HSS.ID.A.2Common CoreMathStatistics and ProbabilityGrades 9-12
HSS.ID.A.2: Comparing Center and Spread of Data Sets
In plain English: HSS.ID.A.2 is the Common Core statistics standard that asks students to compare the center and spread of two or more data sets using statistics that fit the shape of the data. Students use the mean and standard deviation for roughly symmetric data and the median and interquartile range for skewed data. It is usually taught in Algebra I.
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
Common Core State Standards for Mathematics · Domain: Interpreting Categorical and Quantitative Data (ID) · Cluster: Summarize, represent, and interpret data on a single count or measurement variable Also written as HSS-ID.A.2 or S-ID.2 · Official standard
Students compare two or more data sets by their center and their spread, and learn that the shape of a distribution decides which statistics to use. For roughly symmetric data without outliers, the mean and standard deviation give a complete, efficient summary. For skewed data, the median and interquartile range (IQR) are better, because they are resistant: a few values in a long tail barely move them.
Students compute all four statistics by hand on small data sets, then use technology for the standard deviation. The goal throughout is a comparison, not a single number: every calculation ends with a sentence that compares the groups' centers and spreads in the context of the data.
Learning Objectives
By the end of this lesson, students will be able to:
Identify whether a distribution is roughly symmetric or skewed from a dot plot, histogram or box plot
Compute the mean, median, interquartile range and standard deviation of a small data set
Choose the mean and standard deviation or the median and IQR based on the shape of the data
Compare the centers and spreads of two or more data sets using the same statistics for each group
Prior Knowledge Required
Students should already be comfortable with:
Computing the mean, median and IQR of a data set 6.SP.B.5
Comparing two populations with measures of center and variability 7.SP.B.4
Drawing dot plots, histograms and box plots HSS.ID.A.1
Show the points scored by two basketball players over their last five games.
Warm-Up Prompt
"Player X scored 11, 12, 12, 12, 13. Player Y scored 2, 5, 12, 17, 24. Both averaged 12 points. If you needed 12 points in the next game, whom would you play? What single number could capture the difference between them?"
Let students argue for a few minutes. They usually agree that X is more reliable, and some suggest the range (2 for X, 22 for Y). Tell them that the mean describes center only, and that today they learn two standard ways to measure spread, the interquartile range and the standard deviation, and how the shape of the data decides which center and spread to use.
Direct Instruction25 minutes
Part 1: Matching statistics to shape. Give students the decision rule, and justify it with the examples below:
Roughly symmetric, no outliers: report the mean for center and the standard deviation for spread.
Skewed, or with outliers: report the median for center and the IQR for spread, because a few extreme values pull the mean and standard deviation toward the tail.
Comparing groups: use the same pair of statistics for every group. If any group is skewed, use the median and IQR for all of them.
Part 2: Computing the standard deviation. The standard deviation measures the typical distance from the mean. Model it once by hand with a table, using the hours 5 musicians practiced last week: 3, 5, 6, 9, 12.
Standard deviation of 3, 5, 6, 9, 12 by hand
Value
Deviation from mean 7
Squared deviation
3
-4
16
5
-2
4
6
-1
1
9
2
4
12
5
25
Sum
0
50
Divide the sum of squared deviations by n to get the variance, 50 / 5 = 10, and take the square root: SD = √10 ≈ 3.16 hours. Point out that the deviations always add to 0, which is why they are squared. Calculators show two versions: σx divides by n and Sx divides by n - 1. This lesson uses σx for hand work; whichever version students use, they must use the same one for every group they compare.
Symmetric data: mean and SD
Quiz scores out of 10. Class 1: 6, 7, 7, 8, 8, 8, 9, 9, 10. Class 2: 4, 5, 6, 8, 8, 8, 10, 11, 12.
Equation: Both means = 8; SD ≈ 1.15 for Class 1 and ≈ 2.54 for Class 2 (see Diagram 2)
Skewed data: median and IQR
Home sale prices in thousands of dollars. Town A: 210, 225, 240, 250, 265, 280, 300, 420, 610. Town B: 180, 195, 205, 215, 230, 240, 255, 270, 290.
Equation: Medians 265 and 230; IQRs 360 - 232.5 = 127.5 and 262.5 - 200 = 62.5
Daily screen time in hours. Group 1 (symmetric): 3, 4, 4, 5, 5, 5, 6, 6, 7. Group 2 (right-skewed): 1, 2, 2, 2, 3, 3, 4, 7, 12.
