stats 3 & 4
Lower Limit Upper Limit Frequency 30 50 5 51 71 14 72 92 5 93 113 8 114 134 9 determine the class width
51-30=21
Lower Limit Upper Limit Frequency 30 50 5 51 71 14 72 92 5 93 113 8 114 134 9 choose the interval that contains 59.9
51-71
Lower Limit Upper Limit Frequency 0.27 0.38 12 0.39 0.50 6 0.51 0.62 9 0.63 0.74 14 0.75 0.86 8 whats the midpoint for the fourth class
0.685
Bimodal
00 and 11 would be repeated three times and there would be two modes. When this occurs, the data is said to be bimodal
Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.62 and a standard deviation of 0.40 Using the empirical rule, what percentage of the students have grade point averages that are between 1.42 and 3.82?
1.42-2.62/0.4=-3 3.82-2.62/0.4=3 according to the empirical rule 3 deviation is 99.7%
Lower Limit Upper Limit Frequency 19 25 11 26 32 7 33 39 12 40 46 7 47 53 11 Determine the relative frequency for the third class as a simplified fraction.
12/48 simplified to 1/4
Calculate the value of the range 14 -12 -10 14 -10 14 -10
14+-12=26 biggest number minus smallest number
21-B Book Street Books sells about 47004700 books each month. The pie chart displays the most popular book categories, by percentage, each month. Find the number of reference books sold each month. Round your answer to the nearest integer. reference book 34%
1598
If the standard deviation of a data set is zero, then all entries in the data must equal zero.
false is SD is zero then all of the data values are equal to the mean
Calculate the value of the sample variance. Round your answer to one decimal place. 14 -12 -10 14 -10 14 -10
find the mean of the number given = 0 then find the deviations of each number 14-0(mean)=14 then square those and add them for the total take the total/ n-1 so in this case 1032/6 = 172
Masterful Pocketwatches: Standard deviation of stock prices =$9.63 Handy Prosthetics: Standard deviation of stock prices =$1.25 Based on the data and assuming these trends continue, which company would give Clara a stable long-term investment?
handy prothestics has smalled SD and less variability
Pareto Chart
is a bar graph whose bars are arranged in decreasing order of frequency.
stem and leaf pot
is a graph representing quantitative data that separates each data value into two parts: the stem and the leaf
Variance
standard deviation squared
deviation from the mean
the amount that a score in a sample differs from the mean of the sample; also called a deviation
mean absolute deviation
the average distance between each data value and the mean
range
the difference between the highest and lowest scores in a distribution
Mode
the most frequently occurring score(s) in a distribution
z-score
the number of standard deviations a particular score is from the mean
Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below. Tobias got a score of 84.5; this version has a mean of 66.9 and a standard deviation of 11. Kiersten got a score of 281.8; this version has a mean of 261 and a standard deviation of 26 Pierce got a score of 7.69; this version has a mean of 7.2 and a standard deviation of 0.7 If the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job?
tobias
A graph should have a title describing the topic being presented
true
Graphs can be more attractive and interesting to viewers.
true
It is possible to have a standard deviation of 120,000 for some data set.
true any value greater or equal to zero
A/An measures the number of standard deviations that a particular value is away from the mean.
z score
Chebyshev's Theorem
A theorem that can be used to make statements about the proportion of data values that must be within a specified number of standard deviations of the mean. 1-1/k^2 Chebyshev's Theorem, at least 88.9% of data values lie within how many standard deviations of the mean K=3: At least 1−1/3 squared =89≈88.9% of the data lies within three standard deviations of the mean. K2= 75%
class width formula
(largest data value - smallest data value)/number of classes
a pie chart
(or circle graph) is a graph used to display categorical data as slices of a circle. The size of each slice is proportional to the amount or frequency in each category. The proportion of the total that each slice represents is often displayed as a percentage on the chart. These percentages should total 100%
Suppose that prices of a gallon of milk at various stores in one town have a mean of $3.60with a standard deviation of $0.09. Using Chebyshev's Theorem, state the range in which at least 88.9% of the data will reside. Please do not round your answers.
3.87 and 3.33 mean + - standard deviation times 3
empirical rule
About 68% of the data should lie within 1 standard deviation of the mean. About 95% of the data should lie within 2 standard deviations of the mean. About 99.7% of the data should lie within 3 standard deviations of the mean. applies only to bell-shaped distributions
The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 35hours and the median is 31.2 hours. Twenty-four of the families in the sample turned on the television for 20 hours or less for the week. The 14th percentile of the data is 20 hours.
Based on the given information, determine if the following statement is true or false. The 55th percentile is less than 30 hours **FALSE Approximately how many families are in the sample? Round your answer to the nearest integer. **171 14/100 (n)=24 24(100)=2400 /14=171 Based on the given information, determine if the following statement is true or false. Approximately 86 families turned on their televisions for less than 35 hours. ***FALSE What is the value of the 50th percentile? **31.2 Based on the given information, determine if the following statement is true or false. The first quartile is greater than or equal to 2020 hours. TRUE***
Multimodal
Describes a graph of quantitative data with more than two clear peaks.
Empirical Rule
The rules gives the approximate % of observations w/in 1 standard deviation (68%), 2 standard deviations (95%) and 3 standard deviations (99.7%) of the mean when the histogram is well approx. by a normal curve
standard deviation
The standard deviation is always nonnegative. It is zero only if all the data values are exactly the same. The standard deviation can increase dramatically if there are one or more outliers in the data. The standard deviation is expressed in the same units as the original data values.
