Central Tendency & Range
State the formulas for mean and range, and explain how to find the median and mode.
Mean = sum of all data points divided by number of data points
Range = Biggest data -smallest data
Median: Organize the data from smallest to largest, then cross off values starting from the outsides until you get the central most value.
Mode: Most repeated value
State the formula for weighted mean.
Weighted mean = sum of all data points multiplied by their weights, and then divided by the sum of the weights
State the formulas for IQR and the lower and upper fences.
IQR: 3rd quartile - 1st quartile
Lower Limit: 1st quartile - 1.5(IQR)
Upper Limit: 3rd Quartile + 1.5(IQR)
State the formulas for population variance and sample standard deviation.
Population Variance = the sum of squares divided by the number of data points
Sample Standard Deviation = the square root of the sum of squares divided by the number of data points subtracted by one
Name the five-number summary.
Min, 1st Quartile, Median, 3rd Quartile, Max
Find the mean of 4, 6, 8, 10, 12.
Scores of 80 and 90 have weights 2 and 3. Find the weighted mean.
Weighted mean = 86
If 1st quartile = 8 and 3rd quartile = 20, find the IQR.
IQR = 12
Find the population and sample variance of 2, 4, 6.
Population Variance = 2.667
Sample Variance = 4
I did a survey of how many miles it takes teaches to get to work. If my five number summary is 12, 16, 18.5, 21, 25; draw a box and whisker plot to match.
Draw on whiteboard, all parts should be accurate. No credit for incorrect parts.
For 14, 7, 16, 9, 11, 4, 9, find the mean, median, mode, and range.
Mean = 10
Median = 9
Mode = 9
Range = 12
A grade consists of 82 weighted at 20%, 90 at 30%, and 76 at 50%. Find the weighted mean.
Weighted Mean = 81.4
If 1st quartile = 8 and 3rd quartile = 20, is 40 an outlier? How do you know (prove algebraically)?
Yes, because the upper fence is 38 and 40 is greater than 38.
For the data 2, 4, 6, my standard deviation was 2.Was this data based off of a sample or a population?
Sample
A box plot has 1st quartile = 20, median = 28, and the IQR is 18. Is 72 an outlier? How do you know (show algebraically)?
Yes, 3rd quartile is 38 and so, the upper fence is 65. 72 is greater than 65, and thus an outlier.
Six quiz scores have a mean of 80. Five scores are 68, 74, 79, 83, and 91. Find the missing score and the median of all six scores.
Missing score = 85
Median = 81
A final grade uses 82 at 25%, 90 at 35%, and x at 40%. The weighted mean is 88. Find x.
x = 90
Tom did a study to see how many minutes it takes people to drink a starbucks venti iced shaken espresso: 3, 5, 6, 8, 9, 11, 13, 15, 18, 20
Find 1st quartile, 3rd quartile, and what percentage of people take 15 minutes or less to drink a starbucks venti iced shaken espresso.
1st Quartile = 6
3rd Quartile = 15
Percentage: 75% of people
Population A is 4, 6, 8. Population B is 2, 6, 10. Find their standard deviations. Which is more variable? How do you know?
Population A's standard deviation = 1.633
Population B's standard deviation =3.266
Population B is more variable because it's standard deviation is higher.
Where would the whiskers start and end on a box plot of this data?
Lower whisker: 1
Upper whisker: 70
Company A: 10, 12, 14, 16, 18
Company B: 10, 12, 14, 16, 38.
Find each mean and median. For each Company, what would the better measurement of center be to use to describe the "average" and why?
Company A mean: 14
Company A median: 14
Company B mean: 18
Company B median: 14
Use mean for Company A because no outliers affecting mean and use median for Company B because there is an outlier affecting the mean.
(Plus 100 points if they algebraically show that 38 is an outlier)
Three scores are 80, 90, and 100. Class A weights them 20%, 30%, 50%; Class B weights them 50%, 30%, 20%. Which class would you have a higher average in given the scores above? How do you know?
Class A because the weighted mean is higher.
A math class's test scores first semester are: 70, 34, 85, 90, 80, 92, 100, 67, 89. In the second semester: 88, 90, 100, 65, 78, 97, 83, 77, 23.
Which semester did the middle 50% of the class do better in? How do you know (show work)?
Second semester. Even though the median for second semester is lower, the middle 50% of the class data lies at higher values than the first semester.
A group of zoologists were performing a study on 10 apes to measure their IQ. They found within their sample study that the mean IQ was 80 and their sum of squares was 630. Would the IQ scores of 67 and 76 be considered "relatively close to the mean?" How do you know (show work)?
67 would not be considered close to the mean because it more than one standard deviation away from the mean. 76 is considered close to the mean because it falls within one standard deviation away from the mean.
Given this 5 number summary about quiz scores: 23, 65, 72, 89, 105
What would the distribution look like assuming the lowest data point I could have is zero and the highest data point could be 110? Additionally, what scores are considered in the top 25%?
Skewed left, 89 to 110.