Equation: Medians 5 and 3; IQRs 6 - 4 = 2 and 5.5 - 2 = 3.5
Three data sets
Battery life in hours for five batteries of each brand, all roughly symmetric. P: 9.8, 10.0, 10.2, 10.4, 10.6. Q: 8.8, 9.8, 10.8, 11.8, 12.8. R: 9.2, 9.4, 9.6, 9.8, 10.0.
Equation: Means 10.2, 10.8, 9.6; SDs ≈ 0.28, 1.41, 0.28
For the home prices, show Diagram 1: in Town A the mean (about 311) sits to the right of the box's median line because of the 420 and 610 sales, while in Town B the mean (about 231) and median (230) nearly agree. For the batteries, model a comparison sentence: "Brand Q lasts longest on average, about 0.6 hours more than P, but it is the least consistent, with a standard deviation five times as large as P's or R's."
Guided Practice15 minutes
Pairs compare the wait times, in minutes, at two coffee shops. Shop 1 (8 customers): 2, 3, 4, 4, 5, 5, 6, 7. Shop 2 (9 customers): 1, 1, 2, 2, 2, 3, 4, 9, 14. First they sketch a dot plot of each set and name the shape; then they choose statistics and write a comparison. Shop 2 is skewed to the right, so both shops are summarized with the median and IQR: Shop 1 has median 4.5 and IQR 5.5 - 3.5 = 2; Shop 2 has median 2 and IQR 6.5 - 1.5 = 5. A good comparison sentence: "A typical wait is shorter at Shop 2, but its waits are much less predictable." Ask one pair who used the mean for Shop 2 (about 4.2) to explain why it overstates a typical wait there.
Independent Practice10-15 minutes
Students compare the growth, in centimeters, of bean plants given two fertilizers. Fertilizer 1: 10, 12, 13, 13, 14, 16. Fertilizer 2: 12, 13, 15, 15, 17, 18. Both sets are roughly symmetric, so students compute the mean and standard deviation of each (13 cm with SD ≈ 1.83, and 15 cm with SD ≈ 2.08) and write two sentences: one comparing centers and one comparing spreads. Early finishers check their standard deviations with a calculator and note which of σx or Sx matches their hand work.
Closure5 minutes
Exit ticket: The minutes 7 students took to finish a lab were 5, 6, 6, 7, 8, 9, 30. (1) Which pair of statistics fits these data, and why? (2) Compute them. (Answer: median 7 and IQR 9 - 6 = 3; the 30 makes the data skewed, and the mean, about 10.1, is larger than 6 of the 7 values.)
Differentiation Strategies
For Struggling Students
Provide a blank three-column table (value, deviation, squared deviation) for every standard deviation calculation
Give a two-question flowchart: "Is either set skewed or does it have outliers? If yes, use median and IQR for both; if no, use mean and SD for both"
Provide sentence frames: "The typical ___ in group A is about ___ more than in group B. The ___ in group ___ vary more, since its ___ is larger."
For Advanced Students
Ask students to build two data sets of 6 values with the same mean and median but standard deviations that differ by a factor of 3
Have students compute both σx and Sx for a small set and explain why the difference shrinks as n grows
Ask students to find a data set in which the IQR is 0 but the standard deviation is not, and explain what that says about each measure
Assessment Guidance
What to Look For
Listen for a reason tied to shape whenever a student picks a statistic: "I used the median because the data are skewed right" earns more than a correct number. Check that students use the same pair of statistics for every group they compare, and that their comparisons mention both center and spread in context, with units. In standard deviation work, watch for dividing before squaring, forgetting the square root, and mixing σx and Sx within one comparison.
02
Classroom Activities
3 Activities
1
Pick the Right Pair
20 minGroups of 3
Each group receives three pairs of data sets. For each pair they sketch dot plots, decide the shape, choose one pair of statistics for both sets, compute them and write a comparison. Groups then defend one of their choices to another group.
