Domanda del libro di testo
Use frequency distribution formulas to estimate the sample mean and the sample standard deviation of the data set in Exercise 2.
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Ch. 2 - Descriptive Statistics
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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TOC.tableOfContents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Capitolo 2, Problema 2.T.1a
The overall averages of 12 students in a statistics class prior to taking the final exam are listed.
67 72 88 73 99 85 81 87 63 94 68 87
a. Find the mean, median, and mode of the data set. Which best represents the center of the data?
Guida verificata passo dopo passo1
Step 1: To find the mean, calculate the sum of all the data points and divide by the total number of data points. Use the formula: , where is the sum of all values and is the number of values.
Step 2: To find the median, first arrange the data in ascending order: 63, 67, 68, 72, 73, 81, 85, 87, 87, 88, 94, 99. Since there are 12 data points (an even number), the median is the average of the 6th and 7th values in the ordered list. Use the formula: .
Step 3: To find the mode, identify the value(s) that appear most frequently in the data set. In this case, check the frequency of each value in the list: 63, 67, 68, 72, 73, 81, 85, 87, 87, 88, 94, 99.
Step 4: Compare the mean, median, and mode to determine which best represents the center of the data. Consider the distribution of the data (e.g., whether it is symmetric, skewed, or has outliers) to decide which measure of central tendency is most appropriate.
Step 5: Conclude which measure (mean, median, or mode) is the best representation of the center of the data based on the context and the characteristics of the data set.
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Mean
The mean is the average of a data set, calculated by summing all the values and dividing by the number of values. It provides a central value that represents the overall data but can be influenced by extreme values (outliers). In the context of the given student scores, calculating the mean will give a quick overview of their performance.
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Percorso guidato
04:52
Calculating the Mean
Median
The median is the middle value of a data set when the numbers are arranged in ascending order. If there is an even number of observations, the median is the average of the two middle numbers. It is a robust measure of central tendency that is less affected by outliers, making it useful for understanding the typical performance of the students.
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Percorso guidato
03:26Calculating the Median
Mode
The mode is the value that appears most frequently in a data set. It can be particularly useful in identifying the most common score among the students. In cases where data is categorical or has repeated values, the mode can provide insights into trends that the mean and median may not reveal.
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07:10How to Create Histogram - TI-84 Calculator
Pratica correlata
Domanda del libro di testo
The overall averages of 12 students in a statistics class prior to taking the final exam are listed.
67 72 88 73 99 85 81 87 63 94 68 87
d. Display the data in a stem-and-leaf plot. Use one line per stem.
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Domanda del libro di testo
"According to data from the city of Toronto, Ontario, Canada, there were nearly 112,000 parking infractions in the city for December 2020, with fines totaling over 5,500,000 Canadian dollars. The fines (in Canadian dollars) for a random sample of 105 parking infractions in Toronto, Ontario, Canada, for December 2020 are listed below. (Source: City of Toronto)
In Exercises 1–5, use technology. If possible, print your results.
Draw a histogram for the data. Does the distribution appear to be bell-shaped?"
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Domanda del libro di testo
The number of minutes it took 12 students in a statistics class to complete the final exam are listed. Use a scatter plot to display this data set and the data set in Exercise 1. The data sets are in the same order. Describe any patterns.
61 85 67 48 54 61 59 80 67 55 88 84
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Domanda del libro di testo
According to data from the city of Toronto, Ontario, Canada, there were nearly 112,000 parking infractions in the city for December 2020, with fines totaling over 5,500,000 Canadian dollars. The fines (in Canadian dollars) for a random sample of 105 parking infractions in Toronto, Ontario, Canada, for December 2020 are listed below. (Source: City of Toronto)
In Exercises 1–5, use technology. If possible, print your results.
Find the sample mean of the data.
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Domanda del libro di testo
The data set represents the number of movies that a sample of 20 people watched in a year.
121 148 94 142 170 88 221 106 18 67
149 28 60 101 134 168 92 154 53 66
c. Display the data using a relative frequency histogram.
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