Common Core Learning Standards s4

Common Core Learning Standards

GRADE 6 Mathematics

STATISTICS & PROBABILITY

Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Develop understanding of statistical variability. / Statistical questions / Identify statistical questions. / § statistical question
§ non-statistical question
§ variability
§ data
Contrast statistical and non-statistical questions.
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. / Define a statistical question as a question that allows for the gathering of variable data.
SAMPLE TASKS
I. a. Of the following list of questions group them according to statistical and non statistical questions., then explain what distinguishes between a statistical and non statistical question.
a. What is Karen’s shoe size?
b. What are the shoe sizes of students my age?
c. How tall are my classmates?
d. How tall is John?
e. How old is Sue’s pet?
f. How old are my friends’ pets?
g. How far goes Joe drive to work?
h. How far do the employees of the store drive to work?
b. Then explain what distinguishes between a statistical and non statistical question.
II. Farmer Fred will weigh the chickens in both pens at the end of his experiment. Is the question “How much do the chicken in each pen weigh?” a statistical question? Why or why not?
The weights that Farmer Fred records are shown in the tables.
Pen A – Premium Star
Chicken’s Weights (lb)
6.4 / 5.2 / 7.5 / 8.3 / 5.6
7.6 / 8.1 / 7.7 / 6.2 / 6.4
8.1 / 4.8 / 5.5 / 6.6 / 6.7
4.9 / 5.1 / 8.1 / 7.9 / 7.5
Pen B – Rapid Growth
Chicken’s Weights (lb)
6.6 / 5.1 / 7.7 / 8.1 / 5.7
5.7 / 4.5 / 7.4 / 6.1 / 6.3
7.9 / 4.9 / 5.6 / 6.4 / 6.8
4.7 / 5.3 / 6.0 / 8.0 / 6.6
a. How many chickens are in each pen?
b. What units are used to measure the chicken’s weights?
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Develop understanding of statistical variability. / statistical variability / Describe a set of data in terms of its center (mean, median), spread (range, interquartile range, mean absolute deviation), and overall shape. / § Center
§ Mean
§ Median
§ Spread
§ Range
§ interquartile range
§ mean absolute deviation
§ overall shape
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.
SAMPLE TASKS
I. Joshua’s math scores were 81, 94, 90, 97, 50 ,and 86. Find the median and mean of the data. Which better describes the data, the median or the mean? Explain your answer.
II. The ages of Abe’s grandchildren are: 20, 15, 23, 8, 20, 10, 15, 25, 16, and 18.
What are the first quartile, third quartile, and interquartile range og the grandchildren’s age?
What is the mean absolute deviation of the ages of Abe’s grandchildren?
What do the interquartile range (IQR) and the mean absolute deviation (MAD) tell you about the age’s of Abe’s grandchildren?
III. Create a data set of five different numbers whose mean is 10. Explain your method.
IV. Suppose you have test scores of 92, 85, 86, and 90. What would you need to score on the next test to have a mean score of 90?
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Develop understanding of statistical variability. / center and variation of data / Define measure of center for a data set as the summary of all its values as one number. / § measure of center
§ measure of variation
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. / Define measure of variation for a data set as how the data varies as one number.
SAMPLE TASKS
I. The following low temperatures were recorded for ten days in February. All temperatures are in degrees Fahrenheit:
15, 18, 10, 17, 17, 20, 16, 17, 15, 14
a. Construct a dot plot for the temperatures.

10 11 12 13 14 15 16 17 18 19 20
b. Which measure of center best describes the data, the median or the mean? Explain your answer.
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Summarize and describe distributions. / statistical displays / Display numerical data as plots on a number line. / § dot plot
§ histogram
§ box plot
§ number line
Display numerical data as plots in a dot plot.
6.SP.4.
Display numerical data in plots on a number line, including dot plots, histograms, and box plots. / Display numerical data in a histogram.
Display numerical data in a box plot (box-and-whisker plot).
SAMPLE TASKS
I. a. 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, 5, 6,
4, 0. Make a dot plot for the data.
b. How does a dot plot describe a data set?
II. Make a box plot of the following data. 250, 175, 215, 350, 320, 235, 250, 280. Find the least and greatest values, the quartiles, and the median.
III. Students’ scores on Mrs. Rothwell’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.
a. Use the data to complete the frequency table below:
Mrs. Rothwell’s Math Test Scores
Score / Tally / Frequency
76-80
81-85
86-90
91-95
96-100
b. Make a histogram of the data.
Mrs. Rothwell’s Math Test Scores
8
6
4
2
0
76-80 81-85 86-90 91-95 96-100
Score
IV. a. Display the following numbers on a number line: 7, 6, 9, 10, 11, 6, 8, 12, 0, 13
b. Identify any outliers in the data.
c. Find the mean, median and mode.
d. How does the outlier affect the mean and explain.
V. At the end of the 1994-1995 season, these colleges had the most bowl wins: Alabama, 27; University of Southern California, 24; Oklahoma, 20; Penn State, 19; and Tennessee, 19. Name the types of data displays you could use to show this information. Make at least two of these displays and explain how each type helps you understand the data.
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Summarize and describe distributions. / Summarizing numerical data sets / Record the number of observations within a numerical data set. / § Observations
6.SP.5.
Summarize numerical data sets in relation to their context, such as by:
6.SP.5a.
Reporting the number of observations.
SAMPLE TASKS
I. 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
a. How many chickens does Ann have?
b. What unit is used to measure the chicken’s weights?
c. What is the mean weight of the chickens?
d. What is the median weight of the chickens?
e. Does the mean or median better describe the center of this data? Explain.
f. Find the lower quartile and the upper quartile.
g. Find the interquartile range.
h. Make a dot plot of the weights.
Amy’s Chickens

