Math 1029

Suppose you are interested in whether or not the students at your high school would favor a grading system in which students may receive final 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.

true or false: A sample is the set of all the people or objects whose properties are to be described and analyzed by the data collector

False. A population is the set of all the people or objects whose properties are to be described and analyzed by the data collector.

true or false: One disadvantage of a​ stem-and-leaf plot is that it does not display the data items.

False. One advantage of a​ stem-and-leaf plot is that it displays the data items.

A company has twenty employees. Eighteen of them earn between​ $35,000 and​ $45,000 a year. The owner and his assistant both earn over​ $100,000 a year. Which is a best measure of​ salaries?

Median, as the salary of the owner and his assistant are very high.

The government of a large city needs to determine whether the​ city's residents will support the building of a new Middle School. The government decides to conduct a survey 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

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, 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 the list. If the number of data items is​ even, the median is the mean of the two middle data items.

In a class of 40​ students, 21 have examination scores of​ 77%. Which measure or measures of central tendency can you immediately​ determine? Explain your answer.

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 ordered​ list, regardless of the other data items. No other measures can be determined.

Describe how to construct a​ stem-and-leaf plot from a set of data. Assume that the data consist of​ two-digit numerical values.

The plot is constructed by separating each data item into two parts. The first part is the stem. The stem consists of the tens digit. The second part is the leaf. The leaf consists of the units digit for a given value. Write all of the stems in the first column.​ Then, write each leaf in the second​ column, writing the leaf of each data item in the row corresponding to its associated stem.

true or false: A data set can contain more than one​ median, or no median at all.

The statement is false. To make the statement​ true, change​ "median" to​ "mode" in each instance.

true or false: A​ call-in poll on radio or television is not reliable because the sample is not chosen randomly from a larger population.

The statement is true because people choose to call in. They are not randomly selected.

true or false: Numbers representing what is average or typical about a data set are called measures of central tendency.

The statement is true because these numbers are generally located toward the center of a distribution.

Determine whether the following statement makes sense or does not make​ sense, and explain your reasoning. Improperly worded questions can steer respondents towards answers that are not their own.

The statement makes sense because if a question is worded​ improperly, respondents might not know what is actually being asked.

true or false: When finding the​ mean, it is necessary to arrange the data items in order.

When finding the​ mean, it is necessary to arrange the data items in order.

sample

a subset or subgroup of the population.

frequency​ distribution

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

If data values are listed in one column and the adjacent column indicates the number of times each value​ occurs, the data presentation is called a​ _______

frequency distribution

If the midpoints of the tops of the bars of a histogram are connected with straight​ lines, the resulting line graph is a data presentation called​ a/an _______. To complete such a graph at both​ ends, the lines are drawn down to touch the​ _______.

frequency polygon horizontal axis

Suppose a data presentation is given where data values are listed in one column and the adjacent column indicates the number of times each value occurs. If this data presentation is varied by organizing the data into​ classes, the data presentation is called​ a/an _______. If one class in such a distribution is​ 80-89, the lower class limit is​ _______ and the upper class limit is​ _______.

grouped frequency division 80 89

Data can be displayed using a bar graph with bars that touch each other. This visual presentation of the data is called​ a/an _______. The heights of the bars represent the​ _______ of the data values.

histogram frequencies

the sum of all the data items divided by the number of data​ items, is the measure of central tendency called the

mean

The measure of central tendency that is the data item in the middle of​ ranked, or​ ordered, data is called the​ _____.

median

The measure of central tendency that is found by adding the lowest and highest data values and dividing the sum by 2 is called the

midrange

The measure of central tendency that is the data item in the middle of​ ranked, or​ ordered, data is called the​ _____.

mode

A sample obtained in such a way that every element in the population has an equal chance of being selected is called​ a/an _______ sample

random

A data presentation that separates each data item into two parts is called a​ _______

stem-and-leaf plot

Population

the set containing all the people or objects whose properties are to be described and analyzed by the data collector

Measures of dispersion are used to describe the spread of data items in a data set.

true

The sum of the deviations from the mean for a data set is always zero.

true

A college vice president of business is considering bids for a new​ cafeteria/dining service. He surveys 100 students in the middle of the day on Tuesday. Is this a good​ sample?

​No; he is not considering students at night or on other days.