Histograms: 동영상 및 연습문제

A researcher recorded the drive-thru service times (in seconds) at a local fast-food restaurant during dinner hours. Construct a histogram for yourself using the provided frequency distribution and answer the following question: Using an interpretation of the criteria for normality, does the histogram suggest the data follows a normal distribution?

A large random sample of adults is taken, and their heights are represented in a histogram. If the heights of adults follow a normal distribution, what is the shape of the histogram?

A voluntary response sample of 7000 adult heights is collected. If the population of adult heights follows a normal distribution, will the histogram of the sample be bell-shaped? Give reason.

A large dataset of household electricity consumption (in kWh) is collected and displayed in a histogram. If a single household has an unusually high electricity consumption compared to the rest, how will this outlier appear in the histogram?

Use the following histogram generated by statistical software, which represents the battery life (in hours) of a sample of smartphones. (The values on the horizontal scale are rounded.)

What is the approximate number of smartphones represented in the three bars farthest to the right?

Use the following histogram generated by statistical software, which represents the battery life (in hours) of a sample of smartphones. Provide the estimated class width, along with the lower- and upper-class limits of the fourth bar from the left in the histogram.

Use the following histogram generated by statistical software, which represents the battery life (in hours) of a sample of smartphones. (The values on the horizontal scale are rounded.)

How would the shape of the histogram be affected if the vertical axis displayed relative frequencies in percentages instead of actual frequency counts?

The graph below illustrates the fuel efficiency (in miles per gallon) of cars starting from $\text{1980}$, labeled as year $1$, along with a red curve depicting the quadratic equation that best fits the data.

Give a feature of the graph that justifies the value of ${\text{R}}^2=0.25$ for the quadratic model.

A traffic study recorded the commute times (in minutes) of $50$ individuals traveling to work in Chicago. 

The frequency distribution of commute times is given below.

Using the frequency distribution above, construct a histogram. Then, determine whether the histogram suggests that the data follow a normal distribution.

A researcher collects data on the commute times (in minutes) of employees in a company. The following frequency distribution summarizes the results:

Using the frequency distribution above, construct a histogram using class midpoints for the horizontal axis. Does the histogram suggest that the data is normally distributed?

Vehicle Speeds on a Highway: Utilizing the following frequency distribution data, construct a histogram to answer the given question: Does the histogram appear to be skewed? If so, identify the type of skewness.

Create a histogram using the frequency distribution of coffee brewing times (in seconds) shown below. 

Does the histogram appear to show data from a normal distribution when the requirements for normal distribution are strictly applied?

Create a histogram using the frequency distribution of the last digits of reported package weights (in kg) shown below. What conclusions can be drawn from the digit distribution? Do the weights appear to have been reported or actually measured?

The following frequency distribution represents the delivery times (in minutes) for packages shipped from a logistics center.

Construct the histogram corresponding to this frequency distribution. Which of these best describes the distribution: uniform, normal, skewed left, or skewed right?

In a health study, the resting pulse rates (beats per minute) of a group of adult males were recorded. The recorded pulse rates are given below:

62, 70, 72, 80, 74, 66, 78, 84, 88, 92, 70, 78, 66, 72, 80

(a) Construct a dot plot for the given data.

(b) Is there a pulse rate that appears to be an outlier? What is the outlier’s value?

A sports scientist recorded the resting respiratory rates (breaths per minute) of a group of athletes. The recorded values are given below:

12, 14, 16, 18, 20, 20, 20, 22, 24, 24, 24, 26, 26, 26, 28, 28, 30, 30, 32, 34, 36, 36 

Construct a dot plot for the given data.

Are there any outliers? If so, identify their values.

Shown below is a histogram of the last digits (units place) of scores from a large set of test results from a high school math department. Each score is out of $100$, and the last digit ($0$ through $9$) is recorded for analysis. Identify the frequencies of each digit. Then, test the claim that the last digits of the scores are uniformly distributed—that is, each digit from $0$ to $9$ is equally likely. Use $5\%$ level of significance. Does the data suggest any potential grading bias or irregularity in how scores are assigned?

What is the approximate shape of the distribution in this histogram?

What is the approximate shape of the distribution in this histogram?

Class boundaries are used to ensure that adjacent bars in a histogram do not touch. Decide whether the preceding statement is true or false. If it is false, rewrite it correctly.

The following histogram displays the heights (in centimeters) of a group of employees. Use the histogram to determine the number of classes.

The following histogram shows the heights (in centimeters) of a group of employees. Use the histogram to describe any patterns or trends observed in the data.

The following histogram shows the weights (in kilograms) of a group of athletes. Use the histogram to describe any patterns or trends observed in the data.

The data below shows the number of study hours and the quiz scores of $10$ students.

Hours of study: $1$, $2$, $1.5$, $3$, $2.5$, $4$, $3.5$, $5$, $4.5$, $6$

Quiz score: $50$, $58$, $54$, $66$, $63$, $72$, $69$, $78$, $75$, $82$

Based on the data, which of the following best describes the relationship between hours of study and quiz score?

The following histogram shows the relative frequencies of different daily water intake levels among a group of athletes. Use the histogram to approximate the greatest and least relative frequencies from the data.

The histogram shown illustrates a binomial distribution with $6$ trials.

Identify the correct probability of success $p$ from the options below.

The following data set shows the number of hours $24$ employees worked overtime last month:

Construct a relative frequency histogram with $5$ classes.

A group of $29$ students reported the number of books they read last year. The data set (number of books): $3$, $7$, $5$, $4$, $6$, $8$, $5$, $6$, $7$, $9$, $4$, $5$, $7$, $8$, $6$, $5$, $7$, $4$, $6$, $7$, $8$, $5$, $6$, $7$, $8$, $5$, $4$, $6$, $7$. Construct a frequency distribution and a frequency histogram using $4$ classes. Describe the shape of the histogram as symmetric, uniform, negatively skewed, positively skewed, or none of these.

The histogram below shows the number of vacation days used by employees in a company over the past year. The letters X, Y, and Z are marked at various points on the horizontal axis. Describe the shape of the data distribution and determine which letter (X, Y, or Z) corresponds to the mean, median, and mode.

A researcher is analyzing the daily caffeine intake of $30$ college students. A previous survey found that daily coffee intake is normally distributed, with a mean of $12.5$ fluid ounces and a standard deviation of $3.2$ fluid ounces. Draw a frequency histogram to display this data. Use seven classes. Do the consumptions appear to be normally distributed?