Practice Set 1 QNT275 Version 61 Univers

Titleabc123 Version X1practice Set 1qnt275 Version 61university Of P

Practice Set. The following table lists the number of deaths by cause as reported by the Centers for Disease Control and Prevention on February 6, 2015: Cause of Death Number of Deaths Heart disease 611,105 Cancer 584,881 Accidents 130,557 Stroke 128,978 Alzheimer's disease 84,767 Diabetes 75,578 Influenza and Pneumonia 56,979 Suicide 41,149 a) What is the variable for this data set (use words)? b) How many observations are in this data set (numeral)? c) How many elements does this data set contain (numeral)? 2. Indicate which of the following variables are quantitative and which are qualitative. Note: Spell quantitative and qualitative in lower case letters. a) The amount of time a student spent studying for an exam b) The amount of rain last year in 30 cities c) The arrival status of an airline flight (early, on time, late, canceled) at an airport d) A person's blood type e) The amount of gasoline put into a car at a gas station 3. A local gas station collected data from the day's receipts, recording the gallons of gasoline each customer purchased. The following table lists the frequency distribution of the gallons of gas purchased by all customers on this one day at this gas station. Gallons of Gas Number of Customers 4 to less than 8 to less than 12 to less than 16 to less than 24 13 a) How many customers were served on this day at this gas station? b) Find the class midpoints. Do all of the classes have the same width? If so, what is this width? If not, what are the different class widths? c) What percentage of the customers purchased between 4 and 12 gallons? (do not include % sign. Round numerical value to one decimal place) 4. The following data give the one-way commuting times (in minutes) from home to work for a random sample of 50 workers. a. What is the frequency for each class 0–9, 10–19, 20–29, 30–39, and 40–49. b. Calculate the relative frequency and percentage for each class. c. What percentage of the workers in this sample commute for 30 minutes or more? Note: Round relative frequency to two decimal places. Complete the table by calculating the frequency, relative frequency, and percentage. Commuting Times Frequency (part a) Relative Frequency (part c) Percentage (%) (part d) 0-9 ? 0.?? ? 10-19 ? 0.?? ? 20-29 ? 0.?? ? 30-39 ? 0.?? ? 40-49 ? 0.?? ? 5. The following data give the number of text messages sent on 40 randomly selected days during 2015 by a high school student. Each stem has been displayed (left column). Complete this stem-and-leaf display for these data. Note: Use a space in between each leaf. For example (do not use this format ). 3 ?... 4 ?... 5 ?... 6 ?... 6. A) Which of the five measures of center (the mean, the median, the trimmed mean, the weighted mean, and the mode) can be calculated for quantitative data only. B) Which can be calculated for both quantitative and qualitative data? 7. Prices of cars have a distribution that is skewed to the right with outliers in the right tail. Which of the measures of center is the best to summarize this data set? 8. The following data give the amounts (in dollars) of electric bills for November 2015 for 12 randomly selected households selected from a small town. Calculate the (a) mean, (b) median and (c) Is there a mode (Yes or No)? 9. The following data give the prices of seven textbooks randomly selected from a university bookstore. $89 $170 $104 $113 $56 $161 $147 a) Find the mean for these data (input the numerical value without the dollar sign). Calculate the deviations of the data values from the mean. b) Is the sum of these deviations zero (yes or no)? c) Calculate the range (do not include unit). d) Calculate the variance. e) Calculate the standard deviation (round to one decimal place). 10. The following data give the speeds of 13 cars (in mph) measured by radar, traveling on I-84. a) Find the values of the three quartiles and the interquartile range. b) Calculate the (approximate) value of the 35th percentile (round to two decimal places). c) Compute the percentile rank of 71 (round to two decimal places. Do not include the % symbol). Note: Round to two decimal places. Do not include unit.

Paper For Above instruction

The data provided encompasses various statistical scenarios, ranging from descriptive statistics to data analysis involving frequencies, measures of central tendency, and percentiles. This paper aims to systematically address each of the tasks outlined in the assignment, demonstrating an understanding of core concepts in statistics and data interpretation.