Data Cards
Pair 1, quiz scores out of 20: morning class 12, 14, 15, 16, 16, 17, 18, 20; afternoon class 13, 15, 15, 16, 16, 17, 17, 19
Pair 2, minutes on hold for two help lines: line 1: 1, 1, 2, 2, 3, 4, 6, 11, 18; line 2: 2, 3, 3, 4, 4, 5, 6, 8, 14
Pair 3, daily steps in thousands for two friends over a week: Ana 6, 7, 8, 8, 9, 10, 11; Ben 3, 4, 4, 5, 6, 9, 14
Answer Key for the Teacher
Pair 1, both symmetric: both means 16; SD ≈ 2.29 (morning) and ≈ 1.66 (afternoon). Same center, and the afternoon scores are more consistent
Pair 2, both skewed right: medians 3 and 4; IQRs 8.5 - 1.5 = 7 and 7 - 3 = 4. Line 1 has the shorter typical hold but much more variable holds
Pair 3, Ana symmetric and Ben skewed: use median and IQR for both. Medians 8 and 5; IQRs 10 - 7 = 3 and 9 - 4 = 5. Ana is typically more active and more consistent
Discussion Questions
In Pair 3, what goes wrong if you compare Ana's mean with Ben's median?
In Pair 2, which statistic would change most if the 18 were a 40?
Could two sets with the same IQR have very different standard deviations?
2
Standard Deviation Step by Step
20 minPairs
Partners compute the standard deviation of two small data sets by hand, one set each, using the deviation table, then check with technology. They finish by ranking four sets by spread before computing, to build intuition for what a standard deviation measures.
Procedure
Partner A works with 20, 22, 23, 25, 27, 28, 30 (mean 25, sum of squared deviations 76, SD = √(76/7) ≈ 3.30)
Partner B works with 8, 9, 10, 10, 11, 12 (mean 10, sum of squared deviations 10, SD = √(10/6) ≈ 1.29)
Partners swap papers and check each row, then confirm both answers with a calculator's σx
Each pair writes one sentence comparing the two spreads relative to their means
Discussion Questions
Why do the deviations in every table add to 0?
Which value in each set contributes the most to the standard deviation? Why?
What would happen to the standard deviation if every value were doubled?
Modification for Distance Learning
Share a spreadsheet with columns for value, deviation and squared deviation. Pairs fill in formulas in a breakout room, then compare their result with the spreadsheet's population standard deviation function.
3
Ruler Drop Reaction Times
25 minPairs, then whole class
Students collect their own data and compare two groups. One partner drops a ruler between the other's fingers, and the catch distance in centimeters measures reaction time. Each student catches five times with the dominant hand and five times with the other hand.
Procedure
Record each catch distance to the nearest centimeter; each student reports the median of their five catches for each hand
Pool the class results into two data sets: dominant hand and non-dominant hand
Draw two dot plots above a shared scale on the board and discuss the shape of each
Choose statistics based on the shapes, compute them with technology and write a two-sentence comparison of center and spread
Discussion Questions
Did the shapes lead you to the mean and SD or to the median and IQR? Would another class's data lead to the same choice?
Why did we use each student's median of five catches instead of a single catch?
Challenge Variation
Add a third group, such as catches made while counting backward by 7s, and compare all three groups with one consistent pair of statistics.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Box Plots of Skewed and Symmetric Prices
Box plots of the home prices in Town A and Town B, drawn to scale, with each mean marked by a diamond. Town A's two high sales stretch the right whisker and pull the mean (about 311) well above the median (265). In Town B the mean (about 231) and median (230) nearly agree.
Diagram 2: Same Mean, Different Standard Deviations
Dot plots of the two classes' quiz scores. The dashed line marks the shared mean, 8, and the bar spans one standard deviation on each side. Class 2's scores sit farther from 8, so its standard deviation (about 2.54) is more than twice Class 1's (about 1.15).
04
Homework Assignment
~30 min
HSS.ID.A.2 Homework: Comparing Center and Spread
Directions: For every comparison, first state the shape of each data set and the statistics you chose, then compute them and write a comparison of center and spread in context, with units. Compute standard deviations by dividing by n, and round to the nearest hundredth. Find quartiles by splitting the ordered data in half, leaving the median out when n is odd.
Part 1: Computing and Comparing (Problems 1-3)
Two machines cut bolts that should be 50 mm long. Samples of 6 bolts: Machine 1: 49.8, 49.9, 50.0, 50.0, 50.1, 50.2. Machine 2: 49.4, 49.7, 50.0, 50.0, 50.3, 50.6. Both sets are symmetric. Compute the mean and standard deviation of each and decide which machine is more reliable.
The numbers of text messages sent in one day by 9 ninth graders were 5, 8, 10, 12, 15, 20, 28, 45, 90, and by 9 twelfth graders were 10, 14, 18, 20, 25, 30, 35, 60, 120. Describe the shape of each set, choose statistics and compare the two grades.
