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Ch. 2 - Descriptive Statistics
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLarson 8th EditionCh. 2 - Descriptive StatisticsProblema 2.1.20d
Capitolo 2, Problema 2.1.20d

Use the frequency histogram
describe any patterns with the data..
A frequency histogram showing roller coaster heights in feet, with the highest frequency at 125 feet.

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Step 1: Observe the histogram and identify the key components. The x-axis represents the height of roller coasters (in feet), divided into intervals, while the y-axis represents the frequency (number of roller coasters) within each height interval.
Step 2: Note the distribution of the data. The histogram shows that the majority of roller coasters fall within the height range of 125 to 178 feet, as this interval has the highest frequency (approximately 40).
Step 3: Identify any patterns or trends. The data appears to be skewed to the right, as the frequency decreases for higher height intervals (231-284 feet and beyond). This suggests that taller roller coasters are less common.
Step 4: Consider the spread of the data. The heights range from 72 feet to 337 feet, indicating a wide variety of roller coaster heights. However, most roller coasters are concentrated in the lower height intervals.
Step 5: Summarize the findings. The histogram indicates that roller coasters are most commonly built within the height range of 125 to 178 feet, with fewer roller coasters at extreme heights. This could reflect design or safety considerations in roller coaster construction.

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Frequency Histogram

A frequency histogram is a graphical representation of data that shows the frequency of data points within specified ranges, or bins. Each bar's height indicates the number of observations that fall within that range, allowing for a visual interpretation of the distribution of the data. In this case, the histogram displays the heights of roller coasters, making it easy to identify which height ranges are most common.
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05:54
Intro to Histograms

Central Tendency

Central tendency refers to the statistical measures that describe the center of a data set, commonly represented by the mean, median, and mode. In the context of the histogram, the mode is particularly relevant as it indicates the height range with the highest frequency, which is 125 feet in this case. Understanding central tendency helps in summarizing the data and identifying typical values.
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04:52
Calculating the Mean

Data Distribution Patterns

Data distribution patterns refer to the way data points are spread across different values, which can reveal trends, clusters, or gaps in the data. Analyzing the histogram can help identify whether the data is normally distributed, skewed, or has outliers. In this histogram, the concentration of roller coasters around 125 feet suggests a common height preference, while the tapering off at higher heights indicates fewer roller coasters at those elevations.
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Visualizing Qualitative vs. Quantitative Data
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Extending Concepts


Golf The distances (in yards) for nine holes of a golf course are listed.

336 393 408 522 147 504 177 375 360


d. Use your results from part (c) to explain how to quickly find the mean and the median of the original data set when the distances are converted to inches.

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Using and Interpreting Concepts


Using and Interpreting Concepts Finding Quartiles, Interquartile Range, and Outliers In Exercises 11 and 12,

(c) identify any outliers.


56 63 51 60 57 60 60 54 63 59 80 63 60 62 65

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Song Lengths Side-by-side box-and-whisker plots can be used to compare two or more different data sets. Each box-and-whisker plot is drawn on the same number line to compare the data sets more easily. The lengths (in seconds) of songs played at two different concerts are shown.

d. Can you determine which concert lasted longer? Explain.

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Use the frequency histogram

d. describe any patterns with the data..

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Studying Refer to the data set in Exercise 23 and the box-and-whisker plot you drew that represents the data set.


c. You randomly select one student from the sample. What is the likelihood that the student studied less than 2 hours per day? Write your answer as a percent.

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Pearson’s Index of Skewness The English statistician Karl Pearson (1857–1936) introduced a formula for the skewness of a distribution.

P = 3 (x̄ - median) / s

Most distributions have an index of skewness between -3 and 3. When P > 0, the data are skewed right. When P < 0, the data are skewed left. When P = 0, the data are symmetric. Calculate the coefficient of skewness for each distribution. Describe the shape of each.


c. x̄ = 9.2, s = 1.8, median = 9.2

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