Statistics: Mode, Standard Deviation, and More

Questions and Answers

Find the mode for the given sample data: 20, 32, 46, 32, 49, 32, 49.

32 (correct)

37.1

Obtain the population standard deviations for the given data: 65, 69, 48, 67, 68, 43, 73, 41, 93.

272.7

243.3

15.6 (correct)

16.5

Determine whether the elevated group is a population or a sample: A researcher examines the records of all the registered voters in one city and finds that 43% are registered Democrats.

Sample

Population (correct)

Classify the variable: The number of people on a jury.

Quantitative Signup and view all the answers

Find the deviation for a sample of data: Here are the prices for 8 randomly selected CD players: $422, $407, $384, $236, $265, $210, $375, $166.

$99.9 Signup and view all the answers

Identify outlier(s) in the given data: The test scores of 15 students are: 37, 55, 48, 65, 67, 69, 71, 73, 74, 77, 80, 82, 87, 90, 99.

37 Signup and view all the answers

Find the percent of a standard Normal model found in the given region: z < 1.13.

87.08% Signup and view all the answers

In a standard Normal model, state what value(s) of z cuts off the described region: the lowest 96%.

1.75 Signup and view all the answers

Solve the problem: The volumes of soda in quart soda bottles can be described by a Normal model with a mean of 32.3 oz and a standard deviation of 1.2 oz. What percentage of bottles can we expect to have a volume less than 32 oz?

40.13% Signup and view all the answers

Solve the problem: A bank's loan officer rates applicants for credit described by a Normal model with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, what percentage can be expected to be between 200 and 275?

43.85% Signup and view all the answers

Select the best answer: A statistics student looked at the grade point averages of all 892 students enrolled at a small college. She determined that GPA was not related to the month that students were born. What are the variables?

GPA, month of birth Signup and view all the answers

Describe the expected distribution: Heights of a group of male professional athletes, half of whom are gymnasts and half of whom are basketball players.

The distribution would probably be bimodal Signup and view all the answers

Would you expect a distribution of the variable to be? The heights of adult females attending a concert.

The distribution would probably be symmetric Signup and view all the answers

Construct a boxplot: The ages of the 21 members of a track and field team are: 15, 18, 18, 19, 22, 23, 24, 24, 24, 25, 25, 26, 26, 27, 28, 28, 30, 32, 33, 40, 42.

15, 22.5, 25, 29, 33, 40, 42 Signup and view all the answers

Fill in the blanks by standardizing the normally distributed variable: The amount of time that customers wait in line is normally distributed with a mean of 15 minutes and a standard deviation of 3 minutes. The percentage of time that the waiting time lies between 15 and 17 minutes is equal to the area under the standard normal curve between _ and _.

0, 0.67 Signup and view all the answers

Construct a boxplot: The test scores of 40 students are: 25, 35, 43, 44, 47, 48, 54, 55, 56, 57, 59, 62, 63, 65, 66, 68, 69, 69, 71, 71, 73, 73, 74, 76, 77, 77, 78, 79, 80, 81, 81, 82, 83, 85, 89, 92, 93, 94, 97, 98.

None of these is correct Signup and view all the answers

Provide an appropriate response: A poll asked adults which activities they engaged in during the past month. Is it reasonable to conclude that 70.8% of those polled had seen a movie or gone to a sporting event?

No Signup and view all the answers

Provide an appropriate response: For a given set of data, will the shapes of the frequency distribution and the relative frequency distribution be the same?

Yes Signup and view all the answers

Provide an appropriate response: Which of the variables below do you think will be roughly normally distributed? a. Weights of 40-year-old males, b. Incomes of 40-year-old adults, c. The numbers that show up when you roll a balanced die once, d. The amount of coffee which a filling machine puts into '4 ounce jars'.

d only Signup and view all the answers

Provide the requested table entry: The data reflect the amount of time 40 students spend on homework each day. Determine the value that should be entered in the Relative Frequency column for the class 30-44.

0.25 Signup and view all the answers

Find the mean of the data. The employees at Frank's Furniture earned: $443.52, $441.04, $530.17, $471.67, $359.36, $320.75.

