Stats Test #1

(3.3) sample mean/sample standard deviation (formula)

i=frequency. n= frequency. You multiply the midpoint by the f to find each (xf). Divide the sum of the xf by the sum of the frequencies. * x=midpoint- sample mean just calculated. * plug in standard deviation formula

(3.4/ 3.5) How do you find outliers?

If the number they provide is larger than the upper fence or lower than the lower fence then it is an outlier. (usually only an upper fence outlier)

(2.2) The ________ class limit is the smallest value within the class and the __________ class limit is the largest within the class

lower, upper

(3.2) The standard deviation is used in conjunction with the _______ to numerically describe distributions that are bell shaped. The ______ measures the center of the distribution, while the standard deviation measures the _______ of the distribution.

mean, mean, spread

(4.1/ 4.2) What does positive and negative association mean?

pos- one variable increases, so does the other neg- one variable increases, the other decreases

(4.1/ 4.2) What is r?

r is the relationship between the two variables. If its a -1 it's a perfect negative association, if it's 1 then its a perfect positive association.

(2.3) How can bar graphs be misleading?

If the vertical axis starts at a larger number than 0. This indicates frequency changes faster than they actually did. In the correct graph it may seem like the frequencies remain about the same.

(3.4/ 3.5) When is the interquartile range a preferred measure of dispersion?

It's preferred when the data is skewed or has outliers. An advantage of the standard deviation is that it uses all the observations in it's computation.

(3.3) Empirical Rule: 95% of the data is between what two values?

Know your .15, 2.35, 13.5, 34, 34, 13.5, 2.35, .15 values to see what percentage data lies between.

(3.1) What measure of central tendency best describes the "center" of distribution?

Median

(4.1/ 4.2) If r= 0, what does this mean?

No linear relationship exists between the variables.

(3.1) How do you calculate population mean?

Other than looking on the calulator... - you find it like the regular mean. Add and divide by the number or numbers. Use the symbol for population.

(3.1) How do I calculate sample mean?

Other than looking on the calulator... - you find it like the regular mean. Add and divide by the number or numbers. Use the symbol for sample.

(3.2) How do I find the sample/ population variance?

Plug the set of numbers in to "data", 2nd data, enter, enter, enter, enter. Number 3 and 4 will show the sample/population standard deviation. Square that number to find the sample variance.

(3.4/ 3.5) How do you find the lower fence?

Q1- 1.5(IQR)

(3.4/ 3.5) How do you find the upper fence?

Q3+ 1.5(IQR)

(3.2) What type of histogram depicts a higher standard deviation, a bell or uniform shape?

The bell histogram depicts a higher standard deviation because the distribution has more dispersion.

(3.4/ 3.5) Which of the accompanying boxplots likely has the data with the larger standard deviation?

The boxplot with the largest length will have a larger standard deviation.

(4.1/ 4.2) What is a residual?

The difference between an observed value of hte response variable y and the predicted value of y. If it's positive then the observed is greater than the predicted.

(3.1) Why is the median resistant, but the mean is not?

The mean is not resistant because when data are skewed, there are extreme values in the tail, which tend to pull the mean in the direction of the tail. The median is resistant because the median of a variable is the value that lies in the middle of the data when arranged in ascending order and does not depend on the extreme values of the data.

(3.1) A histogram of a set of data indicates that the distribution of the data is skewed right. Which measure of central tendency will likely be larger, the mean or the median?

The mean will likely be larger because the extreme values in the right tail tend to pull the mean in the direction of the tail.

(3.1) When the graph is skewed left, which value is larger, median or mean (sample or population)?

The median is larger than the mean.

(3.2) What makes the range less desirable than the standard deviation as a measure of dispersion.?

The range does not use all the observation.

(3.4/ 3.5) What is the 5-number summary?

The smallest number of the data, the Q1, half or Q2, Q3, and the largest number in the data.

(3.2) Why is the standard deviation of class heights as a whole more than the class being split up by gender?

The standard deviation of the entire class is more than the standard deviation of the males and females considered separately because the distribution of the entire class has more dispersion.

(3.2) What is meant by the phrase "degrees of freedom" as it pertains to the computation of the sample standard deviation?

There are n-1 degrees of freedom in the computation of s because an unknown parameter is estimated by the sample mean. For each parameter estimated, 1 degree of freedom is lost.

