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Comparing Two Distributions
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Comparing Two Distributions
Compare distributions by looking at their centers, spreads, shapes, and overlap. Show calculations where requested. For quartiles, divide each ordered data set into lower and upper halves; if a half has an even number of values, average its two middle values.
Reading measures of center and spread
1.Which measure of center is usually affected most by a single extremely high value?
- Mean
- Median
- Mode
- Lower quartile
2.A box plot has Q1 = 18 and Q3 = 30. What does the distance from Q1 to Q3 describe?
- The middle half of the data
- The full distance from the minimum to the maximum
- The average of all the data values
- The most common data value
3.Select every feature that can help you compare two distributions.
- Their medians or means
- Their ranges or interquartile ranges
- Their shapes, such as symmetry or skew
- How much their values overlap
- Only the largest value in each set
4.Two data sets have nearly equal medians, but Set P has a much larger IQR than Set Q. What does this suggest?
- The middle half of Set P is more spread out.
- Set P must have a larger mean.
- The two sets cannot contain any of the same values.
- Set Q must be skewed.
5.Match each statistical term with its description.
- Median
- Range
- Interquartile range
- Mean
- Outlier
- Q3 minus Q1
- Sum of the values divided by their count
- A value unusually far from the rest
- The middle value in ordered data
- Maximum minus minimum
Analyze two distributions
The table shows the number of minutes two groups of students spent reading on one evening. The values in each row are already in order.
Group Cedar
Group Maple
24, 28, 30, 32, 34, 36, 38, 42
18, 22, 26, 30, 34, 38, 42, 46
6.Find the mean and median reading time for Group Cedar. Show your calculations.
7.Find the mean and median reading time for Group Maple. Show your calculations.
8.For Group Cedar, calculate the range, Q1, Q3, and IQR.
9.For Group Maple, calculate the range, Q1, Q3, and IQR.
10.Use the data in the table to make side-by-side box plots for Group Cedar and Group Maple on the number line. Label each plot with its minimum, Q1, median, Q3, and maximum.
11.Compare the reading-time distributions for the two groups. Discuss center, spread, and overlap, then state one reasonable informal inference.
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