A/An is calculated by dividing the difference between a data value and the mean by the standard deviation.
Z score
standard deviation
a computed measure of how much scores vary around the mean score is the square root of the variance.
No mode
no data value is repeated
In order to help decide when and where to advertise, an electronics repair company decided to pull invoices and tally what types of products were repaired. There were twenty-five products repaired that month. What is the level of measurement for the data? Are the data qualitative or quantitative?
nominal qualitative
A legend is optional if a data table accompanies the graph.
false
Graphs are relatively dull in comparison to the raw data.
false
The population standard deviation and sample standard deviation are the same value for the same set of data.
false
The population variance and sample variance are the same value for the same set of data
false
It is possible to have a standard deviation of −1−1 for some data set.
false cannot be negative becasue square root cant be negative
Histogram
is a graphical representation of a frequency or relative frequency distribution. The horizontal scale corresponds to classes of quantitative data values and the vertical scale corresponds to the frequency or relative frequency of each class.
trimmed mean
is a modification of the arithmetical mean which ignores an equal percentage of the highest and lowest data values in calculating the mean.
skewed distribution
is a nonsymmetric (or asymmetric) distribution that extends more to one side than the other. The distribution is said to be skewed to the right (or positively skewed) if the tail to the right of the peak of the distribution is longer than the tail to the left of the peak. The distribution is said to be skewed to the left (or negatively skewed) if the tail to the left of the peak of the distribution is longer than the tail to the right of the peak.
the bar chart
is a simple graphical display in which the length of each bar corresponds to the number of observations in a category.
frequency distribution
is a summary technique that organizes data into classes and provides in tabular form a list of the classes along with the number of observations in each class
pth percentile
is a value, say x, such that approximately P percent of the data is less than or equal to x and approximately (100−P)100−P percent of the data is greater than or equal to X.
moving average
is obtained by adding consecutive observations for a number of periods and dividing the result by the number of periods included in the average
class width
is the difference between the lower limits or upper limits of two consecutive classes of a frequency distribution.
cumulative relative frequency
is the proportion of observations in a particular class and all preceding classes.
cumulative frequency
is the sum of the frequency of a particular class and all preceding classes.
proportion
measures the fraction of a group that possesses some characteristic X=X= the number of observations that possess the characteristic, N=N= the number of observations in the population, and n=n= the number of observations in the sample, then p=XN=p=XN= the population proportion, and pˆ=Xn=p^=Xn= the sample proportion.
For the following type of data set, would you be more interested in looking at the mean, median, or mode? The price of cars on a car lot
median
median
of a set of observations is the data value in the middle of an ordered array. The same number of data values is on either side of the median value.
relative frequency
of any class is the number of observations in the class divided by the total number of observations.
A reviewer decides to interview viewers to see how they would rate a particular movie. The following table lists the responses from twenty-five viewers. What is the level of measurement for the data? Are the data qualitative or quantitative?
ordinal qualitative
A reviewer decides to interview guests to see how they would rate a particular hotel. The following table lists the responses from twenty-five guests. What is the level of measurement for the data? Are the data qualitative or quantitative?0 5 diamonds-7 4 diamonds-6 3 diamonds-5 2 diamonds-3 1 diamond-4
ordinal, qualitative
Clara is looking into investing a portion of her recent bonus into the stock market. While researching different companies, she discovers the following standard deviations of one year of daily stock closing prices. Perfect Plungers Plus: Standard deviation of stock prices =$1.22 Eye Remember Enterprises: Standard deviation of stock prices =$9.73 Based on the data and assuming these trends continue, which company would give Clara a stable long-term investment?
perfect plungers plus A smaller standard deviation indicates that the data values are closer together, while a larger standard deviation indicates that the data values are more spread out. A smaller standard deviation also indicates less variability in the data set.
For the following type of data set, would you be more interested in looking at the mean, median, or mode? The size of popcorn containers sold at a local movie theater
popcorn sizes are mode and qualitative data
A manufacturer makes bags of popcorn and bags of potato chips. The average weight of a bag of popcorn is supposed to be 3.03 ounces with an allowable deviation of 0.03 ounces. The average weight of a bag of potato chips is supposed to be 5.06 ounces with an allowable deviation of 0.04 ounces. A factory worker randomly selects a bag of popcorn from the assembly line and it has a weight of 3.08 ounces. Then the worker randomly selects a bag of potato chips from the assembly line and it has a weight of 5.02 ounces. Which description closely matches the findings on the assembly line?
potaot bag asembly line is closer to the standard * the closer the z-score is to the standard, the closer the specifications are met on the assembly line,
Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data. 16,16,16,16,16,16,16,16,16,16
range 0 P variance 0 P standard dev 0
Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.11 and a standard deviation of 1.46. Using the empirical rule, what percentage of American women have shoe sizes that are no more than 5.19? Please do not round your answer.
we determined that we need to subtract from the 50% of the data that is below the mean in order to calculate the percentage of data values in the region shaded on the graph to the right. The empirical rule says that approximately 95% of data lies within 2 standard deviations of the mean. Because of the symmetry of the distribution, half of this 95% is above the mean and half is below. Finally, use this information to calculate what percentage of American women have shoe sizes that are no more than 5.19 2.5%
Consider the bar graph, which shows the numbers and percentages of bachelor's degrees in engineering and engineering technologies earned by women at U.S. schools. Determine the ratio of the number of men to the number of women earning bachelor's degrees in engineering and engineering technologies in 1970-71. Please enter your answer as decimal number, rounded to two decimal places.
woman 0.8% men 99.2% 99.2/0.8=124
