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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 2.3.65a
Capitolo 2, Problema 2.3.65a

Extending Concepts


Data Analysis Students in an experimental psychology class did research on depression as a sign of stress. A test was administered to a sample of 30 students. The scores are shown in the table at the left.


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a. Find the mean and the median of the data.

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Step 1: Organize the data. Write down all the test scores from the table in a single list: [44, 51, 11, 90, 76, 36, 64, 37, 43, 72, 53, 62, 36, 74, 51, 72, 37, 28, 38, 61, 47, 63, 36, 41, 22, 37, 51, 46, 85, 13].
Step 2: Calculate the mean. To find the mean, sum all the test scores and divide by the total number of scores (30). Use the formula: Mean=∑xn, where ∑x is the sum of all scores and n is the number of scores.
Step 3: Sort the data in ascending order to find the median. The sorted list is: [11, 13, 22, 28, 36, 36, 36, 37, 37, 37, 38, 41, 43, 44, 46, 47, 51, 51, 51, 53, 61, 62, 63, 64, 72, 72, 74, 76, 85, 90].
Step 4: Identify the median. Since there are 30 scores (an even number), the median is the average of the 15th and 16th values in the sorted list. Use the formula: Median=x15+x162, where x15 and x16 are the 15th and 16th values in the sorted list.
Step 5: Perform the calculations for both the mean and the median using the formulas provided in steps 2 and 4. Ensure accuracy by double-checking the sum and the sorted list.

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Mean

The mean, or average, is calculated by summing all the values in a dataset and dividing by the number of values. It provides a central value that represents the dataset, but can be influenced by extreme values (outliers). For example, in the given test scores, the mean would give an overall sense of the students' performance.
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Calculating the Mean

Median

The median is the middle value of a dataset when it is ordered from least to greatest. If there is an even number of observations, the median is the average of the two middle numbers. This measure is less affected by outliers and provides a better representation of the central tendency in skewed distributions, making it useful for analyzing the test scores.
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03:26
Calculating the Median

Data Distribution

Data distribution refers to how values are spread or arranged in a dataset. Understanding the distribution helps in identifying patterns, trends, and the presence of outliers. In the context of the test scores, analyzing the distribution can reveal insights about the overall performance of the students and how their scores relate to each other.
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Visualizing Qualitative vs. Quantitative Data
Pratica correlata
Domanda del libro di testo

Archaeology The depths (in inches) at which 10 artifacts are found are listed. 

20.7 24.8 30.5 26.2 36.0 34.3 30.3 29.5 27.0 38.5


a. Find the range of the data set.

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Using the Empirical Rule In Exercises 29–34, use the Empirical Rule.


Use the sample statistics from Exercise 29 and assume the number of vehicles in the sample is 75.


a. Estimate the number of vehicles whose speeds are between 63 miles per hour and 71 miles per hour.

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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.

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Protein Powder During a quality assurance check, the actual contents (in grams) of six containers of protein powder were recorded as 1525, 1526, 1502, 1516, 1529, and 1511.


a. Find the mean and the median of the contents.

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Yoga Classes The data sets at the left show the ages of all participants in two yoga classes.

a. Make a back-to-back stem-and-leaf plot as described in Exercise 41 to display the data.

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Drawing a Box-and-Whisker Plot In Exercises 15–18,

(a) find the five-number summary


4 7 7 5 2 9 7 6 8 5 8 4 1 5 2 8 7 6 6 9

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