Statistics
The accompanying histogram represents the total tax collected by a federal tax collection service for fifty regions of varying sizes and populations in a certain country. Explain why the graph is misleading.
it does not take into account the size and population of each region. Different regions could have drastically different population sizes. The region with the largest population is going to pay a lot more in taxes than the region with the smallest population. The moral of the story here is that many variables should be considered on per capita (per person) basis. For example, this graph should be drawn taxes paid per capita.
Determine the original set of data. 1I 016 2I 14479 3I 355579 4I 01 Legend: 1|0 represents 10
10,11,16,21,24,24,27,29,33,35,35,35,37,39,40,41
What is a bar graph? What is a Pareto chart?
A bar graph is a horizontal or vertical representation of the frequency or relative frequency of the categories. The height of each rectangle represents the category's frequency or relative frequency. A Pareto chart is a bar graph whose bars are drawn in decreasing order of frequency or relative frequency.
What are classes?
the grouping of data into categories
A researcher wanted to determine the number of televisions in households. He conducts a survey of 40 randomly selected households and obtains the data in the accompanying table. Complete parts (a) through (h) below. (b) Construct a frequency distribution of the data. (c) Construct a relative frequency distribution of the data. (d) What percentage of households in the survey have three televisions? (e) What percentage of households in the survey have four or more televisions? (f) Construct a frequency histogram of the data. Choose the correct graph below. (g) Construct a relative frequency histogram of the data. Choose the correct graph below. (h) Describe the shape of the distribution.
(a) The given data are discrete because they can only have whole number values. (b) 0-1 1-15 2-13 3-8 4-2 5-1 (c) .025 .375 .325 .2 .05 .025 (d) 20% (e) 7.5% (f) A-Skewed to the right (g) B-bell shaped (h) Skewed right
An experiment was conducted in which two fair dice were thrown 100 times. The sum of the pips showing on the dice was then recorded. The frequency histogram to the right gives the results. Use the histogram to complete parts (a) through (f). (a) What was the most frequent outcome of the experiment? (b) What was the least frequent? (c) How many times did we observe a 5? (d) How many more 7's were observed than 3's? (f) Describe the shape of the distribution. Choose the correct answer below.
(a) 5 (b) 2 (c) 19 (d) 10 (e) 19 (f) Skewed Right
(a) The graph to the right represents the favorite colors of 28 children. (b) What could be done to improve the graphic?
(a) The graph is not misleading (b) The graph does not need to be changed
A frequency distribution lists the _____________ of occurrences of each category of data, while a relative frequency distribution lists the ____________ of occurrences of each category of data.
A frequency distribution lists the number of occurrences of each category of data, while a relative frequency distribution lists the proportion of occurrences of each category of data.
A researcher wanted to determine the number of televisions in households. He conducts a survey of 40 randomly selected households and obtained the data to the right. Draw a dot plot of the televisions per household.
A-Skewed right
The _________________ is the difference between consecutive lower class limits.
Class Width
Why shouldn't classes overlap when summarizing continuous data in a frequency or relative frequency distribution?
Classes shouldn't overlap so there is no confusion as to which class an observation belongs. If classes were to overlap, there would be confusion as to which class an observation belongs. For example, with a first class of 20-30 and a second class of30-40, there would be confusion as to which class an observation of 30 belongs. This could also lead to an observation such as 30 being included in both clases, which would lead to a distribution that does not accurately represent the data.
The pie chart below depicts the beverage size customers choose while at a fast food restaurant. Complete parts (a) through (c). What is the most popular size? What percentage of customers choose this size? What is the least popular size? What percentage of customers choose this size? What percent of customers choose a small-sized beverage?
Medium 60% Large 6% 13%
A newspaper article claimed that the afternoon hours were the worst in terms of robberies and provided the graph to the right in support of this claim. Explain how this graph is misleading.
Not all of the time intervals are the same size. Redistributing the time interval so they are all the same size may lead to a different shape. 12p - 6p covers more hours than all the other bars.
The following Pareto chart shows the position played by the most valuable player (MVP) in a certain baseball league for the last 84 years. Use the chart to answer parts (a) through (d). Which position had the most MVPs? How many MVPs played short stop (SS)? How many more MVPs played outfield (OF) than short stop? There are three outfield positions (left field, center field, right field). Given this, how might the graph be misleading?
OF (Outfield) 8 20 The chart seems to show that one position has many more MVPs because three positions are combined into one. They should be separated.
For a number of people living in a household, state whether you would expect a histogram of the data to be bell-shaped, uniform, skewed left, or skewed right. For IQ scores of students, state whether you would expect a histogram of the data to be bell-shaped, uniform, skewed left, or skewed right.
Skewed Right Bell shaped
The ______ class limit is the smallest value within the class and the ______ class limit is the largest value within the class.
The lower class limit is the smallest value within the class and the upper class limit is the largest value within the class.
An airline offers discounted flights from Atlanta to five American cities. Below is a frequency distribution of the number of tickets purchased for each location based on a random sample of purchased tickets. Complete parts (a) through (f).
add al frequency numbers then use the sum of all to divide into the individual numbers.
To predict future enrollment in a school district, fifty households within the district were sampled, and asked to disclose the number of children under the age of five living in the household. The results of the survey are presented in the table. Complete parts (a) through (c) below. (b) What percentage of households has two children under the age of 5? (c) What percentage of households has one or two children under the age of 5?
Use the numbers collected from the data then divide that number by 50. (a) 0-14 = .28 1-13 = .26 2-17 = .34 3-3 = .06 4-3 = .06 (b) 34% (c) 60%
