6.3 Standard Deviation and z-Scores
Chapter
Chapter 6
Section
6.3
Solutions 20 Videos

Adam is building a doorway and wants the height of the door to be three standard deviations above the mean Canadian height.

How high must the door be if the mean is 210 cm with a standard deviation of 10 cm?

A. 230cm

B. 250 cm

C. 200 cm

D. 240 cm

Q1

Which is an incorrect statement about standard deviation?

A. The variance is the square root of the standard deviation.

B. The standard deviation is often called the average distance of the measurements from the mean.

C. The standard deviation is expressed in the same units as the data.

D. The standard deviation is always a positive quantity.

Q2

The mean of a data set is 25.3 cm, and the standard deviation is 3.6. Determine the z-score of each of the following and interpret the results.

a) 27.2

b) 24.1

c) 21.9

d) 29.8

Q3

Calculate the standard deviation for each data set and interpret the results.

Lengths, in centimetres, of fish caught on a fishing trip.

15.4, 12.3, 18.2, 9.9, 17.4, 12.6, 16.3, 11.8, 12.3, 12.6, 16.7

Q4a

Calculate the standard deviation for each data set and interpret the results.

The number of home runs in a season by the players on a team.

3, 10, 0, 12, 5, 6, 10, 16, 34, 11, 6, 7, 21

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Q4b

Calculate the standard deviation for each data set and interpret the results.

Final scores by the figure skaters in a competition.

Q4c

For each of the situations, decide whether you would use the sample or population standard deviation formula. Explain your decisions.

a) A researcher recruits females ages 35 to 50 years old for an exercise training study to investigate risk markers for heart disease (e.g., cholesterol).

b) One of the questions on a national survey asks for the respondentâ€™s age. Researchers want to describe the variability in all ages received from the survey.

c) A teacher administers a test to her students. The teacher wants to summarize the results the students attained as a mean and standard deviation.

Q5

As part of a report on its employees, a company published this graph.

a) The standard deviation is given as 4.1 years. Identify which numbers of years worked are within one standard deviation of the mean.

b) What percent of the employees are within two standard deviations of the mean?

c) How does this graph help to explain z-scores?

Q6

The actual volume of milk in 1-L cartons of milk was checked by measuring a selection of 120 cartons. The chart shows the results.

a) Calculate the mean and standard deviation, accurate to three decimal places.

b) Did you use the population or sample formulas? Why?

c) The company has decided that a sample that is within two standard deviations of the mean is acceptable. A random sample was taken and the volume was 0.98 L. Would this be an acceptable sample?

d) On the following day, the mean volume of milk per carton was 1.012 L, with a standard deviation of 0.009 L. Compare the two daysâ€™ test results.

Q10

Along with their application to a particular university, students were instructed to submit a 700-word essay. The table shows the lengths of 16 of the essays that were submitted.

a) Calculate the mean, variance, and standard deviation to the nearest whole number for the data set.

b) Did you use the sample or population formulas? Why?

c) Make an appropriate graph of the data. Mark the interval that is within one standard deviation of the mean.

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Q12
Lectures 6 Videos

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Measures of Spread Part II Standard Deviation for Grouped Data

Measures of Spread Part III Standard Deviation Sample vs Population

3.47mins
Measures of Spread Part III Standard Deviation Sample vs Population

Measures of Spread Part IV Quartiles and Box Plots