HW 6(12-1,2,3)

The government of large city needs to determine whether the city's residents will support the repair of several roads. The government decides to conduct a surveys of a sample of the city's residents. Which one of the following procedures would be the most appropriate for obtaining a sample of the city's residents?

Survey a random sample of persons within each neighborhood

Describe how to find the range of a data set

The range is found by finding the difference between the highest and lowest data values

Described what is misleading in the following visual display of data

The scale of the vertical axis makes the difference in a bar height look larger than they really are

Describe what the standard deviation reveals about a data set.

The standard deviation reveals the level of variation in a data set.

I made a distribution of the heights of the 12 players on out basketball team. Because one player is much taller than the others, the team's median is greater than its mean height.

The statement does not make sense because one outlier will affect the mean by making it go up and will not affect the median

If professors use the same test scores for a particular student and calculate measure of a central tendency correctly, they will always agree on the student's final course grade

The statement does not make sense since some professors can decide to use different central tendencies to score how well the student did in the course

I'm working with a data set for which neither the mean nor the median is one of the data items.

The statement makes sense because it is possible to have a set of data that does not include the mean or median

The standard deviation for the heights of a group 5-year old children is smaller than the standard deviation for the heights of a group children who range in age from 3 to 15

The statement makes sense because the range of data for the heights of a group of 5-year-old children is larger than the range of data for the heights of a group of children who range in age from 3 or 15

The mean can be misleading if you don't know the spread of data items

The statement makes sense because there may exist some outliers (maybe much greater or much less than the rest of the data) in the data items

I'm working with data sets with different means and the same standard deviation

The statement makes sense. Data sets can have different means and the same standard deviation. For example, if two data sets contained the values {1,3} and {2,4} the means for each would be 2 and 3 respectively, but they both have the same standard deviation of approximately 1.41421

I'm working with data sets with the same means and different standard deviations.

The statement makes sense. Different data sets can have the same mean and different standard deviations

Two classes took a statistics test. Both classes had a mean score of 73. The scores of class A had a standard deviation of 5 and those of class B had a standard deviation of 10. Discuss the difference between the two​ classes' performance on the test

The students in class A received scores that different from the mean less than the student in class B

The death rate from this new strain of flu is catastrophic because 25% of the people hospitalized with the disease have died

This does not make sense because it is not clear whether the facts are derived from a sample of patients which is representative of the entire population of the patients suffering from the disease

A public radio station needs to surveys its contributors to determine their programming interests so they should select a random sample of 100 of their largest contributors

This does not make sense because the sample must include all the contributors, not only the largest contributors

Describe what is misleading in the chart display of data below

Time intervals on the horizontal axis do not represents equal amounts of time

More college graduates had starting salaries in the $61,000- $65,000 range than in the $46,000- $50,000 range.

True, because the bar for 61-65 is taller than the bar for 46-50

Over a one-month period, stock A had a mean daily closing price of 120.2 and the standard deviation of 12.3 By contrast, stock B had a mean daily closing price of 75.5 and a standard deviation of 5.6. Which stock was more volatile?

- A - standard deviation -larger

What is a population? What is a sample?

-A population is the set containing all the people or objects whose properties are to be described and analyzed by the data collector -A sample is a subset or subgroup of the population

A questionnaire was given to students in an introductory statistics class during the first week of the course. One question asked, "How stressed have you been in the last 2 1/2 weeks, on a scale of 0 to 10, with 0 being as stressed as possible?" The students' responses are shown in the frequency destruction. How many students were involved in study?

154 students

Use the data 6, 7, 8, 10, 11, 12. Without actually computing the standard deviation, determine the value below that best approximates the standard deviation

2

What is frequency distribution

A frequency distribution is a type of data presentation. The data values are listed in one column. That adjacent column indicates the number of times each value occurs.

