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|5A: Statistical Measures |Check for Understanding|

|1 = Need more help 2 = Understanding, need more practice 3 = Got It! | | | |

| |1 |2 |3 |

|6.SP.1: I can identify the difference between a non-statistical and statistical question, where as a statistical question has more than | | | |

|one right answer (non-bias). | | | |

| | | | |

|6.SP.2: I can describe the distribution of a set of data in terms of center, spread and overall shape. e.g., data clusters, peaks, gaps, & | | | |

|symmetry | | | |

|6.SP.2: I can describe a set of data by its center. e.g., mean, median & mode | | | |

| | | | |

|6.SP.3: I can recognize that measures of center (mean, median & mode) for a data set summarizes the data with a single number. | | | |

|6.SP.3: I can recognize that measures of variation for a data set describes how its values vary with a single number. (One number added or | | | |

|one number deleted can change the values of mean, median & mode.) Measures of variation include: range, interquartile range and mean | | | |

|absolute deviation. | | | |

|5B: Data Displays | | | |

|6.SP.4: I can identify the components of dot plots, histograms, and box plots. | | | |

|6.SP.4: I can find the median, quartile and interquartile range of a set of data. | | | |

|6.SP.4: I can create a dot plot to display a set of numerical data. | | | |

|6.SP.4: I can create a histogram to display a set of numerical data. | | | |

|6.SP.4: I can create a box plot to display a set of numerical data. | | | |

| | | | |

|6.SP.5 a: I can report the number of observations. | | | |

|6.SP.5 b: I can describe the data being collected, including how it was measured and its units of measurement. | | | |

|6.SP.5 c: I can calculate quantitative measures of center. e.g., mean, median, mode | | | |

|6.SP.5 c: I can calculate quantitative measures of variance. e.g., range, interquartile range, mean absolute deviation | | | |

|6.SP.5 c: I can identify outliers. | | | |

|6.SP.5 c: I can determine the effect of outliers on quantitative measures of a set of data. e.g., mean, median, mode, range, interquartile | | | |

|range, mean absolute deviation | | | |

|6.SP.5 d: I can choose the appropriate measure of central tendency to represent the data. | | | |

|6.SP.5 d: I can analyze the shape of the data distribution; the context in which the data were gathered to choose the appropriate measures | | | |

|of central tendency & variability and justify why this measure is appropriate in terms of the context. | | | |

Key Vocabulary

Statistics: is the science of collecting, organizing, analyzing, and interpreting data.

Statistical Question: A statistical question is one for which you do not expect to get a single answer. Instead, you expect a variety of answers, and you are interested in the distribution and tendency of those answers.

Measure of Variation: is a measure that describes the distribution of a data set. A simple measure of variation to find is the range (see below).

Measure of Center: is a measure that describes the typical value of a data set. The mean, median & mode are three examples of measure of center.

Mean: the average; the sum of all the data divided by the number of data.

1. Add all of the numbers together.

2. Divide by the number of items that were added together

[pic]

Median: the middle number in an ordered set of data

Example:

[pic]

The median of 1, 3, 4, 6, and 7 is 4.

Mode: the number that occurs most often in a set of data. (There can be more than one mode or no mode.)

Example:

[pic]

The mode of 1, 3, 4, 4, and 6 is 4.

Data: A set of information; facts or figures from which conclusions can be formed.

Range: the difference between the greatest value and the least value.

Example:

Month |Jun |Jul |Aug |Sep |Oct |Nov | |Temperature |82°F |83°F |83°F |82°F |82°F |80°F | |

The greatest temperature is 83°F.

The least temperature is 80°F.

Since 83 - 80 = 3, the range is 3°F.

Quartiles: The quartiles of a data set divide the data into four equal parts. Recall that the median (second quartile) divides the data set into two halves.

[pic]

Example : Find the first and third quartiles of the data set {3, 7, 8, 5, 12, 14, 21, 13, 18}.

First, we write data in increasing order: 3, 5, 7, 8, 12, 13, 14, 18, 21.

Therefore, the lower half of the data is: {3, 5, 7, 8}.

The first quartile, Q1, is the median of {3, 5, 7, 8}.

Since there is an even number of values, we need the mean of the middle two values to find the first quartile:

[pic][pic].

Similarly, the upper half of the data is: {13, 14, 18, 21}, so

[pic][pic].

First Quartile: the median of the lower half.

Third Quartile: the median of the upper half.

Interquartile Range (IQR): The difference between the third quartile and the first quartile is called the interquartile range. The IQR represents the range of the middle half of the data and is another measure of variation. (See above.)

Absolute Deviation: is an average of how much data values differ from the mean.

Example: number of raisins in 8 scoops of cereal. To find and interpret mean absolute deviation of the data……. 1, 2, 2, 2, 4, 4, 4, 5

Step # 1: Find the mean: 24 ÷ 8 = 3

Step # 2: Use a dot plot to organize the data.

Step # 3: The sum of the distances is 2 + 1 + 1 + 1 + 1 + 1 + 1 + 2 = 10

Step # 4: The mean absolute deviation is 10 ÷ 8 = 1.25

Therefore, the data values differ from the mean by an average of 1.25 raisins.

Stem and Leaf Plot: uses the digits of data values to organize a data set. Each data value is broken into a stem (digit or digits on the left) and a leaf (digit or digits on the right)

Example:

[pic]

This plot shows the number of sit-ups a group of students did in one minute.

Frequency Table: Groups data values into intervals. The frequency is the number of values in an interval.

Histogram: is a bar graph that shows the frequency of data values in intervals of the same size. The height of a bar represents the frequency of the values in the interval.

Example:

[pic]

Box and Whisker Plot: represents a data set along a number line by using the least value, the greatest value, and the quartiles of the data. A box and whisker plot shows the variability of a data set.

Example:

[pic]

Least Value (lower extreme): 15

First Quartile (lower quartile): 19

Median: 21.5

Third Quartile (upper quartile): 25

Greatest Value (upper extreme): 29

Outlier: is a data value that is much greater or much less than the other values. When included in the data set, it can affect the mean.

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