(3.2) How do you find what percentage of data is one, two, three and four standard deviations away from a bell-shaped graph (empirical rule)?

They will give you a mean on a bell-shaped graph only. You add and subtract the mean by the given standard deviation (SD). Between each direction one SD away will be 34%. Two SD away is 34+ (13.5%). Three SD away is all those plus 2.35% and the fourth SD is .15%. in order going one direction: 34%, 13.5%, 2.35%, .15%

(3.4/ 3.5) What should you keep in mind when calculating z-score?

- As the magnitude of the​ z-score increases, the relative difference of the observation from the mean increases. -smaller score is less the larger score is more -if the lower z-score is more desirable like fastest time then the better z-score is lower

(3.3) Attendance is 5%, quizzes are 10%, exams are 60% and the final exam is 25%. If someone had 100% attendance, 89% on quizes, 82% for exams, and 85% on the final, what's the student's average?

- change all the percents to decimals - multiply the corresponding grade -add up all the values -divide by 100

(4.1/ 4.2) If they give you the least-squares regression equation and ask for median income, slope and if it makes sense to interpret the y-intercept.

- find the median by plugging in all stats to the provided equation - slope is the (a)x in the provided equation -it does not make sense to interpret the y-intercept because an x-value of 0 is outside of hte scope of the model.

(2.3) How can intervals be misleading?

- if not all the intervals are the same size EX) 1-10, 11-55 - if the interval includes the same slot as the next interval. Ex) 9am -10am, 10am-11am

(3.3) What mistakes did you miss on the quiz you should look out for?

- put commas in between your stem-and-leaf plot numbers - watch out for when they say median and range. Read carefully, not the same thing. -when they say less than or greater you add both values together -make sure you match up sample mean/deviation or population mean/deviation -when you list what is least or most frequent they mean the x-axis not frequency.

(3.4/ 3.5) How do you find the length destroyed if they give you # of deviations from the mean, the mean length and the standard deviation?

-The standard deviation from the mean is going to be set up in an inequality as negative and another as positive. -Plug in the other numbers to the z-score formula and solve for both equations.

(2.2) How do I find relative frequency on a graph?

Add all the frequencies together (y-values) and divide each individual frequency by the new sum frequency you just found.

(2.2) How do you determine the class width by looking at a graph?

Along the X axis will be numbers in order. You see how far it jumps between columns. EX) 0, 10, 20, 30. This has a class width of 10.

(2.2) What are classes?

Are the categories by which data are grouped

(3.1) Why would you use median for the average price of a home in the US?

Because the data is skewed right.

(2.2) What type of graph would show scores of a standardized test?

Bell-shaped

(4.1/ 4.2) What does each point on the least-squares regression line represent?

Each point represents the predicted y-value at the corresponding x.

(3.1) What does it mean if a statistic is resistant?

Extreme values (very large or small) relative to the data do not affect its value substantially.

(2.2) Stem-and-leaf are particularly useful for large set of data

False

(4.1/ 4.2) T or F: correlation = causation

False

(3.2) Empirical Rule: How do you find the minimum percentage that lies within prices (provided) and (provided)?

First find out how many standard deviations away from the mean are the numbers they gave you. Mean- (provided), divide by the given standard deviation price. Plug that number in to Chebyshev's formula as K. That will give you the percentage.

(2.2) What is an disadvantage of using a stem-and-leaf plot instead of a histogram?

Histograms easily organize data of all sizes where stem-and-leaf plots do not.

(2.2) How are the data points organized in a class?

If the class width is 10 between each column you use 9 numbers to classify the data within the class. EX) 60-69, 70-79, 80-89

(3.2) True or False: Chebyshev's inequality applies to all distributions regardless of shape, but the empirical rule holds only for distributions that are bell shaped.

True, Chebyshev's inequality is less precise than the empirical rule, but will work for any distribution, while the empirical rule only works for bell-shaped distributions.

(2.2) How is cumulative frequency different than relative frequency?

With cumulative frequency you add the frequencies as you go up in class, down the table. EX) if the first clas had a frequency of 2, the next class4, and the next 5 your cululative would read: 2, 6, 11.

(4.1/ 4.2) How can you tell if there's a linear relation given the mean and critical value?