Neighborhood X: mean income $92,000, median $68,000, SD $55,000, IQR $30,000; its histogram is skewed right. Neighborhood Y: mean $74,000, median $71,000, SD $15,000, IQR $18,000; its histogram is roughly symmetric. Which statistics should you use to compare the neighborhoods? Write the comparison.
Part 2: Three or More Groups (Problem 4)
Five runners from each of three relay teams ran 100 m, with times in seconds. Team 1: 12.0, 12.4, 12.5, 12.6, 13.0. Team 2: 11.8, 12.0, 12.2, 12.4, 12.6. Team 3: 11.5, 12.0, 12.6, 13.2, 13.7. All three sets are roughly symmetric. Compute the mean and standard deviation for each team, then rank the teams by typical speed and by consistency.
Part 3: Shape and Choice of Statistics (Problems 5-6)
The ages of the 9 people at a child's birthday party were 5, 6, 6, 6, 7, 7, 8, 35, 38. Compute the mean and the median. Which one describes a typical age at the party? Explain using the shape of the data.
Travel times, in minutes, over 8 days for two routes to school are Route A: 22, 23, 24, 25, 25, 26, 27, 28 and Route B: 18, 19, 20, 20, 21, 22, 24, 40. Describe each shape, choose one pair of statistics for both routes, compute them and recommend a route.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Shape and Choice
Shape named for each set; statistics chosen and justified by shape, same pair for all groups
Choice correct but not justified, or different pairs used
No shape or choice given
Computation
Means, medians, IQRs and SDs correct
One or two computation errors
Several errors or work missing
Comparison in Context
Compares both center and spread with units and context
Compares only center or only spread
No comparison
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Work through the questions in order. Your score updates as you answer, and Reset quiz clears everything so you or your students can try again. Standard deviations divide by n unless a question says otherwise.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
A histogram of the prices of used cars on a lot has a long tail to the right. Which pair of statistics best describes its center and spread?
Answer: B
Skewed data call for resistant statistics: the median and the IQR are not pulled toward the long tail. Choice A uses statistics that the few expensive cars would pull upward. Choice C mixes a non-resistant center with a resistant spread, and choice D uses the range, which depends only on the two most extreme prices.
Question 2 of 20 · Multiple Choice
What is the mean of 4, 7, 9, 10, 15?
Answer: A
The sum is 4 + 7 + 9 + 10 + 15 = 45, and 45 / 5 = 9. Choice C is the sum, not divided by the count. Choice D is the second value in the list, not a center.
Question 3 of 20 · Multiple Choice
Find the standard deviation of 2, 4, 6, 8, 10, dividing by n (the population standard deviation). Round to the nearest hundredth.
Answer: C
The mean is 6 and the deviations are -4, -2, 0, 2, 4. Their squares add to 40, so the variance is 40 / 5 = 8 and the standard deviation is √8 ≈ 2.83. Choice A is the variance, before the square root. Choice B divides by n - 1 = 4, giving √10, which is the sample standard deviation.
Question 4 of 20 · Multiple Choice
What is the interquartile range of 5, 7, 8, 10, 12, 13, 15, 20?
Answer: D
With 8 values, the lower half is 5, 7, 8, 10, so Q1 = 7.5, and the upper half is 12, 13, 15, 20, so Q3 = 14. IQR = 14 - 7.5 = 6.5. Choice A is the range, 20 - 5.
Question 5 of 20 · Multiple Choice
Two roughly symmetric data sets have the same mean. Set R has a standard deviation of 3 and set S has a standard deviation of 8. Which statement is true?
Answer: A
Standard deviation measures the typical distance of values from the mean, so S is more spread out. Choice B confuses spread with size: both sets have the same mean. Standard deviation says nothing about the number of values (choice C), and a large spread does not require an outlier (choice D).
Question 6 of 20 · Multiple Choice
A distribution of household incomes is skewed to the right. How do the mean and median usually compare?
Answer: C
The few very high incomes in the right tail pull the mean up, while the median stays with the middle value, so the mean is usually greater than the median. Choice B describes a left-skewed distribution.
Question 7 of 20 · Multiple Choice
Wait times at Clinic 1 are roughly symmetric, and wait times at Clinic 2 are strongly skewed to the right. To compare the two clinics fairly, which statistics should you use?
Answer: B
Compare like with like, and choose statistics that are appropriate for both shapes. The median and IQR describe symmetric data well too, but the mean and SD mislead for skewed data, so use the median and IQR for both. Choice A compares a mean with a median, which is not a fair comparison.
