Mth115 S20 HW 12.1-12.3

Give the names of two other statistics that have the same value as the 50th percentile.

2nd quartile; median

Twenty students in a geology class were asked how many college credits they had earned. The responses are to the right. Construct a​ stem-and-leaf display.

2| 246779 3|247 4|13599 5|66 6|2246

The table to the right shows the median age that a person from a certain region first married for the years 2002 to 2012. Draw a bar graph that makes the increase in the median age of men for the years shown appear to be small and another that makes the increase in the median age of men for the years shown appear to be large.

A.) highest age (y) straight B.) lowest age (y)

The table to the right shows the average price of a movie ticket in a certain theater for the years 2009 to 2013. Draw a line graph that makes the increase in the average price of a movie ticket for the years shown appear to be small and another that makes the increase in the average price of a movie ticket for the years shown appear to be large.

A.) highest priced(y) graph B.) lowest priced (y) graph

The mean is the​ "most sensitive" average because it is affected by any change in the data. ​a) Determine the​ mean, median,​ mode, and midrange for 2​, 4​, 5​, 7​, 7​, 8​, 14. ​b) Change the 8 to 13 in part​ (a). Determine the​ mean, median,​ mode, and midrange. ​c) Which averages were affected by changing the 8 to 13​? ​d) Which averages will be affected by changing the 14 to 13 in part​ (a)?

A.The mean is 6.7​, the median is 7​, the​ mode(s) is/are 7​, and the midrange is 8. B. The mean is 7.4​,the median is 7,the​ mode(s) is/are 7​, and the midrange is 8. C. mean D. midrange and mean

Joe smoked two packs a day for his whole life and lived to be 100. So smoking is not really bad for you. What is wrong with this​ conclusion?

Anecdotal evidence

A researcher takes a random sample of grade school children and finds a clear relationship between shoes size and reading scores. As shoe size​ increases, test scores increase. The researcher concludes high reading scores are caused by large feet. What is wrong with​ this?

Correlation does not imply causation

A histogram is used to graph categorical data while a bar graph is used to graph frequency distributions.

False

In​ statistics, average always indicates mean.

False

A group of people are classified according to race and then random samples of people from each group are taken.

Stratified sampling

The cost to attend a public university in a recent year is $15,880. The circle graph to the right shows the percentage of that cost for​ tuition/fees, room,​ board, and computer costs. Determine the​ cost, in​ dollars, for each category.

The cost of tuition and fees is ​$5875.6. The cost of room is ​$5843.84. The cost of board is ​$3271.28. The computer costs are ​$889.28.

At a certain middle ​school, half of the students are below average in English. ​Therefore, the school should receive more federal aid to raise student scores.

The statement is invalid because half of the students in population are expected to be below average in English​, so the school itself is not below average.

Company X sells a microwave that costs more than the microwave sold by Company Y. Therefore the Company X microwave will last longer than the Company Y microwave

The statement is not valid because more expensive microwaves are not guaranteed to last longer than less expensive microwaves.

In a normal polulation mean​ = median.

True

Median is the best measure of center when working with populations like income and housing prices.

True

A local paper​ asks, " Do you support a third regional Chicago​ airport?" YES call​ 555-5551 NO​ 555-5552

Voluntary Response sample

The table gives the distribution on annual salaries at a small company. Use the information in the table to answer the following. ​a) Determine the mean annual salary. ​b) Determine the median annual salary. ​c) Determine the mode annual salary. ​d) Determine the midrange annual salary. ​e) Which do you believe is the best measure of central tendency for this set of​ data? Explain your answer.

a) The mean annual salary is ​$30680. ​b) The median annual salary is ​$25,000. ​c) Find the mode or​ modes, (if​ any). Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. $17000 ​d) The midrange annual salary is ​$63000. ​e) Which do you believe is the best measure of central tendency for this set of​ data? Explain your answer. Choose the correct answer below. The median because one of the data values is significantly higher than the others.

Use the frequency distribution to determine ​a) the total number of observations. ​b) the width of each class. ​c) the midpoint of the second class. ​d) the modal class​ (or classes). ​e) the class limits of the next class if an additional class were to be added.

a.) 37 b.) 11 c.) 23 d.) 18-28,29-39 e.) 73-83

The following graph shows the average price of a movie ticket for the years 2009 and 2010. Complete parts​ (a) and​ (b) below. ​a) Draw a bar graph that shows the entire scale from​ $0 to​ $8. Choose the correct graph below. b) Does the new graph give a different​ impression? Explain. Choose the correct answer below.

a.) make sense of it b.) Yes, the price difference appears the same in the new graph

The table shows the sales of the 15 top selling colors and chassis for a car​ company, in thousands of​ vehicles, during the month of October. ​a) Construct a frequency distribution with a first class of 18-24. ​b) Construct a histogram. ​c) Construct a frequency polygon.