If the absolute value of the mean is greater than the highest critical value on the provided chart then there is a linear relation.

(2.2) What is an advantage of using a stem-and-leaf plot instead of a histogram?

Stem-and-leaf plots contain original data values where histograms do not.

(3.2) What's the difference between the Empirical Rule and Chebyshev's Theorem?

The Empirical Rule assumes the distribution is approximately symmetric and bell-shaped and Chebyshev's Theorem makes no assumptions.

(3.2) True or False: When comparing two populations, the larger the standard deviation, the more dispersion the distribution has, provided that the variable of interest from the two populations has the same unit of measure.

True, because the standard deviation describes how far, on average, each observation is from the typical value. A larger standard deviation means that observations are more distant from the typical value, and therefore, more dispersed.

(4.1/ 4.2) Does the least-squares regression always travel through the (x,y)

Yes!

(2.2) What do I set up the class sets? ___-___ ___-___ ___-___ ___-___ ___-___

You have to look at your data and figure out the highest and lowest numbers. Then you find the range between those two numbers and divide by the number of classes. If its a decimal, round up to the nearest whole (even if it's already a whole number). Your first value will be the lowest number so add on the range number you just got- add this going down VERTICALLY and fill in hte left side values.

(4.1/ 4.2) If they give you a percent and ask if it would make sense to predict the y-intercept.

You have to see if the number fits in the model applied equality. No, if its too less or too high because the provided x-value is outside of the scope of the model.

(3.1) If the mean score of the exam was 83 of 15 students and the mean of 14 is 87. What is the missing score on the 15th student?

You multiply 83(15) - 87(14)= 27 as the missing score.

(3.4/ 3.5) If they provide Standard deviation away from the mean, the mean and a random standard deviation for a selective student admission then what is the minimum score the applicant can have?

You solve for x in the equation when the "z" = SD away from the mean, the provided standard deviation and the mean the right side of the equation.

(3.1) If one of the first two numbers in an ordered set is missing and they give you the median, find the missing value.

You take one of the middle numbers provided, add by x and divide by two and set that equal to the provided median

(3.2) How do I calculate the percentage of data within the standard deviation of the mean using Chebyshev's Theorem?

You use this formula. K= number of Standard deviations away.

(2.2) How do I input the data for a back to back stem-and-leaf plot display?

You write the right side data just as you would but for the left you write it backwards. The further away from the median the larger your numbers will be. EX) 9, 8, 6, 3, 1, 0 [3] 1, 1, 1, 2, 3, 8, 9

(3.2) What does the sum of deviations about the mean always equal?

Zero

(3.3) When they give you class and frequency and they ask for population mean/ deviation.

-find the midpoint of all the classes; plug that in for L1. -plug the frequencies in for L2 -make sure FRQ: L2 -divide sum (Ex=)/(n=) to get the mean - standard deviation is (ox=)

(3.3) Mary earned a B-4hr credit math, D- 1hr credit gov., B-4hr credit physics, and D-2hr credit art. If A=4, B=3, C=2, D=1 and F=0, what's her GPA?

-find the total number of hours taken -change all the letter grades in to their corresponding credit number -multipy each hour and credit number; add them up to the other values -divide the sum you just found by the total number of hours taken

(3.3) To make soup all the ingredients costed: 4lbs- $2.29, 4lbs-$3.84, 5lbs- 3.56. How much per pound did it cost to make the soup?

-multiply the price by the pound -add up all the number of pounds -divide the sum of the cost by the total number of pounds.

(3.3) How do you find the sample mean/ standard deviation when you're given a graph?

Plug the x values on L1, plug the frequencies on L2. Press 1-Var Stats, make sure the data is on L1 and the FRQ: is on L2. Sx= sample standard deviation.

(2.2) How do I input data if the stem number is repeated?

Put the ones values on the leaf area where is it less than the stem value. The leaf value can go with the stem it's the same number EX) 5| 5, 6, 7, 9

(3.4/ 3.5) How do you solve for interquartile range?

Q3-Q1= 50% of the range

(2.2) Why shouldn't classes overlap when summarizing continuous data in a frequency or relative frequency distribution?

So that there is no confusion as to which class an observation belongs.

(2.2) The ___________________ is the difference between consecutive lower class limits.

class width