Describe how to construct a frequency polygon from a histogram

A frequency polygon can be created by connecting the midpoints at the top of each bar in a histogram with line segments

What is a frequency polygon

A frequency polygon is a line graph with a series of points connected by lines to visually display the data from a frequency distribution

What is a histogram

A histogram is bar graph with bars that touch can be used to visually display the data from a frequency distribution

Describe what is meant by a random sample

A random sample is a sample obtained in such a way that every element in the population has an equal chance of being selected for the sample

The "average" income in a country can be given by the mean or the median. Consider a country where the wealthiest 20% of the population earns about 50% of the total income. a. Which measure would be used in propaganda opposing this country? b. Which measure would be used in propaganda supporting this country?

A. The median would be used, since it would likely show a smaller value the mean. B. The mean would be used, since it would likely show a larger value than the median

On an examination given to 30 students, no student scored below the mean

All 30 students had grades of B or better

Suppose you are interested in whether or not the students at your high school would favor a grading system in which students may receive grades of A+ A, A-, B+, B, B-, C+, C,C-, and so on. Describe how you might obtain a random sample of 100 students from the entire student population

Assign each student at the school a number, write each number on a card, and place all of the cards in a box. Then, randomly select 100 cards

Describe two way that graphs can be misleading

Graphs can be misleading by using the scale of the axes to inflate or deflate trends and by choosing a subset of a larger data set to emphasize a specific data trend

The histogram shows the starting salaries(rounded to the nearest thousand dollars) for college graduates bases on a random sample of recent graduates.

False, because the total number of data is larger.

If a set of test scores has a standard deviation of zero, what does this mean about the scores?

It means the all the scores are the same value

If a set test scores has a large range but a small standard deviation, describe what this means about students' performance on the test.

Most of students' test scores are around the mean, except that few students got scores much greater than the mean and few students got scores much less than the mean

The graph shown below indicates that for the period from 2016 to 2019, the percentage of Americans whose educational attainment was high school graduate or more has rapidly increased

No, it does not make sense; the scale on the vertical axis is stretch to create an overall impression of the percentage of Americans with a high school education or better increasing rapidly

Suppose you are interested in whether or not the students at your high school would favor a grading system in which students may receive grades of A+ A, A-, B+, B, B-, C+, C,C-, and so on. Would questioning every fifth student as they are leaving the school library until 100 students are interviewed be a good way to obtain a random sample.

No, since students who do not go to the library have no chance of being included in the sample

In one common system for finding a grade-point average, or GPA A= 4 B= 3 C= 2 D= 1 F= 0 The GPA is calculated by multiplying the number of credit hours for a course and the number of credit hours for a course and the number assigned to each grade, and then adding these products. The divide this sum by the total number of credit hours. Because each course grade is weighted according to the number of credits of the course, GPA is called a weighted mean. Calculated the GPA for the transcript

The grade point average is

What is the mean and how it is obtained?

The mean is a measure of central tendency obtained by adding all the data items and then dividing the sum by number of items.

Find the median for the data items in the given frequency distribution

The median

What is the median and how is it obtained?

The median of a data set is the data item in the middle of the ordered set. To find the median, the first arrange the data items in order, from smallest to largest. If the number of data items is odd, the median is the data item in the middle of this list. If the number of data items is even, the median is the mean of the two middle data items.

In class of 40 students, 21 have examination score of 77%. Which measures of central tendency can you immediately determine?

The mode is 77% because the majority of scores are 77%. The median is 77% because 77% will be the 20th and 21st data items in an order list, regardless of the other data items. No other measures can be determined.

What is the mode and how is it obtained?

The mode is a measure of central tendency obtained by identifying the data value that occurs most often in a data set

Find the mode for the data items in the given frequency distribution

The mode(s) is/are 3

A professor had student keep track of their social interactions for a week. The number of social interactions over the week is shown in the grouped frequency distribution table to the right. How many students were involved

The number of students was 103

A professor had students keep track of their social interactions for a week. The number of social interactions over the week is shown in the following grouped frequency distribution. How many students had at least 40 social interactions for the week?

The number of students was 13

Describe what is misleading in the visual display of data below

The percentages do not add up to 100%

Describe why the range might not be the best measure of dispersion

The range is a quick but rough measure of dispersion. It is the difference between the highest and lowest data values in a data set. On the other hand, the standard deviation is a measure of dispersion that is dependent on all of the data items, and therefore is generally more useful.