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# Understanding Standard Deviation (Grades 11-12)

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## Understanding Standard Deviation

Instructions: When asked to calculate the standard deviation, unless stated otherwise, calculate the population standard deviation.

1.
For a given data set, the standard deviation is a measure of how spread out the values are.
1. True
2. False
2.
Standard deviation is best described as
1. the difference between the number and the mean.
2. the sum of the differences between the numbers and the mean.
3. the square root of the sum of the differences between the numbers and the mean squared and divided by the number of terms.
4. the square root of the mean divided by the Z-Score times the sum of the numbers.
3.
A certain store recorded their sales each day, in total dollars, for a month. If they calculate the standard deviation, and find that it is nearly zero, which of the following is the most reasonable to conclude?
1. The store had very few sales for the entire month.
2. The store had almost equal sales each day.
3. The days with high sales equally balanced the days with low sales.
4. There is not enough information to make any conclusion.
4.
Find the mean and sample standard deviation of the data set. Round your final answer to the nearest tenth.

9, 11, 12, 14, 15, 17
1. 13.0; 1.8
2. 12.3; 2.3
3. 7.5; 2.0
4. 13.0; 2.9
5.
Find the standard deviation for the following set of data.
2.2, 2.2, 2.3, 2.4, 2.4, 2.5, 2.5, 2.6
1. 2.2
2. 2.4
3. 1
4. 0.1
6.
Find the standard deviation of the following set of data.
20, 15, 10, 12, 15, 20, 13, 16

7.
Calculate the standard deviation for the given set:

{2, 4, 7, 11, 13, 17}

8.
Calculate the sample standard deviation of the following data set. Round answer to two decimal places.

$\ \ \ {2, 8, 25, 3, 1, 19, 10}$

9.
You and your friends have just measured the heights of your dogs (in millimeters). The heights (at the shoulders) are: 600 mm, 470 mm, 170 mm, 430 mm and 300 mm. Find out the Mean and the Standard Deviation.

10.
Two workers are picking berries on a farm. The following are the number of kg of berries picked each consecutive hour. Please show all of your work!

Worker 1: 3, 4, 3, 5, 6, 1, 2, 3
Worker 2: 2, 3, 4, 3, 4, 2, 3, 3

a) Which person picks more kg per hour?

b) What is the standard deviation of each? Which person is more consistent?

c) Which one would you rather hire and why?

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