Question 1

What part of a poll or survey is considered the 'sample'?

Accepted Answer

The small group of participants in a survey or poll is called the sample (or sample group) because they are theoretically meant to be a sampling of the larger population that the survey or poll aims to describe. For example, when election day exit polls are conducted, random voters are asked about their vote as they walk out of their polling place. This takes place in myriad locations nationwide. Only a small portion of voters ultimately participate in an exit poll, but the results of exit polls are used to predict what the entire body of voters did that day. The voters who actually participate in the exit poll are the sample group.

Question 2

In which of the following scenarios would a pie chart be the most effective way to display data?

Accepted Answer

Pie charts are best used in situations where there is a finite value that is being divided into portions, such as a manager's presentation about how he wants to appropriate the next year's budget. The budget is a set amount; even if the exact dollar amount is not known, a budget is, in general, a whole. Each area of the company that receives a portion of the budget is represented by a wedge of the pie chart.

Question 3

What are the two primary categories of fractions?

Accepted Answer

Most fractions fall into one of two categories: decimal fractions or common fractions. Any time a number has a digit other than '0' to the right of the decimal it is a decimal fraction. Digits to the right of a decimal represent values of less than one or a fraction of one whole unit. Common fractions are the expressions in which there is a numerator and denominator separated by a diagonal or horizontal line. The denominator represents how many fractional units comprise one whole; the numerator represents how many fractional units comprise the subject of the fraction. For example, in the word problem, "Jack and Jane are sharing a pizza with 12 slices. Jack eats four slices and Jane eats three. How much of the pizza did they eat altogether?" 12 slices represents the whole and seven is the subject of the fraction (7/12).

Question 4

What is the mean for the following distances? 206 miles, 410 miles, 97 miles, 125 miles, 999 miles, 234 miles

Accepted Answer

The mean for the data set above is 345.17 miles. The median or middle number when the numbers are in ascending order (97 miles, 125 miles, 206 miles, 234 miles, 410 miles, 999 miles) is 220 miles. There is no mode because each number is unique to the set.

Question 5

In a jar of candy there are 127 red candies, 92 orange ones, 108 yellow ones, 77 green ones, and 13 blue candies. If a person reaches into the jar without looking and grabs one piece of candy, what is the probability of that piece being red?

Accepted Answer

A person reaching into the candy jar would have a 30% chance of pulling out a piece of red candy. There are 417 pieces of candy in the jar altogether, which means the person has 127 chances in 417 to pull out a piece of red candy (or 127/417 if the candy is red). To convert that to a percentage, divide the number of chances to get a red candy (127) by the total number of pieces (417), then multiply the quotient by 100.

Question 6

A company just distributed candy bars wrapped with golden tickets hidden within ordinary shipments of their product. The company spokesperson announces that there is a "one in one thousand chance" of someone finding a golden ticket when they open a candy bar, and that 500,000 candy bars have been distributed in the golden ticket promotion. If a person buys three of the candy bars, what is their chance of finding a golden ticket?

Accepted Answer

A person with three eligible candy bars has a 0.3% chance of receiving one of the golden tickets. There is one golden ticket in every 1000 candy bars and there are 500,000 candy bars that could possibly have the prize. That means there are 500 golden tickets waiting to be found, and each candy bar has a 0.1% chance of having a ticket (500/500,000). If the person has three candy bars, that triples their 0.1% chance of finding a golden ticket.

Question 7

Data that is weighted toward one end of the numerical range in which it occurs is:

Accepted Answer

Data that is asymmetrically concentrated at one end of a numerical range is skewed. This may be the result of faulty data collection (such as a poor poll or survey) or may be a completely natural phenomenon. A skewed graph or data set is not necessarily an indication of fault, flaw or wrongdoing, but may merely demonstrate a disproportionate relationship.

Question 8

All data can be divided into four equal sections that are called:

Accepted Answer

Each of the four sections into which data can be divided is called a quartile. Quartiles are commonly used when analyzing data in which time is a significant variable or influence, such as the crime rate in an urban center over the course of a year. A lot of financial data is customarily divided into quartiles.

Question 9

A variable that affects the data collected but is not accounted for or demonstrated in the statistical measure of the data is a:

Accepted Answer

A lurking variable is information directly related to the independent and dependent variables in statistical analysis, that has an effect on the data being analyzed, but is not accounted for in the analysis. Lurking variables that are not accounted for in data analysis can cause the resulting predictions to be inaccurate or incomplete.

Question 10

In which of the following scenarios would a bar graph be the best graphic organizer for the data?

Accepted Answer

Bar graphs are best utilized to compare single-factor numerical data, like the number of units competing brands sold in the same month. Any data that demonstrates the relationship between two factors (like migration as it relates to construction or malnutrition in relation to war) are best demonstrated by line graphs.

