Stats Quiz Questions

You measure weight, age and marital status. How many variables and what types did you measure? Be specific.

2 Quantitative Variables: weight and age. 1 Qualitative Variable: marital status.

The height of American men aged 18 to 24 are approximately normally distributed with a mean of 68 in and a standard deviation of 2.5. About what percentage of the men are over 70.5 in?

70.5 is one standard deviation above the mean. Since 68% are within one standard deviation, the remaining 32% are evenly divided into the regions above and below that interval.

What percentile is Q3?

75%

The height of American men aged 18 to 24 are approximately normally distributed with a mean of 68 in and a standard deviation of 2.5. Only about 5% of young men have Heights outside what range?

95% of the ages should be within two standard deviations of the mean which is the interval 68 - 5 to 68 + 5 or 63 to 73. Thus 5% are outside the interval6

Which of the following properties is true for all normal density curves? I. They are symmetric II. The curve reaches its peak at the mean. III. 95% of the area under the curve is within one standard deviation of the mean.

All normal curves are symmetric and peek at the main but 95% of the area is within two standard deviations of the mean not one.

Create a stemplot for the following data as it relates to commute times (in minutes) collected from a random sample: 5, 10, 10, 10, 10, 12, 15, 20, 20, 25, 30, 30, 40, 40, 60.

Create a vertical line with numbers 0 through 9 on the left side of the line (these represent the first digit of each data value), and list the 2nd digit of each data value on the right side of the line next to it's 1st digit.

Fire Department in a rural County reports that its response time to fires is approximately normally distributed with a mean of 22 minutes and a standard deviation of 11.9. Approximately What proportion of their response times is over 30 minutes?

First step is to calculate the Z score for the data point of 30. 30 - the mean of 22 then divided by the standard deviation 11.9 = .67. This equates with the 75th percentile of a standard normal curve so about 25% of the times are above that value

Create a boxplot given the number of home runs Hank Aaron hit in each of 23 seasons: 13, 27, 26, 44, 30, 39, 40, 34, 45, 44, 24, 32, 44, 39, 29, 44, 38, 47, 34, 40, 20, 12, 10

First you need to put the data in order and find the 5 number summary, then create a number line for the range of your data and draw the box and whiskers, noting each value of the 5 number summary (be careful to note, but not inlcude outliers in your whiskers).

If a distribution is skewed right, which is greater, mean of median?

Mean, because more of the data is made up of higher values than the center.

What is tthe best center for a skweed distribution?

Median

If a distribution is skewed left, which is greater, mean or median?

Median, because more of the data is made up of lower values than the center.

The area under the standard Normal curve corresponding to -0.3 < z < 1.5 is?

Percentile of Z = 1.6 - percentile z = -.3 is .9452 - .3821 = .5631

What is the Outlier Formula to check to outliers?

Q1 - (1.5xIQR) and Q3 + (1.5xIQR)

Calculate the IQR, and explain what it means in context, for the following data as it relates to commute times (in minutes) collected from a random sample: 5, 10, 10, 10, 10, 12, 15, 20, 20, 25, 30, 30, 40, 40, 60.

Q3 - Q1: 30 - 10 = 20; this means that 50% of the commute times fall within a range of 20 minutes of each other

What is the difference between range and IQR?

Range is the difference between the max and min values (Max - Min), and IQR is the difference between Q3 and Q1 (Q3-Q1).

The local post office weighs outgoing mail and finds that the weight of first class letters is approximately Normally distributed with a mean of .69 ounces and a standard deviation of .16 First class letters weighing more than 1 oz require additional postage. What proportion of first class letter at this post office require additional postage?

The Z score for -1 Oz is -.34. This has a proportion of 1 - .9473= .0262 letters above it requiring additional postage

What is the total area under any density curve?

The area under any density curve is equal to 1

The standard deviation of a quiz was 2. What does this tell you?

The average deviation from the mean is 2 points.

The distribution of the time it takes for different people to solve a certain crossword puzzle is strongly skewed to the right, with a mean of 30 minutes and a standard deviation of 15 minutes. The distribution of Z scores for those times are?

The distribution for the Z scores will also be skewed to the right, but with a mean of 0 and a standard deviation of 1

How do you find the IQR of a distribution from a cumulative relative frequency graph?

To find Q1 you look for the 25% on the left margin and trace over to the line on the graph, then trace down to find the corresponding lengths. To find Q3 you look for the 75% on the left margin and trace over to the line on the graph, then trace down to find the corresponding lengths. Finally take the difference between Q3 and Q1 to find the IQR.

Are their any outliers for the following data and if so, what are they? 16, 10, 20, 17, 28, 12, 23, 17, 17, 10, 16, 9, 15, 9

You first have to put the data in numeric order to calculate the IQR, the min and the max, then you can use the 1.5xIQR to determine if and what any outliers are. 9, 9, 10, 10, 12, 15, 16, 16, 17, 17, 17, 20, 23, 28 Median = (16 + 16)/2 = 16 Q1 = 10 Q2 = 17 IQR = 17-10=7 1.5xIQR = 1.5(7)=10.5 Outliers would be any number below Q1-(1.5xIQR) and any number above Q3+(1.5xIQR) Lower than 10-10.5 = -.5 or higher than 17+10.5=27.5 Therefore 28 is an outlier.

How do you find the area under a density curve?

You have to find the proportion of the the overall curve. (Note: a density curve doesn't have to look like a "curve". It can be made up of a straight horizontal or diagnal line.) Regardles of the shape, find the total area and the proportion of your shape, then multiply the proportion to the total area.

Provided are the foot lengths (in cm) for a random sample of seven 14-year olds in Hanford. 25, 22, 20, 25, 24, 24, 28. Calculate the Standard Deviation for the provided data and explain it in context.

You must first find the mean, then calculate the distance from the mean for each data point, next square each distance and add them all up, next devide the sum by number of data points minus 1, and finally find the square root of your number. The standard deviation is approximately 2.52 cm and this means that the average distance each foot length is from the mean is 2.52 cm.

The local post office weighs outgoing mail and finds that the weight of first class letters is approximately Normally distributed with a mean of .69 ounces and a standard deviation of .16 What is the 60th percentile of first class letter weights?

Z for the 60th percentile is .25 and 0.69 + 0.25(0.16)=.73 ounces

"normal" body temperature varies by time of day. A series of readings was taken of the body temperature of a subject. The mean reading was found to be 36.5 degrees celsius with a standard deviation of 0.3 degree celsius. If you wanted to convert the temperature to the Fahrenheit scale what would the new mean and standard deviation be? F=C(1.8)+32

mean is 97.7 degrees Fahrenheit, and standard deviation is 0.54 degrees Fahrenheit

Data from a fast food chain was collected about the fat content (in grams) of 15 of their sandwiches. The Data in order is: 9, 12, 19, 19, 19, 23, 24, 26, 26, 28, 29, 39, 39, 40, 42. What is the 5 number summary of this data?

min, Q1, M, Q3, max: 9, 19, 26, 39, 42

What is the 5 number summary?

min, Q1, median, Q3, max

What is the formula for standard deviation?

the squareroot of the variances