Calculations
Find the mean of the data set: 4, 6, 10, 20.
Sum = 40
Mean = 10
Find the median of: 3, 5, 7, 9, 11.
What is 7?
Find the range of: 12, 15, 18, 21.
What is 9?
Which graph is best for showing the shape of a quantitative data set: bar graph or histogram?
What is a histogram?
A distribution has a long tail to the left. Describe its shape.
What is left-skewed?
The mean of five numbers is 12. Four of the numbers are 8, 10, 14, and 16. Find the fifth number.
Total = 5(12) = 60
Known sum = 48
Fifth number = 12
Find the median of: 4, 6, 8, 10, 12, 14.
What is 9?
Given Q1 = 8 and Q3 = 20, find the IQR.
What is 12?
A boxplot shows the median closer to Q1 than Q3. What does this suggest about the distribution?
What is right-skewed?
If the mean is greater than the median, what is the likely shape?
What is right-skewed?
A data set has a mean of 50. One value of 30 is replaced with 90. What is the new mean if there are 10 data values total?
Change in total = +60
New total increases by 60
Increase in mean = 60 ÷ 10 = 6
New mean = 56
A data set has 7 values with a median of 12. Six of the values are
5, 7, 10, 12, 18, and 20.
Find all possible values of the seventh data point.
What are all values ≥ 12?
The standard deviation of a data set is 4. Explain what this means in context.
What is that data values typically vary about 4 units from the mean?
Two data sets have the same mean but different standard deviations. Which has more variability?
What is the data set with the larger standard deviation?
How does the value 30 affect the mean in the first question of this row?
What is it pulls the mean upward?
The mean of a data set is 40. If each data value is doubled and then 5 is subtracted from each result, what is the new mean?
New mean = (40 × 2) − 5
New mean = 75
For the data set 1, 2, 3, 4, 100, which is more appropriate: mean or median? Explain briefly.
What is the median, because the outlier strongly affects the mean?
Given Q1 = 10 and Q3 = 22, identify any outliers using the 1.5×IQR rule for the value 40.
What is 40 is an outlier?
Why is a boxplot preferred over a histogram when comparing two groups?
What is it clearly shows medians, quartiles, and spread?
If a distribution is symmetric, how do the mean and median compare?
What is they are approximately equal?
The mean of 8 numbers is 20. After removing one number, the mean becomes 18. What was the removed number?
Original total = 8(20) = 160
New total = 7(18) = 126
Removed number = 34
A right-skewed distribution has a median of 40. Predict whether the mean is less than, equal to, or greater than 40.
What is greater than 40?
If all data values are multiplied by 3, how does the standard deviation change?
What is it becomes 3 times as large?
A histogram shows two clear peaks. Describe this distribution
What is bimodal?
Data set: 5, 7, 9, 10, 11, 12, 50. Determine if 50 is an outlier using the 1.5×IQR rule.
Q1 = 7, Q3 = 12 → IQR = 5
Upper = 12 + 1.5(5) = 19.5
50 is an outlier