, the correct statements are:

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6