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Worksheet Grade 11 Math

Windham Creek Dissolved Oxygen: Comparing Seasonal Spread

A grade 11 statistics worksheet comparing summer and winter dissolved-oxygen readings from a fictional creek using mean, median, IQR, standard deviation, and outliers.

Objectives

  1. Students will compute the mean, median, range, IQR, and standard deviation of two data sets.
  2. Students will use the 1.5 times IQR rule to test whether a reading is an outlier.
  3. Students will interpret differences in spread between two seasons in context.

Vocabulary

Dissolved oxygen
Dissolved oxygen is the oxygen gas mixed into water that fish and other underwater animals breathe. Cold, moving water holds more oxygen than warm, still water.

Also: standard deviation, interquartile range, outlier, median

Teacher overview

Dissolved oxygen (DO) is one of the clearest signals of a creek's health, and it swings with the seasons because cold water holds more oxygen than warm water. Windham Creek is a fictional creek where student volunteers recorded DO on eight sampling days each season. This worksheet has students summarize and compare the two seasons with center and spread, then decide whether one unusually low summer reading is a true outlier. A common student error is to compare only the ranges, which can hide the fact that two data sets with different ranges can share the same interquartile range.

Windham Creek Dissolved Oxygen: Comparing Seasonal Spread — Grade 11 Math
Name: ____________________________ Date: ______________

Student Worksheet

Windham Creek is a fictional creek. Volunteers measured dissolved oxygen, in mg/L, on eight days each season:

Season Dissolved oxygen readings (mg/L)
Winter 11, 12, 12, 13, 11, 12, 13, 12
Summer 7, 6, 7, 6, 7, 6, 6, 3
  1. Find the mean dissolved oxygen for the winter readings.
  2. Find the mean dissolved oxygen for the summer readings.
  3. Find the median for each season.
  4. Find the range for each season.
  5. Find the interquartile range (IQR) for each season.
  6. Using the statistics function on your calculator, find the sample standard deviation for each season. Round to the nearest hundredth.
  7. The summer set includes one reading of 3 mg/L. Using the rule that a value below Q1 minus 1.5 times the IQR is an outlier, show whether 3 mg/L is an outlier.
  8. Most fish need dissolved oxygen above 5 mg/L. How many of the eight summer readings fall below 5 mg/L?
  9. Compare the two seasons using the standard deviations from item 6. Which season is more consistent, and what physical reason explains it?
  10. Suppose you remove the 3 mg/L summer reading. What is the mean of the remaining seven summer readings? Round to the nearest hundredth.
  11. Explain why the median is often a better summary than the mean when a data set contains an outlier.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 12.0 mg/L.
    The winter readings sum to 96; 96 divided by 8 = 12.0 mg/L.
  2. Answer: 6.0 mg/L.
    The summer readings sum to 48; 48 divided by 8 = 6.0 mg/L.
  3. Answer: 12 mg/L winter, 6 mg/L summer.
    Winter sorted is 11, 11, 12, 12, 12, 12, 13, 13; the two middle values are 12 and 12, so the median is 12. Summer sorted is 3, 6, 6, 6, 6, 7, 7, 7; the two middle values are 6 and 6, so the median is 6.
  4. Answer: 2 mg/L winter, 4 mg/L summer.
    Winter range = 13 minus 11 = 2. Summer range = 7 minus 3 = 4.
  5. Answer: 1.0 mg/L for both.
    Winter Q1 = 11.5 and Q3 = 12.5, so IQR = 1.0. Summer Q1 = 6 and Q3 = 7, so IQR = 1.0. The two seasons share an IQR even though their ranges differ.
  6. Answer: 0.76 mg/L winter, 1.31 mg/L summer.
    Using sample standard deviation, winter is the square root of 4 divided by 7, about 0.76. Summer is the square root of 12 divided by 7, about 1.31.
  7. Answer: yes, 3 mg/L is an outlier.
    The lower fence is Q1 minus 1.5 times IQR = 6 minus 1.5 times 1.0 = 4.5. Because 3 is below 4.5, it is a statistical outlier.
  8. Answer: 1 reading.
    Only the 3 mg/L reading falls below the 5 mg/L benchmark; every other summer reading is 6 or 7.
  9. Answer: Winter is more consistent.
    Winter's standard deviation (0.76) is smaller than summer's (1.31), so winter DO varies less. Cold winter water holds more oxygen and stays steadier, while warm summer water holds less and swings more.
  10. Answer: 6.43 mg/L.
    The seven remaining summer readings sum to 45; 45 divided by 7 = 6.43. Removing the low outlier raises the mean.
  11. Answer: The median resists outliers.
    A single very low or very high value pulls the mean toward it but barely moves the median, so the median better represents the typical reading when an outlier is present.

Differentiation

Support

Provide the sorted version of each data set and a worked example of the 1.5 times IQR rule on a third, unrelated set before students attempt item 7. Allow the standard deviations to be read directly from calculator output without hand computation.

Extension

Ask students to build box plots for both seasons on a shared scale, mark the summer outlier, and write two sentences explaining what the overlapping or non-overlapping boxes suggest about whether the seasons truly differ.

ELL supports

Pre-teach "spread," "consistent," "outlier," and "median" with a simple number-line sketch showing tightly clustered points versus widely spread points. Provide sentence frames for item 9, "The ___ season is more consistent because ___," and item 11, "The median is better when there is an outlier because ___."