GRADE 6Common Core Mathematics: Unit 6: STATISTICS

TASK 1: 6.SP.1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.
  1. Of the following list of questions, highlight those questions which are statistical.
  1. What is Karen’s shoe size?
  2. What are the shoe sizes of students my age?
  3. How tall are my classmates?
  4. How tall is John?
  5. How old is Sue’s pet?
  6. How old are my friends’ pets?
  7. How far does Joe drive to work?
  8. How far do the employees of the store drive to work?
  1. Explain what distinguishes between a statistical and non-statistical question.

TASK 2: 6.SP.2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
  1. The ages of Abe’s children are: 20, 15, 23, 8, 20, 10, 15, 25, 16, and 18.
  1. What are the first (lower quartile), third (upper quartile), and IQR of the ages?

First ______Third ______IQR ______

  1. What is the mean absolute deviation of the ages of Abe’s children? ______
  1. What do the interquartile range (IQR) and the mean absolute deviation (MAD) tell you about the ages of Abe’s children?
  1. The dot plot shows the writing scores for a group of 6th graders on sentence structure.

Writing Rubric Scores for Sentence Structure

  1. Describe the overall shape and distribution of the data.
  1. Describe the center of the data set. Explain what you used to find the center.

TASK 3: 6.SP.3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
  1. The line plot shows the writing scores for a group of 6th graders on sentence structure.

Writing Rubric Scores for Sentence Structure

  1. How many students are represented in the data set? ______
  1. Find the mean and median.
  1. What is the range of the data? What does the value mean?
  1. Explain the difference between a measure of center and a measure of variance (spread).

TASK 4: 6.SP.4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
  1. In June 2010, opponents of the NY Yankees scored the following number of runs:

4, 4, 9, 0, 2, 4, 1, 2, 11, 8, 2, 2, 5, 3, 2, 4, 0

  1. Make a line plot of the data.

b. Describe the distribution of this data set.

  1. Students’ scores on Mrs. Roth’s last math test are shown below:

82, 96, 91, 100, 94, 78, 100, 90, 95, 88, 92, 98, 100, 82, 93, 80, 94, 90, 76, 90, 84, 100, 82, 96

  1. Use the data to complete the frequency table below:

Mrs. Roth’s Math Test Scores

Score / Tally / Frequency
76-80
81-85
86-90
91-95
96-100
  1. Make a histogram of the data.
  1. Age Data: 7, 6, 9, 10, 11, 6, 48, 12, 5, 13, 8
  1. Identify any outliers in the data.
  1. Find the mean, median and mode.
  1. Which measure of center best describes this data? Explain.
  1. The dot plot shows the number of runs scored by a baseball team in the month of April.

  1. What does each dot represent? ______
  1. How many games did the team play in April? ______
  1. How does the range of the data help you decided the interval for the frequency table?
  1. Make a grouped frequency table (a frequency table with intervals) for the data.
  1. Make a histogram for the data.

TASK 5: 6.SP.5. Summarize numerical data sets in relation to their context, such as by:6.SP.5a.Reporting the number of observations.6.SP.5b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.6.SP.5c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. 6.SP.5d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
  1. Fred recorded the average daily temperatures over several days in the month of March.

23 / 14 / 15 / 33
37 / 44 / 13 / 12
24 / 25 / 22 / 55
57 / 33 / 21 / 21
16 / 55 / 52 / 51

Average Daily Temperature (oF)

  1. How many days did Fred record the temperature? ______
  2. How many days was less than 25oF? ______
  1. What was the range of temperature? ______
  1. Pete is interested in knowing the favorite sports of students in his school. He surveys only the soccer team. Is his sample unbiased or biased? Explain.
  1. Katie is conducting a study to know if students who sit in the front row of their classes have better grades. Of the 100 homerooms in her school, she collects the grades of students from 10 homerooms. Would her sample be a good representation of the population? Explain.
  1. The weights of Ann’s chickens are shown. Use these data for the following questions:

Chicken’s Weights (lb)
14 / 6 / 5 / 7 / 7 / 5 / 6 / 7 / 6 / 6 / 4 / 5
  1. How many chickens does Ann have? ______
  1. What unit is used to measure the chicken’s weights? ______
  1. What is the mean weight of the chickens? ______
  1. What is the median weight of the chickens? ______
  1. Does the mean or median better describe the center of this data? Explain.
  1. Find the lower quartile and the upper quartile. ______
  1. Find the interquartile range. ______
  1. Make a box plot of the weights.

Ann’s Chickens

4 5 6 7 8 9 10 11 12 13 14

Weight (lb)

  1. Describe the shape and overall distribution of the data.
  1. Consider the line plots shown below.
  1. Describe the overall shape and distribution of each dot plot.
  1. In which dot plot would the mean and median be close in value? Explain.
  1. The RBIs (Runs Batted In) for 15 players from the 2010 Seattle Mariners and Baltimore Orioles are shown. Use the data to answer the following questions.

Orioles’ RBIs
55 76 15 28 39
31 69 60 72 32
20 12 9 14 9
Mariners’ RBIs
15 51 35 25 58
33 64 43 33 29
14 13 11 4 10
  1. Find the FIVE NUMBER SUMMARY of the Mariners’ RBIs.

Min ______Maximum ______

Median ______Lower Quartile ______Upper Quartile______

  1. Find the IQR of the Mariners’ data. ______
  1. Find the FIVE NUMBER SUMMARY of the Orioles’ RBIs.

Min ______Maximum ______

Median ______Lower Quartile ______Upper Quartile______

  1. Find the IQR of the Orioles’ data. ______
  2. The MAD for the Mariners’ data is ~15. The MAD for the Orioles’ data is 20.6 What does this tell us about the data?
  1. Make box plots of BOTH sets of data on the number line below.