Measures of Center
Find the mean of this list: 2, 7, 4, 3, 2, 1, 1, 0, 2, 5, 3, 3, 4, 3, 2, 5, 4, 3.
Mean = 3
On the dot plot, how many students watched exactly 3 hours of TV?
8 students
What is the range of the TV-hours data? (Show how you found it.)
Range = 7
Donna scored 83, 89, 96, and 90 on four labs. What score must she get on a fifth lab to have an average of at least 90?
92
What is the median of the data set above?
Median = 3
Using the histogram intervals 0–1, 2–3, 4–5, 6–7 with frequencies 3, 9, 5, 1, how many students watched between 2 and 5 hours?
14 students
What is the interquartile range (IQR) for the TV-hours data if Q1 = 2 and Q3 = 4?
IQR = 2
Allyson has four test scores: 82, 77, 75, 84. The final counts as two test grades. What minimum final exam score will give her an overall average of 80?
81
What is the mode of the data set above? If there are multiple modes, explain how you would report them.
Mode = 3
Given the stem-and-leaf for test scores, what is the maximum value and how do you read 1 | 9 from the key?
Maximum = 94; 1 | 9 = 19
Identify any outliers in the TV-hours data using the 1.5·IQR rule. Show your calculation.
IQR = 2 → 1.5·IQR = 3; lower fence = Q1 − 3 = −1 (no lower outliers); upper fence = Q3 + 3 = 7 → 7 is on the fence
There are seven whole numbers with mean 28, median 29, mode 31, min 22, max 35, and the second number is six less than the median. Find the seven numbers.
22, 23, 25, 29, 31, 31, 35
The mean and median are both 3 for the TV-hours data. Give two different situations (one with an outlier, one without) and explain which measure (mean or median) you'd prefer in each situation.
Without outliers choose mean; with outliers choose median — explain using an extreme value that pulls the mean.
Explain how to construct a box-and-whisker plot from a sorted data list; list the five-number summary for the TV-hours data.
Five-number summary: Min 0, Q1 2, Median 3, Q3 4, Max 7
The dot plot shows clusters at 2–4 and a gap at 6. Explain what "cluster" and "gap" mean in a dot plot and why they matter.
Cluster = group of many points near each other; gap = region with few/no points — they show where data concentrates or is sparse.
Explain step-by-step how to use sample data to estimate the mean number of TV-hours for the whole 6th Grade Home Base class, and describe one reason your estimate might be off.
(Sample mean = mean of sample; estimate may be off due to non-representative sample or small sample size.)
A data set has five numbers with mean 14, median 12, mode 12, smallest number 6, and range 18. Find all five numbers.
6, 12, 12, 16, 24
Create a stem-and-leaf for the list: 48, 70, 60, 68, 27, 53, 38, 52, 72, 35, 52, 51, 63, 71, 67, 19, 73, 28, 61, 94, 67, 85, 54, 59, 61, 72, 68, 67, 57, 35. (Show stems and leaves and give the key.)
Show your work :-)
Compare two data sets: Set A has mean 30 and standard deviation 2; Set B has mean 32 and standard deviation 8. Which set shows more relative variability? Explain using the idea of spread and center.
Set B shows more relative variability because its SD is larger (8 vs 2); discuss comparing ratios or coefficient of variation if needed.
A teacher collects two samples of equal size from different classes. Sample 1 has mean 15 and IQR 2. Sample 2 has mean 18 and IQR 6. Use the measures of center and variability to argue whether the two classes have meaningfully different TV-watching habits. Be explicit about what "meaningfully different" means in your explanation.
(Use difference in centers relative to variability — e.g., means differ by 3 while IQRs differ by 4; discuss whether difference exceeds typical spread.)