a.) picture b.) make the graph with the c.)line graph to make the last one

In a​ stem-and-leaf display, ​a) the left group of digits is called the _______ b) the right group of digits is called the _____

a.)stem b.) leaf

A number that is representative of a set of data is called​ a(n) _______.

average

Graphs that are often used to compare parts of one or more components of the whole to the whole are called pie charts or __________ graphs.

circle

A sample that consists of a random selection of groups or units is called a​ _______ sample.

cluster

A state is divided into regions using area codes. A random sample of 20 area code areas is selected.

cluster

The first 30 students leaving the student center are asked how much money they spent on rent for the semester.

convience

Use the following​ data, which represent the English placement test scores of a sample of 30​ students, to construct a frequency distribution with a first class of 472−492.

count the number found within the groupings asked

The​ collection, organization, and analysis of data is called​ _______ statistics.

descriptive

Twenty members of a health club who jog were asked how many miles they jog per week. The responses are to the right. Construct a​ stem-and-leaf display. For single digit​ data, use a stem of 0.

fill in based on chart

A listing of observed values and the corresponding frequency of occurrence of each value is called a​ _______ distribution.

frequency

The following statistics represent weekly salaries at a construction company.

he most common salary is ​$650. The salary that half the​ employees' salaries surpass is ​$565. The percent of​ employees' salaries that surpassed ​$745 is 25​%. The percent of​ employees' salaries that were less than ​$470 is 25​%. The percent of​ employees' salaries that surpassed ​$841 is 18​%. If the company has 100 ​employees, the total weekly salary of all employees is ​$71000.

A graph with observed values on its horizontal scale and frequencies on its vertical scale and that uses bars to indicate frequency is called a​ _______.

histogram

Making generalizations or predictions from the data collected is called ________ statistics

inferential

A car dealership is interested in the number of cars sold daily. A sample is taken over 40 days to obtain the following data regarding the number of cars sold daily. Construct a frequency​ distribution, letting each class have a width of 1.

just count the numbers asked for

The average that is found by summing the data and then dividing the sum by the number of pieces of data is called the

mean

Using the following​ values, find the​ mean, median, mode and midrange. 32, 40, 43, , 45, 52, 53, 56

mean 10 median 10 no mode midrange 10

7, 9, 9, 9, 14, 16, 21, 22

mean 13.4 median 11.5 mode 9 midrange 14.5

3, 3, 6, 10, 12, 13, 14, 28, 37

mean 14 median 12 mode 3 midrange 20

99 100 110 141 148 157 172 183 198 200 209 223 225 257 261

mean 178.867 median 183 no mode midrange 180

The value in the middle of a set of ranked data is called the

median

The value halfway between the lowest and highest values in a set of data is called the

midrange

In a frequency​ distribution, the class with the greatest frequency is call the _____ class.

modal

The piece of data that occurs most frequently is called the​ _______.

mode

All items or people of interest in an experiment are collectively called a

population

The measures of position that divide a set of data into four equal parts are called​ _______.

quartiles

If a sample is drawn in such a way that each time an item is​ selected, each item in the population has an equal chance of being​ drawn, the sample is called a​ _______ sample.

random

Pool balls in a bin are shaken and then balls are selected from the bin.

random

A subset of a population used by statisticians to make predictions about a population is called a

sample

When a population is divided into​ parts, called​ strata, for the purpose of drawing a​ sample, the procedure is known as a ______ sampling

stratified

When a sample is obtained by drawing every nth​ item, the sample is called a ____ sample.

systematic

When a national sample of heights of kindergarten children was​ taken, a student was told that she was in the 25th percentile. Explain what that means.

taller than

Some subscribers of a magazine that sells and reviews watches respond to an annual questionnaire regarding their satisfaction with the new selection of watches. The information obtained from these questionnaires is then used as a sample from which ratings are made by the magazine. Are the data obtained from these returned questionnaires representative of the entire​ population, or are they​ biased?

the data is baised because the source of the data comes only from people that subscribe to their magazine.

For any set of​ data, what must be done to the data before percentiles can be​ determined?

the data must be ranked

Suppose of eighty-five percent of accidents occur within 9 miles of home. Therefore, it is safer not to drive within 9 miles of home.

the statement is not valid because people may drive within 9 miles of home more often

Thirty students said that they would recommend Professor Wilson to a friend. Twenty students said that they would recommend Professor Malone to a friend.​Therefore, Professor Wilson is a better teacher than Professor Malone.

the statement is not valid because we dont know how many of each professor's students were surveyed and student opinion does not necessarily determine the quality of a professor's teaching abilities.

Fill in the blanks with the appropriate symbols. ​a) The symbol for the sample mean is​ _______. ​b) The symbol for the population mean is​ _______.

x overbar . mu

Use the following​ data, which represent the English placement test scores of a sample of 30​ students, to construct a frequency distribution with a first class of 472−492.

Same as the last (easier to put number in numerical order)