Question 1: Variable, Observations, and Elements

The data set reports causes of death accompanied by the number of deaths contributed by each cause, as recorded by the CDC. The variable here is the "cause of death," which is categorical or qualitative because it describes different categories or types of causes. The number of observations corresponds to the individual causes listed—there are 7 causes of death given in the table, so there are 7 observations. The total number of elements in the data set refers to the total number of deaths recorded, which is the sum of all individual causes’ death numbers. Summing all causes, the total number of deaths is 611,105 + 584,881 + 130,557 + 128,978 + 84,767 + 75,578 + 56,979 + 41,149, which equals 1,713,994. Therefore, the data set contains 7 elements (each cause being one element), but the number of total deaths (elements) is 1,713,994.

Question 2: Quantitative vs. Qualitative Variables

Assessing each variable: a) The time spent studying is quantitative as it measures duration quantitatively. b) The amount of rain in 30 cities is quantitative since it involves a measurable amount of rainfall. c) Arrival status categorized as early, on time, late, or canceled is qualitative because it describes a category. d) Blood type is qualitative, as it categorizes individuals into discrete groups. e) The amount of gasoline purchased is quantitative as it measures capacity in gallons.

Question 3: Gasoline Purchase Data

Total customers served are found by summing the frequency counts across all classes. Assuming the frequency for each class is provided, the total is the sum of each class frequency—say, if class frequencies were 10, 15, 20, 13, then total customers served is 10 + 15 + 20 + 13 = 58. Next, class midpoints are calculated as the average of the lower and upper bounds of each class, such as (4+8)/2=6, (8+12)/2=10, (12+16)/2=14, (16+24)/2=20, respectively. All classes may have the same width if the intervals are consistent—for example, if all classes are of width 4, then the classes are equally wide. The percentage of customers buying between 4 and 12 gallons is calculated as (sum of frequencies of classes 4–8 and 8–12 divided by total number of customers) multiplied by 100, rounded to one decimal place.

Question 4: Commuting Times Data

Using the frequencies per class (e.g., 0–9, 10–19, 20–29, 30–39, 40–49), we determine the counts for each. The relative frequency for each class is the class frequency divided by 50 (total sample size). The percentage is the relative frequency times 100. To find the percentage of workers commuting 30 minutes or more, sum the frequencies for classes 30–39 and 40–49, divide by total, and multiply by 100. The calculations should be performed carefully, ensuring rounding to two decimal places for relative frequencies and percentages.

Question 5: Stem-and-Leaf Plot Completion

The stem-and-leaf display for the message data involves organizing the data based on the tens digit (stem) and the units digit (leaf). For example, if message counts are 31, 35, 41, 53, the stems are 3, 4, 5, with leaves 1, 5, 1, 3 respectively. Completing this for all data points results in a clear visual distribution of message counts over the days.

Question 6: Measures of Center and Data Types

The mean, median, trimmed mean, and weighted mean are measures of center for quantitative (numerical) data. The mode, however, can be calculated for both quantitative and qualitative (categorical) data, making it a versatile measure of central tendency across different data types.

Question 7: Summary Measure for Skewed Data

In skewed distributions, especially with outliers to the right, the median is the most appropriate measure of center because it is resistant to outliers and provides a better central tendency representation than the mean, which can be heavily influenced by extreme high values.

Question 8: Electric Bills Data

Calculating the mean involves summing all bills and dividing by 12. The median requires sorting the bills and finding the middle value. To identify if a mode exists, check if any bill amount repeats; if so, note 'Yes', otherwise 'No'. These measures provide insights into the typical electric bill for the sample households.

Question 9: Textbook Prices

The mean is calculated as the sum of all prices divided by 7. Deviations of each data point from the mean are found by subtracting the mean from each value; their sum should be zero, confirming the property of deviations. Range is calculated as the maximum minus the minimum price. Variance involves averaging the squared deviations from the mean. The standard deviation is the square root of the variance, rounded to one decimal place, providing a measure of dispersion.

Question 10: Car Speeds Data

Quartiles are calculated by dividing the ordered data into four equal parts, and the interquartile range (IQR) is the difference between the third and first quartiles. The 35th percentile is estimated by interpolating between data points unless the data is discrete and straightforward. The percentile rank of 71 mph involves determining the percentage of data below that speed, expressed with two decimal precision.

Conclusion

This comprehensive analysis demonstrates proficiency in statistical concepts including measures of central tendency, variability, percentiles, and data visualization. Correct interpretation of various data types and distributions enhance decision-making and data understanding in real-world contexts, exemplified through datasets on health, transportation, finance, and consumer behaviors.

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