4 5 6 7 8 9 10 11 12 13 14
Weight (lb)
i. Describe the shape of the data. Identify any gaps. clusters, or peaks. Are there any data values that do not fit the general shape? If so, which one(s)?
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Summarize and describe distributions. / Summarizing numerical data sets / Describe how a data set was measured and its units of measurement. / § data set
§ units of measurement
6.SP.5.
Summarize numerical data sets in relation to their context, such as by:
6.SP.5b.
Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
SAMPLE TASKS
I. The dot plot shows the number of runs scored by a baseball team in games played during the month of April. Use the dot plot for 4-9.
Runs Scored
•
•
• • • •
• • • • • • • • • • • •

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Runs
What does each dot represent?
How many games did the team play in April?
Make a frequency table for the data.
Interval / Frequency
0-4
Make a histogram for the data.
Baseball Games in April
10
9
8
7

6
5
4
3
2
1
0
0-4 5-9 10-14 15-19
Runs Scored
What size are the intervals used to make the histogram?
Give an example of information provided by the dot plot that is not provided by the histogram?
Describe the shape of the data in the dot plot. Are there any data values that do not fit the over all shape? If so which ones?
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Summarize and describe distributions. / Summarizing numerical data sets / Calculate measures of center: median and/or mean. / § overall pattern
§ median
§ mean
§ interquartile range
§ mean absolute deviation
Calculate measures of variability: interquartile range and/or mean absolute deviation.
6.SP.5.
Summarize numerical data sets in relation to their context, such as by:
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. / Describe any overall patterns or deviations from the overall pattern in relation to the context of the data collection.
SAMPLE TASKS
II. 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
j. How many chickens does Ann have?
k. What unit is used to measure the chicken’s weights?
l. What is the mean weight of the chickens?
m. What is the median weight of the chickens?
n. Does the mean or median better describe the center of this data? Explain.
o. Find the lower quartile and the upper quartile.
p. Find the interquartile range.
q. Make a dot plot of the weights.
Amy’s Chickens

5 5 6 7 8 9 10 11 12 13 14
Weight (lb)
r. Describe the shape of the data. Identify any gaps. clusters, or peaks. Are there any data values that do not fit the general shape? If so, which one(s)?
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Summarize and describe distributions. / Summarizing numerical data sets / Compare and contrast the measures of center to the data distribution in the context of the data collection. / § measures of center
§ measures of variability
§ data distribution
§ context of data collection
Compare and contrast the measures of variability to the data distribution in the context of the data collection.
6.SP.5.
Summarize numerical data sets in relation to their context, such as by:
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.
SAMPLE TASKS
I. The RBIs (Runs Batted In) for 15 players from the 2010 Seattle Mariners and Baltimore Oriles are shown. Use the data to answer the following questions.
Mariners’ RBIs
15 51 35 25 58
33 64 43 33 29
14 13 11 4 10
Orioles’ RBIs
55 76 15 28 39
31 69 60 72 32
20 12 9 14 9
a. Find the median of the Mariners’ RBIs.
b. Find the lower quartile of the Mariners’ RBIs.
c. Find the upper quartile of the Mariners’ RBIs.
d. Make a box plot of the Mariners’ data.
Mariners’ RBIs

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
e. Find the IQR of the Mariners’ data. Round to the nearest whole number.
f. Find the MAD of the Mariners’ data. Round to the nearest whole number.
g. Find the median of the Orioles’ RBIs.
h. Find the lower quartile of the Orioles’ RBIs.
i. Find the upper quartile of the Orioles’ RBIs.
j. Make a box plot of the Orioles’ data.
Orioles’ RBIs

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
k. Find the IQR of the Orioles’ data. Round to the nearest whole number.
l. Find the MAD of the Orioles’ data. Round to the nearest whole number.
m. Using the information found, make a statement that compares the RBIs for the two teams.