new_practical_questions_statistics.csv

Question,Answer A,Answer B,Answer C,Answer D,Correct Answer,Explanation "A coffee shop tracks the number of customers per hour. If the mean number of customers is 20 with a standard deviation of 5, what is the range within which approximately 68% of customer counts fall?",15 to 25,10 to 30,20 to 30,...

Question,Answer A,Answer B,Answer C,Answer D,Correct Answer,Explanation "A coffee shop tracks the number of customers per hour. If the mean number of customers is 20 with a standard deviation of 5, what is the range within which approximately 68% of customer counts fall?",15 to 25,10 to 30,20 to 30,5 to 35,A,"68% of the data in a normal distribution falls within one standard deviation from the mean. Here, 20 ± 5 gives the range 15 to 25." "If the salaries of employees at a company are normally distributed with a mean of \$50,000 and a standard deviation of \$8,000, what percentage of employees earn between \$42,000 and \$58,000?",50%,68%,95%,99.70%,B,"One standard deviation from the mean (50,000 ± 8,000) covers 68% of the data in a normal distribution." "In a normally distributed dataset, the mean is 100, and 99.7% of the data falls within what range if the standard deviation is 15?",85 to 115,70 to 130,55 to 145,40 to 160,C,99.7% of the data falls within three standard deviations from the mean: 100 ± 3(15) = 55 to 145. "Which measure of spread would you use if a dataset includes an outlier, such as a salary of \$1,000,000 among other salaries between \$40,000 and \$70,000?",Range,Mean,Standard Deviation,Interquartile Range (IQR),D,The interquartile range (IQR) is less affected by outliers and provides a better measure of spread for skewed data. "If a student's test score is 2 standard deviations below the mean, where does this score fall in terms of percentile?",2.5th percentile,16th percentile,84th percentile,97.5th percentile,A,Approximately 2.5% of data in a normal distribution falls below two standard deviations below the mean. A marathon has a mean finish time of 4 hours with a standard deviation of 30 minutes. How unusual is a finish time of 5 hours?,It is typical because it is within one standard deviation,It is somewhat unusual because it is two standard deviations away,It is very unusual because it is three standard deviations away,It is typical because it is within half a standard deviation,B,"5 hours is two standard deviations (30 minutes x 2) away from the mean, making it somewhat unusual." "If a distribution has a mean of 75 and a median of 80, what does this suggest about the skewness of the data?",The distribution is symmetrical,The distribution is skewed to the right (positively skewed),The distribution is skewed to the left (negatively skewed),The distribution is uniform,C,"If the mean is less than the median, the distribution is skewed to the left (negatively skewed)." A teacher finds that the test scores of her class are skewed to the right. Which measure of central tendency should she use to report the average score?,Mean,Median,Mode,Range,B,The median is preferred in a skewed distribution because it is less affected by extreme values. "In a survey, the mean age of participants is 35 years with a standard deviation of 10 years. What age would be considered an outlier?",40 years,30 years,15 years,50 years,C,An age of 15 years is two standard deviations (20 years) below the mean and is considered unusual or an outlier. Why might a biologist prefer using the median instead of the mean when analyzing the weight of a species with a few exceptionally heavy individuals?,The mean gives more precise data,The median is unaffected by extreme values,The median includes all data points,The mean is less sensitive to variability,B,The median is a robust measure of central tendency and is not influenced by extreme outliers. "If the mean score of a class is 85 with a standard deviation of 5, what score would be considered within one standard deviation from the mean?",95,80,70,100,B,One standard deviation from the mean covers scores from 80 to 90 (85 ± 5). A data analyst finds that the standard deviation of a dataset is very large. What does this tell them about the data?,The data points are very close to the mean,The data points are spread out widely around the mean,The data is symmetrical,The mean is greater than the median,B,A large standard deviation indicates that the data points are spread out widely from the mean. "In a dataset, 95% of values fall within what range if the mean is 50 and the standard deviation is 10?",40 to 60,30 to 70,20 to 80,50 to 70,B,95% of values fall within two standard deviations from the mean: 50 ± 2(10) = 30 to 70. "If a study reports that the average income in a town is \$45,000 with a very small standard deviation, what can you infer?","Most residents have incomes very close to \$45,000",Incomes vary greatly among residents,The data is skewed to the right,The mean income is not a reliable measure,A,"A small standard deviation indicates that the incomes are tightly clustered around the mean of \$45,000." A psychologist finds that the distribution of response times in an experiment is positively skewed. Which measure of spread should they use to describe the variability?,Mean,Range,Standard Deviation,Interquartile Range (IQR),D,The interquartile range (IQR) is less affected by skewed data and provides a better measure of variability in this case.