Question 8 of 20 · Multiple Choice
At Company X the median salary is $48,000 and the mean is $71,000. At Company Y the median is $52,000 and the mean is $55,000. Which comparison best describes a typical employee?
Answer: D
The large gap between the mean and median at X suggests a right skew caused by a few high salaries, so the medians are the fair comparison: $52,000 at Y is more than $48,000 at X. Choice A relies on the mean, which the high salaries pull up.
Question 9 of 20 · Multiple Choice
Data set B is made by adding 5 to every value in data set A. How do the two sets compare?
Answer: A
Shifting every value by 5 moves the center by 5 but does not change any distance between values or from the mean, so the spread is the same. Choice B treats the standard deviation like a value in the data instead of a distance.
Question 10 of 20 · Multiple Choice
Which data set has the largest standard deviation?
Answer: C
All four sets have mean 5. The squared deviations add to 0, 2, 32 and 10, so set C, with values farthest from 5, has the largest standard deviation. Choice D comes second, with a sum of 10, but none of its values is as far from 5 as 1 or 9.
Question 11 of 20 · Multiple Choice
The numbers of hours 7 students spent on a project were 3, 4, 4, 5, 6, 8 and 25. Which measure of center is more appropriate, and what is its value?
Answer: B
The value 25 creates a long right tail, so the median is the better center. The 4th of the 7 ordered values is 5. The mean, 55 / 7 ≈ 7.9, is larger than 5 of the 7 values, so it does not describe a typical student. Choice D is the value that appears twice, not the middle value.
Question 12 of 20 · Multiple Choice
What does a standard deviation of 0 tell you about a data set?
Answer: D
Standard deviation is 0 only when every deviation from the mean is 0, so all values are equal. Choice A confuses the spread with the center: 7, 7, 7 has mean 7 and standard deviation 0.
Question 13 of 20 · Multiple Choice
Box plots of two teams' test scores give these five-number summaries. Team A: 60, 70, 76, 82, 95. Team B: 55, 72, 79, 84, 90. Which comparison is correct?
Answer: A
Median: 79 for B and 76 for A, a difference of 3. IQR: 82 - 70 = 12 for A and 84 - 72 = 12 for B, so the middle halves are equally spread. Choice B reverses the medians, and choice C is wrong because the IQRs are equal. (The ranges happen to be equal too: 35 points for each team.)
Question 14 of 20 · Multiple Choice
Three machines fill 500 mL bottles. Their fill amounts are roughly symmetric, with means 500 mL, 502 mL and 499 mL and standard deviations 4.1 mL, 1.2 mL and 2.5 mL. Which machine fills most consistently?
Answer: B
Consistency is about spread, and the smallest standard deviation, 1.2 mL, belongs to the second machine. Choice A answers a different question: the first machine is the most accurate on average, but its fills vary the most.
Question 15 of 20 · Short Answer
Find the mean and the standard deviation (divide by n) of each set, then compare the two sets: X: 7, 8, 10, 12, 13 and Y: 4, 7, 10, 13, 16.
Both means are 10. For X the squared deviations are 9, 4, 0, 4, 9, which add to 26, so SD = √(26/5) ≈ 2.28. For Y they are 36, 9, 0, 9, 36, which add to 90, so SD = √18 ≈ 4.24. The sets have the same center, but Y is almost twice as spread out.
Question 16 of 20 · Short Answer
Delivery times, in minutes, for 7 orders from each of two restaurants are P: 20, 22, 23, 25, 28, 35, 60 and Q: 18, 19, 21, 22, 24, 26, 45. Both sets are skewed to the right. Choose appropriate statistics and compare the restaurants.
Use the median and IQR. P: median 25, Q1 = 22, Q3 = 35, IQR = 13. Q: median 22, Q1 = 19, Q3 = 26, IQR = 7. A typical order from Q arrives 3 minutes sooner, and Q's times are also more consistent.
Question 17 of 20 · Short Answer
A student reports the standard deviation of the salaries at a small business where one person earns far more than everyone else. Explain why that is not a good choice, and what to report instead.
The standard deviation is computed from distances to the mean, and the one very large salary makes both the mean and those distances large. The result describes the gap caused by one person, not the typical variation. Report the median and the IQR, which depend on the middle of the data and are not moved much by one extreme value.