$427.75 Signup and view all the answers

Find the median for the given sample data: A new business had the following monthly net gains: $8519, $3555, $3325, $8084, $6496, $1738, $2369, $8140, $4070, $4811.

$4440.50 Signup and view all the answers

Solve the problem: A meteorological office keeps records of the annual precipitation in different cities. For one city, the mean annual precipitation is 31.8 and the standard deviation of the annual precipitation amounts is 3.6. Determine the standardized version of X.

Z=X-31.8/3.6 Signup and view all the answers

Solve the problem: A survey of patients at a hospital classified the patients by gender and blood type. What percent of the female patients have type-O blood? Round your answer to the nearest tenth of a percent.

43.1% Signup and view all the answers

Two statistics classes (50 students each) took the same test: Use the histograms of the scores for the classes to answer the question. Which class performed better?

Class 2 Signup and view all the answers

Find the specified percentile, quartile, or decile: The amount of Jen's monthly phone bill is normally distributed with a mean of $76 and a standard deviation of $12. Find the first quartile, Q1.

$67.96 Signup and view all the answers

Solve the problem: The test scores of 15 students are listed below: Find the lower quartile (Q1).

57 Signup and view all the answers

Solve the problem: The test scores of 19 students are listed below: Find the interquartile range (IQR).

32 Signup and view all the answers

Study Notes

Mode and Standard Deviation

Mode is the value that appears most frequently in a data set; for the sample data 20, 32, 46, 32, 49, 32, 49, the mode is 32.
Population standard deviation is a measure of the amount of variation in a set of values; for test scores 65, 69, 48, 67, 68, 43, 73, 41, and 93, it is 15.6.

Population vs. Sample

A population includes all members of a defined group; in a study of registered voters where 43% are Democrats, the group analyzed is the entire population of voters in the city.

Variable Classification

Variables can be classified as categorical or quantitative; the number of people on a jury is a quantitative variable.

Deviation and Outliers

Deviation indicates the difference between a value and the mean; for CD player prices, the deviation is approximately $99.9.
Outliers are data points that are significantly different from others in a data set; in student test scores, 37 is identified as an outlier.

Normal Distribution and Standard Scores

A standard normal model is characterized by a mean of 0 and a standard deviation of 1; for z < 1.13, approximately 87.08% of the area under the curve lies to the left.
For the lowest 96%, the z-value is 1.75, indicating the cut-off point.

Percentages in Normal Distribution

The volume of soda bottles typically follows a normal distribution; for a mean of 32.3 oz and standard deviation of 1.2 oz, about 40.13% have volumes of less than 32 oz.
In a normal distribution of loan ratings with a mean of 200 and standard deviation of 50, approximately 43.85% of applicants score between 200 and 275.

Variables and Distribution Shape

When investigating the relationship between GPA and birth month, the variables are GPA and month of birth.
Heights of male athletes likely form a bimodal distribution due to the different athletic groups, while adult female heights are expected to be symmetric.

Boxplots and Quartiles

A boxplot represents a summary of a data set; for the ages of a track team, the calculated six-number summary is 15, 22.5, 25, 29, 33, and 40.
The lower quartile (Q1) of test scores is identified as 57.

Percentages and Relative Frequencies

For a survey asking about recent activities, it is unreasonable to conclude that 70.8% saw a movie or attended a sporting event based on provided percentages.
Relative frequency is calculated by dividing the number of students in a class by total students; for homework time class 30-44, the relative frequency is 0.25.

Mean, Median, and IQR

The mean salary of employees at Frank's Furniture is approximately $427.75.
The median net gain from the new business is $4,440.50, calculated from sorted monthly gains.
The interquartile range (IQR) for the test scores of 19 students is found to be 32.

Standard Scores and Percentiles

The standardized score formula for annual precipitation with a mean of 31.8 and standard deviation of 3.6 is Z = (X - 31.8) / 3.6.
The first quartile of Jen's phone bill is approximately $67.96, representing the 25th percentile in her spending distribution.

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Description

Dive into the essentials of statistics with this quiz covering mode, standard deviation, and the differences between population and sample data. Test your understanding of variable classification, deviations, and outliers. Ideal for students looking to reinforce their statistical knowledge.