Table of contents

1. Intro to Stats and Collecting Data1h 14m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically2h 5m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables3h 6m
6. Normal Distribution and Continuous Random Variables2h 11m
7. Sampling Distributions & Confidence Intervals: Mean3h 23m
8. Sampling Distributions & Confidence Intervals: Proportion1h 25m
9. Hypothesis Testing for One Sample3h 29m
10. Hypothesis Testing for Two Samples4h 50m
11. Correlation1h 6m
12. Regression1h 50m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 57m

3. Describing Data Numerically

Mean

Statistics

3. Describing Data Numerically

Mean

Previous problemNext problem

2:20 minutes

Problem 3.CQQ.1

Textbook Question

Mean of Roller Coaster Speeds Listed below are maximum speeds (km/h) of randomly selected roller coasters in the United States. Find the mean.
7076978157151194651176545105

Verified step by step guidance

Step 1: Understand the concept of mean. The mean is the average of a set of numbers, calculated by summing all the values and dividing by the total number of values.

Step 2: Add all the maximum speeds together. Use the formula:

\sum x_{i}

, where

x_{i}

represents each individual speed value.

Step 3: Count the total number of roller coaster speeds provided. This will be the denominator in the mean formula.

Step 4: Divide the sum of the speeds by the total number of values using the formula:

\frac{\sum x_{i}}{n}

, where

n

is the number of values.

Step 5: Interpret the result as the mean maximum speed of the roller coasters in the dataset.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Mean

The mean, often referred to as the average, is a measure of central tendency that is calculated by summing all the values in a dataset and then dividing by the number of values. It provides a single value that represents the overall level of the data, making it useful for understanding the general trend. In the context of roller coaster speeds, calculating the mean speed helps to summarize the performance of the selected coasters.

Data Set

A data set is a collection of related values or observations that can be analyzed to extract meaningful information. In this case, the data set consists of the maximum speeds of various roller coasters, which are numerical values that can be used to calculate statistical measures like the mean. Understanding the composition of the data set is crucial for accurate analysis and interpretation.

Statistical Calculation

Statistical calculations involve mathematical operations applied to data sets to derive insights or summarize information. For finding the mean, the calculation requires adding all the values together and dividing by the count of those values. This process is fundamental in statistics, as it allows for the quantification of data characteristics and aids in making comparisons across different datasets.

Watch next

Master Calculating the Mean with a bite sized video explanation from Patrick

Start learning

Related Videos

Related Practice

Textbook Question

Body Temperatures Listed below are body temperatures (°F) of adult males (based on Data Set 5 “Body Temperatures” in Appendix B).

97.6 98.2 99.6 98.7 99.4 98.2 98.0 98.6 98.6

a. Find the mean. Does the result seem reasonable?

Textbook Question

Exercises 1–10 are based on the following sample data consisting of costs of dinner (dollars) and the amounts of tips (dollars) left by diners. The data were collected by students of the author.

Predictions Repeat the preceding exercise assuming that the linear correlation coefficient is r = 0.132.

Textbook Question

In Exercises 5–8, use the following two control charts that result from testing batches of newly manufactured aircraft altimeters, with 100 in each batch. The original sample values are errors (in feet) obtained when the altimeters are tested in a pressure chamber that simulates an altitude of 6000 ft. The Federal Aviation Administration requires an error of no more than 40 ft at that altitude.

What is the value of x_double bar In general, how is a value of xbar found?

Textbook Question

Quadratic Mean The quadratic mean (or root mean square, or R.M.S.) is used in physical applications, such as power distribution systems. The quadratic mean of a set of values is obtained by squaring each value, adding those squares, dividing the sum by the number of values n, and then taking the square root of that result, as indicated below:

Quadratic mean = sqrt(∑x^2/n)

Find the R.M.S. of these voltages measured from household current: 0, 60, 110, 0. How does the result compare to the mean?

Textbook Question

Cloud Seeding The “Florida Area Cumulus Experiment” was conducted by using silver iodide to seed clouds with the objective of increasing rainfall. For the purposes of this exercise, let the daily amounts of rainfall be represented by units of rnfl. (The actual rainfall amounts are in or )

Find the value of the following statistics and include appropriate units based on rnfl as the unit of measurement.

15.53 7.27 7.45 10.39 4.70 4.50 3.44 5.70 8.24 7.30 4.05 4.46

a. mean

b. median

Textbook Question

In Exercises 1 and 2, use the following wait times (minutes) at 10:00 AM for the Tower of Terror ride at Disney World (from Data Set 33 “Disney World Wait Times” in Appendix B).

35 35 20 50 95 75 45 50 30 35 30 30

a. Find the mean xbar.

Textbook Question

Birth Weights The table below lists some of the same data used in the preceding exercise, but the seven days of the week are combined into weekday (Monday, Tuesday, Wednesday, Thursday, Friday) and weekend days (Saturday, Sunday). Also, the birth weights are converted to kilograms. What do you conclude?

Textbook Question

For the four test scores 96, 85, 91, and 86, the first 3 test scores are 20% of the final grade, and the last test score is 40% of the final grade. Find the weighted mean of the test scores.

Show more practices