Question

Tall or short? Mr. Walker measures the heights (in inches) of the students in one of his classes. He uses a computer to calculate the following numerical summaries: Mean Std. dev. Min Q1 Med Q3 Max 69.188 3.20 61.5 67.75 69.5 71 74.5 Next, Mr. Walker has his entire class stand on their chairs, which are 18 inches off the ground. Then he measures the distance from the top of each students head to the floor. (a) Find the mean and median of these measurements. Show your work. (b) Find the standard deviation and IQR of these measurements. Show your work.

Answer 1

Answer:

a. x=69.188 +18 =87.188" (mean)

69.5+18=87.5" (median)

b. Standard deviation=3.20, IQR: 3.25

There's no change because your adding a value to all the data points.

Answer 2

From the data-set, we have that:

a) The mean is of 69.188 inches, while the median is of 69.5 inches.

b) The standard deviation is of 3.20 inches and the IQR is of 3.25 inches.

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The data-set information is:

• The mean is of 69.188 inches.
• The standard deviation is of 3.20 inches.
• The minimum height is of 61.5 inches.
• The first quartile(Q1) is of 67.75 inches.
• The median is of 69.5 inches.
• The third quartile(Q3) is of 71 inches.
• The maximum height is of 74.5 inches.

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Item a:

• The mean is of 69.188 inches, while the median is of 69.5 inches.

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Item b:

• The standard deviation is of 3.20 inches.
• The IQR is the difference between Q3 and Q1, thus 71 - 67.75 = 3.25 inches.

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