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Statistics Day 5: Review!

Vocabulary!

|Mean Absolute Deviation |Average distance from the mean. |

| |Calculated from absolute value |

|Standard Deviation |Shows how the data are spread out from the center; variation in a distribution of data. |

| |Always greater than or equal to zero; the larger the number the greater the spread of the |

| |data. |

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|z-score |A measure of how many standard deviations a data element is from the mean. |

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|Mean |Average of the Data. Add all data points up and divide by the number of pieces of data. |

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| |The average value of a set of numbers. |

| |(the balance point) |

| |[pic]or [pic] |

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|Box and Whisker plot | |

|Line Plot | |

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|Range |The difference between the highest and lowest elements in a data set. |

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|Outlier |An extreme value in a data set that is not likely to occur often. It is far from the center |

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|Minimum/ Lower Extreme |The lowest and highest elements in a set of data. |

|Maximum/ Upper Extreme | |

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|Median |The middle element when a set of elements are put in numerical order. |

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|Element(s) |Another name for a data point or plural for a set of data. |

|3rd Quartile |The median of the upper half of the data. |

|Upper Quartile | |

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|Mode |The element occurring most often in a set of data. There may be more than one mode or no |

| |mode! |

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|1st Quartile |The median of the lower half of the data. |

|Lower Quartile | |

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Measures of Central Tendency:

For a class project, a student gathered data from her classmates. She made the request “Tomorrow morning, find out how many minutes it takes you to get ready – from the time you get up until the time you leave your house for school”. Here are the responses:

47 28 78 47 58 93 34 76 35 72 45 53 23

75 27 23 87 33 43 25 35 49 35 48 37 28

Find the: Mean…Median…Mode…Range… for this set of data

Mean: __________ Mode: ___________

Median: ___________ Range: ___________

Make a Frequency chart with the data

Number of Minutes

| |Data |

|10 | |

|20 | |

|30 | |

|40 | |

|50 | |

|60 | |

|70 | |

|80 | |

|90 | |

Now take this information and make a line plot (histogram).

___________________________________________________

0 10 20 30 40 50 60 70 80 90 100

Make Box and Whisker Plots for the set of data

Median: ___________ Inter-Quartile Range: __________

Lower Quartile: _________ 3rd Quartile Value: ___________

Upper Quartile: _________ 1st Quartile Value: ___________

Lower Extreme: _________ Range: _________

Upper Extreme: _________

____________________________________________________

0 10 20 30 40 50 60 70 80 90 100

Find the Standard Deviation

The following are the wind velocities reported at an airport at 4 p.m. on eight consecutive days: 25, 15, 18, 20, 2, 10, 12, and 8 miles per hour. Calculate the standard deviation.

Find the mean ([pic]). Round to the nearest tenth.

[pic]=

|Observations |Mean |Deviations |Squared Deviations |

|[pic] |[pic] |[pic] |[pic] |

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SUM = __________

Variance = [pic]

Standard Deviation = [pic]

Using the TI-84+ to find Standard Deviation:

Enter the data into L1

• From the home screen click on STAT.

• To enter data into lists choose option “1:Edit”

• In L1, enter each element of the data set.

Enter the first element and press enter to move to the next line and continue for all elements.

Calculate standard deviation by computing 1-Variable Statistics for L1

• Press STAT

• Press the Right Arrow (highlight CALC)

• Choose option “1: 1-Var Stats”

• Press enter to compute the 1-variable statistics (defaults to L1).

[pic] = arithmetic mean of the data set

Σx = sum of the x values

Σx2= sum of the x2 values

Sx = sample standard deviation

σ x = population standard deviation

n = number of data points (elements)

Z-Score

Using the above wind data. Find how many standard deviations each of the following observations are from the mean. (Find the Z-Score): [pic]

What you need to know about the data: Mean ([pic]): _______ SD ([pic]): ______

1. 4 mph 2. 10 mph

3. 25 mph 4. 32 mph

Find the Mean Absolute Deviation (MAD) for the Wind Data

|x | | | |

| |(x |x ((x |( x ((x ( |

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Mean ([pic]) = _________

SUM: __________

Statistics Day 5 Homework

1. Create the Vocabulary Flashcards and STUDY THEM!!!

2. Use the Following Data to answer the rest of the questions on this page.

This shows the number of shots made from 50 free throws for 18 players.

Find the: Mean…Median…Mode…Range… for this set of data

Mean: __________ Mode: ___________

Median: ___________ Range: ___________

Make a Frequency chart with the data

Number of Throws

| |Data |

|10 | |

|20 | |

|30 | |

|40 | |

|50 | |

Now take this information and make a line plot (histogram).

__________________________

0 10 20 30 40 50

Make Box and Whisker Plots for the set of data

Median: ___________ Inter-Quartile Range: __________

Lower Quartile: _________ 3rd Quartile Value: ___________

Upper Quartile: _________ 1st Quartile Value: ___________

Lower Extreme: _________ Range: _________

Upper Extreme: _________

______________________________

0 10 20 30 40 50

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|3. How many elements are below the mean? ________ |

|How many elements are above the mean? ________ |

|What is the range of heights from -1 to 1 standard deviations? ___________ |

|How many elements fall within one standard deviation of the mean? ______ |

|What does a standard deviation of 2.3 tell you about the variance of the data? |

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|Find the z-score corresponding to a score of 89 from a normal distribution with mean 81 and standard deviation 7. |

|z-score = [pic] |

|How many standard deviations away from the mean is 56, if the mean is 70 and the standard deviation is 6? |

|z-score = [pic] |

|The average dog is 394 cm tall. The Robo the Rottweiler is 630cm tall. How many standard deviations away from the mean is Robo? The standard |

|deviation is 40 cm. |

|z-score = [pic] |

|What does a negative z-score tell you? |

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4. Calculate the MAD and the SD of the following numbers: 3, 5, 7, 10, 11, 10, 5, 25, 5

Find the mean ([pic]). Round to the nearest tenth. [pic]

MAD Worksheet SD Worksheet

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|x |[pic] |[pic] |( [pic]( |

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|x |[pic] |[pic] |([pic])2 |

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SUM: ________ SUM = _______

Variance = [pic]________

_______ SD = [pic] _________

5. For the data: 3, 5, 7, 10, 11, 10, 5, 25, 5, what is the Interquartile Range?

6. Find the Standard Deviation of the following set of data using your calculator!

66, 62, 68, 63, 72, 69, 59 SD = _______________

7. Find the Standard Deviation of the following set of data using your calculator!

40, 44, 39, 46, 48, 42, 62 SD = _______________

8. What does the Standard Deviation in number 15 make you think?!?

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55

[pic]

56

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