Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 22m
11. Correlation1h 6m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

3. Describing Data Numerically

Mean

Statistics

3. Describing Data Numerically

Mean

Previous problemNext problem

1:30 minutes

Problem 2.3.39

Textbook Question

In Exercises 37– 40, without performing any calculations, determine which measure of central tendency best represents the graphed data. Explain your reasoning.

Verified step by step guidance

Step 1: Observe the graph and note that the data is unimodal and symmetric, meaning it has one peak and the distribution is roughly balanced on both sides of the center.

Step 2: Recall the three measures of central tendency: mean, median, and mode. The mean is the average of all data points, the median is the middle value when data is ordered, and the mode is the most frequently occurring value.

Step 3: For symmetric distributions, the mean is typically the best measure of central tendency because it takes into account all data points and reflects the center of the distribution accurately.

Step 4: The mode, which represents the most frequent heart rate, could also be considered, but it may not fully represent the center of the data if the distribution is symmetric.

Step 5: Conclude that the mean is the best measure of central tendency for this data because the graph is symmetric and unimodal, ensuring the mean accurately represents the center of the distribution.

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.

Measures of Central Tendency

Measures of central tendency, including the mean, median, and mode, summarize a set of data by identifying the central point within that data. The mean is the average, the median is the middle value when data is ordered, and the mode is the most frequently occurring value. Each measure provides different insights, making it essential to choose the one that best represents the data's distribution.

Distribution Shape

The shape of a data distribution, such as normal, skewed, or uniform, influences which measure of central tendency is most appropriate. For instance, in a normal distribution, the mean, median, and mode are similar, while in a skewed distribution, the mean may be pulled in the direction of the skew, making the median a better representative of the central tendency.

Frequency Distribution

A frequency distribution displays how often each value occurs within a dataset, often represented in a histogram. In the provided graph, heart rates are plotted against their frequencies, allowing for visual analysis of the data's central tendency. Observing the highest bars can help identify the mode, while the overall shape can indicate whether the median or mean might be more representative.

Watch next

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

Start learning

Related Videos

Related Practice

Textbook Question

Finding the Mean of a Frequency Distribution In Exercises 49–52, approximate the mean of the frequency distribution.

Social Media The average daily amounts of time (in minutes) spent on Snapchat

views

Textbook Question

Finding the Mean of a Frequency Distribution In Exercises 49–52, approximate the mean of the frequency distribution.

Populations The populations (in thousands) of the counties in Montana in 2019 (Source: U.S. Census Bureau)

views

Textbook Question

Extending Concepts

Trimmed Mean To find the 10% trimmed mean of a data set, order the data, delete the lowest 10% of the entries and the highest 10% of the entries, and find the mean of the remaining entries.

a. Find the 10% trimmed mean for the data in Exercise 65.

views

Textbook Question

Extending Concepts

Trimmed Mean To find the 10% trimmed mean of a data set, order the data, delete the lowest 10% of the entries and the highest 10% of the entries, and find the mean of the remaining entries.

c. What is the benefit of using a trimmed mean versus using a mean found using all data entries? Explain your reasoning.

views

Textbook Question

Finding a Weighted Mean In Exercises 41– 46, find the weighted mean of the data.

Final Grade The scores and their percents of the final grade for a statistics student are shown below. What is the student’s mean score?

views

Textbook Question

Finding a Weighted Mean In Exercises 41– 46, find the weighted mean of the data.

Credit Card Balance For the month of October, a credit card has a balance of $115.63 for 12 days, $637.19 for 6 days, $1225.06 for 7 days, $0 for 2 days, and $34.88 for 4 days. What is the account’s mean daily balance for October?

views

Textbook Question

Which statistic is the best unbiased estimator for μ?

a. s

b. xbar

c. the median

d. the mode

views

Textbook Question

Constructing a Confidence Interval In Exercises 25–28, use the data set to (a) find the sample mean. Assume the population is normally distributed.

SAT Scores The SAT scores of 12 randomly selected high school seniors

views