Question 11

Which type of chart or graph would be the best graphic organizer to demonstrate the relationship between foreign aid to a nation and the decrease in child mortality rates among its citizens?

Accepted Answer

Line graphs are the best graphic organizer to demonstrate a relationship between two factors over a period of time, such as the effect of foreign aid on the child mortality rate of an impoverished nation. Histograms are best suited for displaying the distribution of probability. Pie charts are best for displaying how a whole unit is divided into parts. Bar graphs are best for displaying discrete information in a comparative manner.

Question 12

In a graph, the horizontal line going from left-to-right in usually which axis?

Accepted Answer

The horizontal line going from left-to-right in a graph is generally the X-axis. It is the "bottom" line of the graph and it is divided into segments or categories to demonstrate some of the data that are the subject of the graph.

Question 13

What is the mean for the following expenditures? $79.84, $278.99, $342.16, $466.25, $111.39, $502.47, $98.12

Accepted Answer

The mean for the data set above is $268.46. The median or middle number when the numbers are in ascending order ($79.84, $98.12, $111.39, $278.99, $342.16, $466.25, $502.47) is $278.99.

Question 14

What is the outlier in the following set: 11, 22, 33, 44, 55, 112, 23, 34 and 45?

Accepted Answer

The outlier is 112. An outlier is any number that is widely divergent from the rest of a data set, and it can be deduced logically, in many cases. It can be found arithmetically as well. An outlier is usually any number that is more than two standard deviations from the mean. The mean of the number set is about 42 (42.11). The standard deviation for the set is about 29.5. 42 + 29.5 + 29.5 = 101; therefore, any number greater than 101 is an outlier in this set. 101 < 112, therefore 112 is an outlier.

Question 15

People who score in the 95th percentile on an exam:

Accepted Answer

A test taker who scores in the 95th percentile scored as well or better than 95% of the people who took the exam. It is a comparative measure of success that has nothing to do with the number of questions on the exam, the number of correct responses given or the "score" of the exam in a 1 to 100 grading scheme. Early education exams are typically evaluated solely on this measure. Secondary school, higher education and professional exams vary in their emphasis on this method, but most report comparative percentile scores as a frame of reference.

Question 16

On a trip to the Netherlands you spend €275 per night in a hotel, €37.58 per day on meals and €50 per day on transportation. If you were there for four days and three nights, and the exchange rate from U.S. dollars to euros was $1.00 : €0.7515, about how much did you spend altogether, in U.S. dollars?

Accepted Answer

An expense of €1175, at an exchange rate of $1.00 : €0.7515, would total $1564. The total expenses were (€275 x 3) + (€37.58 x 4) + (€50 x 4), with the final sum being €1175.32. If the exchange rate was $1.00 : €0.7515, then €1175.32 is 75.15% of the total expense in U.S. dollars. Cross-multiply €1175.32 to find the dollar value of the expense. (€1175.32 x 100) ÷ 75.15 = $1563.97.

Question 17

The test scores for eight students are 97, 94, 98, 97, 89, 92, 68 and 96. What would the seventh score be considered?

Accepted Answer

A piece of data that is atypical or significantly different from the rest of its data set is called an outlier. While true outliers are often easy to spot with critical thinking skills alone, there is also a mathematical precept for assessing these anomalies. Generally, a number that is two or more standard deviations from the mean is considered an outlier. In some cases, outliers can skew data significantly, which is why identifying them is critical. Occasionally, an outlier can be removed justifiably from a data set to improve the data's reliability.

Question 18

What is the median for the numbers 89, 87, 94, 82, 89, 91, 95, 88, 90, 87, 92 and 93?

Accepted Answer

The median of the number set above is 89.5. The median is the number that falls in the middle of the set when the numbers are ordered by numeric value (least to greatest). The set above should be ordered as follows: 82, 87, 87, 88, 89, 89, 90, 91, 92, 93, 94, 95. When there is an even number of entrants in the set, the middle two numbers should be averaged together to find the median. This sequence has 12 numbers and the middle two are 89 and 90, which equal 89.5 when averaged.

Question 19

What is the mode for the numbers 34, 62, 58, 49, 37, 85, 22, 44, 37 and 52?

Accepted Answer

The mode for the number set above is 37. It is the number that occurs most frequently in a number set. 37 occurs twice, while all of the other numbers occur once. The order of the numbers is not relevant nor is the number of entrants in the set.

Question 20

What is the median for the following set of numbers? 15, 62, 47, 33, 89, 4, 76, 40, 54

Accepted Answer

The median or the middle number when the numbers are in ascending order (4, 15, 33, 40, 47, 54, 62, 76, 89) for the number set above is 47. The mean is about 46.7. There is no mode because each number occurs only one time in the set.

Quiz 23: Mathematics