Question 18 of 20 · Short Answer
A data set has mean 15 and median 11. What does this suggest about the shape, and which statistics should you use to compare it with another data set?
A mean well above the median suggests the data are skewed to the right: a few large values pull the mean up. Use the median and IQR, and use the same pair for the other data set.
Question 19 of 20 · Short Answer
Three classes took the same test, and each distribution is roughly symmetric. Class A: mean 78, SD 6. Class B: mean 74, SD 12. Class C: mean 81, SD 5. Write two sentences that compare the classes' centers and spreads.
Class C scored highest on average (81), then A (78), then B (74). Class C was also the most consistent (SD 5) and Class B the least (SD 12), so B's scores were spread about twice as widely around its mean as A's or C's.
Question 20 of 20 · Short Answer
The commute times, in minutes, of 10 employees are 12, 14, 15, 15, 16, 18, 19, 22, 35, 50. Find the mean, the median and the IQR. Which center would you report, and why?
Mean = 216 / 10 = 21.6. Median = (16 + 18) / 2 = 17. Q1 = 15 and Q3 = 22, so IQR = 7. Report the median: the two long commutes, 35 and 50, pull the mean above 7 of the 10 values.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does HSS.ID.A.2 mean?
HSS.ID.A.2 means students compare the center and spread of two or more data sets with statistics suited to each distribution's shape. In practice: mean and standard deviation for roughly symmetric data, median and interquartile range for skewed data or data with outliers. The standard is about comparing groups, so every calculation should end in a comparison.
Is HSS.ID.A.2 part of Algebra 1?
Yes, in most course sequences it is part of the statistics unit of Algebra I, right after students review dot plots, histograms and box plots (HSS.ID.A.1). The standard deviation is often new to students at this point; the median, mean and IQR come from middle school.
When should I use the median instead of the mean?
Use the median when the data are skewed or have outliers. The mean uses every value's size, so a long tail drags it toward the tail; the median depends only on the middle of the ordered list. Home prices, incomes and waiting times are common examples of skewed data where the median is the usual choice.
Why is the mean paired with the standard deviation, and the median with the IQR?
Each spread measures distance around its own center. The standard deviation is built from distances to the mean, and the IQR is the width of the middle half of the data, which is centered on the median. Mixing them, such as reporting a median with a standard deviation, describes the center one way and the spread another, which confuses readers.
Should students divide by n or by n - 1 for the standard deviation?
Either is acceptable at this level, as long as students are consistent. Dividing by n gives the population standard deviation (σx on many calculators); dividing by n - 1 gives the sample standard deviation (Sx), which is slightly larger and is used when the data are a sample from a larger population. The difference matters more in later inference courses than for the comparisons in this standard.
How can students tell the shape of a distribution?
From a picture. In a dot plot or histogram, a roughly symmetric distribution looks similar on both sides of its center, while a skewed one has a longer tail on one side. In a box plot, a much longer whisker or a median line close to one end of the box suggests skew. A large gap between the mean and median is a numerical clue as well.
What does "two or more different data sets" mean in practice?
Students compare groups, such as two classes, three brands or several years. With three or more groups, the same rules apply: pick one pair of statistics that fits all the groups and rank or contrast the groups on center and on spread separately. Side-by-side box plots on one number line make multi-group comparisons easier to see.
What mistakes do students make when comparing data sets?
Common ones are comparing only the centers and ignoring the spread, reading a large standard deviation as "large values", and using different statistics for different groups. Another is reporting numbers without context: "the IQR of A is 4 and of B is 9" is not yet a comparison. Ask for a sentence that names the variable, the units and which group varies more.
Do students need to compute the standard deviation by hand?
A few times, with small data sets, so that they understand what it measures. After that, technology is the sensible tool, and class time is better spent choosing statistics and interpreting them. Hand calculation with a table of deviations makes it clear why values far from the mean increase the standard deviation so much.
How does HSS.ID.A.2 connect to other standards and tests?
It builds on 7.SP.B.4, where students first compare two populations using center and variability, and it leads to HSS.ID.A.3, which interprets differences in shape, center and spread and the effect of outliers, and HSS.ID.A.4, which uses the mean and standard deviation to fit a normal distribution. On the digital SAT, questions about comparing means, medians and spreads appear in the Problem-Solving and Data Analysis domain.
07
Related Standards
6 standards
These standards connect to HSS.ID.A.2: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
6.SP.B.5Prerequisite
Summarize numerical data with measures of center and variability tied to shape
