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You passed Intro to Statistics Milestone 2 1 In which of these cases should mode be used?
category
When the data is represented using ratio scale
- When the data has extreme values
- When the data is represented using interval scale
RATIONALE
If the data is qualitative, it is only descriptive. In this case, the mode is a good measure since the mode examines the most frequently occurring value. The data can be non-numeric.
CONCEPT
Measures of Center 2 Which of the following statements is true?
When the data is qualitative and we talk about the most frequent
According to the Central Limit Theorem, the mean of the sampling distribution is greater than the standard deviation.
- 52 RATIONALE Note the value for Q1 is the left edge of the box, which is 33. CONCEPT Five Number Summary and Boxplots 4 Let x stand for the percentage of an individual student's math test score. 64 students were sampled at a time. The population mean is 78 percent and the population standard deviation is 14 percent. What is the standard deviation of the sampling distribution of sample means?
14
64
RATIONALE The standard deviation of the sampling distribution, , is equal to the standard deviation of the original population, , divided by the square root of the sample size,. If the standard deviation of the population is 14 and the sample size is 64, then the standard deviation of the sampling distribution is: CONCEPT 5 Center and Variation of a Sampling Distribution The mean of any standard normal distribution is.
- 1
- ±0.
- 0 RATIONALE The standard normal is always centered at 0. It also has a standard deviation of 1.
A distribution in which two distinct values are more frequent than the other values.
- A distribution in which the values are distributed uniformly.
- A distribution in which one value is more frequent than other values. RATIONALE Recall the mode is the most frequently occurring value. If a distribution is unimodal, it simply means there is one value that occurs most frequently. CONCEPT Shapes of Distribution 8 At Priscilla's school, the final grade for her Calculus course is weighted as follows:
- Tests: 50%
- Quizzes: 30%
- Homework: 20% Priscilla has an average of 87% on her tests, 100% on her quizzes, and 20% on her homework. What is Priscilla's weighted average?
69%
73.4%
- 77.5% RATIONALE In order to get the weighted average we use the following formula: CONCEPT Weighted Mean 9 In a survey to rate the pizzas served by a pizza parlor, 250 people rated their agreement with the statement, “The pizzas here are one of the best I’ve ever had.” The answers were put into a table. Rating Frequency Strongly Agree 27 Agree 50 Neutral 75 Disagree 54 Strongly Disagree 44 The relative frequency of people who strongly agree with the statement is.
17.6%
RATIONALE The dotplot is a number line that shows the number of items at each value, which is designated with an X. So the largest value we can see is at 10. CONCEPT Dot Plots 11 Select the statement that is TRUE.
- The interquartile range is the average value of a data set.
- The interquartile range covers 100% of a data set.
- The interquartile range is calculated by adding the first quartile with the third quartile.
- The interquartile range is calculated by subtracting the first quartile fromthe
third quartile.
RATIONALE Recall that the interquartile range is the difference between Q3 and Q1 and can be calculated by subtracting the first quartile from the third quartile: CONCEPT
Range and Interquartile Range (IQR) 12 The formula for the standard deviation of a sample is: Select the true statement for the following data set that has a mean of 6.75: 4, 6, 7, 10 Answer choices are rounded to the hundredths place.
- The variance is 4.71 and the standard deviation is 2.17.
- The variance is 6.25 and the standard deviation is 2.50.
- The variance is 2.50 and the standard deviation is 6.50.
- The variance is 6.75 and the standard deviation is 6.25. RATIONALE We can first calculate the variance of the data, , by using the part of the formula under the square root: Next, we can find the standard deviation, , by simply taking the square root of the variance:
CONCEPT 1 Stack Plots 4 Jerry graded seven standardized tests with the following scores: 60, 74, 41, 87, 94, 79, 57 Which standardized test score represents the 50th percentile?
- 57
- 79
- 74
- 41 RATIONALE The 50th percentile will be the median, or middle number. Make sure to first order the data. The middle number is the 4th value, or 74. CONCEPT Percentiles 15
Which of the following is NOT a step used in calculating standard deviation?
- Dividing the sum of each value by the total number of values plus 1.
- Subtracting the value of each data set from the mean.
- Squaring the difference of x - u.
- Calculating the mean of the data set. RATIONALE Recall the standard deviation. So there is no addition of 1 to any values. CONCEPT Standard Deviation 16 Dave drives to work. While driving the car over nine days, he observes his daily average speed and lists it in the table below. Day Average Speed (MPH) 1 45 2 62 3 44 4 70 5 59 6 66 7 54 8 63
- 124°
- 5°
- 41°
- 150° RATIONALE Recall that to get the angle for something in a pie chart we use the following formula: So in this case, the central angle for the chocolate ice cream sector would be: CONCEPT 1 Bar Graphs and Pie Charts 8 Sara wonders what percentage of her students answered at least half of the quiz questions incorrectly. The relative cumulative frequency of students who earned a score of 21 or higher on the quiz is.
RATIONALE To get the relative cumulative frequency of 21 or greater, we need to first find the cumulative number of 21 or more. We simply add up any bin that has the number 21 or more, such as the bin that shows scores of 21-25, 26-30, 31-35, and 36-40. This would be: To calculate relative cumulative frequency, we will take this cumulative number and divide it by the total number of students. CONCEPT Cumulative Frequency 19 The average daily rainfall for the past week in the town of Hope Cove is normally distributed, with a mean rainfall of 2.1 inches and a standard deviation of 0.2 inches. If the distribution is normal, what percent of data lies between 1.9 inches and 2.3 inches of rainfall?
The approximate percent of values lying within three standard deviations of the mean is 49.85%.
- Approximately 68% of the values lie within one standard deviation of the mean.
- The approximate percent of values lying within two standard deviations of the mean is 47.5%. RATIONALE The normal distribution follows the empirical rule. This tells us that within one standard deviation of the mean, we should find roughly 68% of the data. CONCEPT Normal Distribution 21 Ralph records the time it takes for each of his classmates to run around the track one time. As he analyzes the data on the graph, he notices very little variation between his classmates’ times. Which component of data analysis is Ralph observing?
The overall shape of the data
The center of the data set
- The overall spread of the data
An outlier in the data set RATIONALE Since Ralph is looking at the variation of data, this is examining the spread of the data. CONCEPT Data Analysis 22 The midterm exam scores obtained by boys and girls in a class are listed in the table below What does the circled section represent?
- Two boys scored between 80 and 89 marks on the exam.
- Twelve boys scored 8 marks on the exam.
- Eight boys scored 12 marks on the exam.
- Eight boys scored over 10 marks on the exam. RATIONALE
