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Dealing with Data. 7 th grade math. What is data?. Data is information. Raw data can come in many different forms, the two most common are: Categorical data – data with specific labels or names for categories (usually in word form)

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Dealing with data

Dealing with Data

7th grade math


What is data
What is data?

  • Data is information.

  • Raw data can come in many different forms, the two most common are:

    • Categorical data – data with specific labels or names for categories (usually in word form)

    • Numerical data – data that are counts or measures (usually in number form)


Variability
Variability

  • Variability – indicates how widely spread or closely clustered data values are

    • Students collect data on the amount of change in the pocket of every student at NHM. (Clustered or spread?)

    • Students survey current students at NHM to find out their grade level – 6th,7th, or 8th.

      (Clustered or spread?)


How do you display data
How do you display data?

  • The easiest way to display data is in a graph or chart.

    • Pictograph Circle Graph

    • Histogram Line Plot

    • Bar Graph Scatter Plot

    • Line Graph Box-and-Whisker Plot

    • Frequency Distribution

    • Stem and Leaf Plot


What makes a good graph
What makes a good graph?

  • A good graph…

    • Fits the data you have collected.

    • Has a title and labels.

    • Accurately displays your data.

    • Allows a reader to easily draw conclusions.

    • Catches the reader’s attention.

    • Is easy to read and understand.


Where does data come from
Where does data come from?

  • ????

  • Surveys

  • Studies

  • Questionnaires

  • Census data


Populations samples and statistics
Populations, Samples, and Statistics

  • Population – the entire set of items from which data can be selected (ex. Every 7th grade student, every girl at NHM)

  • If we collected data from EVERY member of a population we would refer to this as a census.

  • Collecting data from an entire population can be a long and difficult process, but the data obtained would be extremely accurate and reliable.


Populations samples and statistics1
Populations, Samples, and Statistics

  • Sample – a selected group of a population that is representative of the entire population. (ex. Twenty 7th grade students in Mr. Ridley’s math class)

  • Samples can be:

    • Random – data is obtained from random members of a population

    • Systematic – data is obtained using a system for selection (ex. Every 10th person)

    • Convenient – data is obtained from the easiest source available within your population (ex. People who sit next to you in class)


Populations samples and statistics2
Populations, Samples, and Statistics

  • Anytime you obtain data about a measured characteristic of your sample, you have collected a statistic.

  • If you obtain data about a measured characteristic of an entire population, you have collected a parameter.

  • If you find a data point that is not consistent with your other results (way too high, way too low) we call it an outlier and it can be removed.

  • Which data would be more reliable?


Interpreting data
Interpreting Data

  • Raw data does not come in a user-friendly format.

  • It must be processed and presented in a form that is easy to read and understand.

  • One system for doing this is graphing, which allows for a visual picture of a data set.


Measures of central tendency
Measures of Central Tendency

  • Another system for interpreting data are the measures of central tendency.

  • Also called measures of center, these numbers attempt to summarize a data set by describing the overall clustering of data in a set

  • The goal of these numbers is to find one single numerical value that can represent the “average” value found in the entire set.


Measures of central tendency1
Measures of Central Tendency

  • The 3 most common measures are:

    • Mean – the average, found by dividing the sum of all the numbers in a data set by the number of pieces of data you collected.

    • Median – the middle value, found by locating the middle number in a ordered data set

    • Mode – the most common value, found by locating the most frequently appearing value in a data set


Tricks of the trade
Tricks of the Trade

  • Median – the cross out method

    • Order your data set from least to greatest

    • Repeatedly cross out the smallest and largest value in your data set until you arrive at the median

    • If you have two values left, add them together and divide by two.

  • Mode – it’s the “MOST”

    • Both four letter words

    • Both begin with MO


Tricks of the trade1
Tricks of the Trade

  • Mean – sorry =(

    • I really am sorry, but you just have to do the math.

    • Add them up, divide by the number of pieces of data in your set.


Practice
Practice

  • Its almost report card time and Sam is worried about his grade. He has made the following scores on his 7 tests in math: 77, 84, 83, 78, 92, 90, 84. Help Sam out by finding his …

    • Mean

    • Median

    • Mode


Practice1
Practice

  • Sam’s football coach told him he was going to be benched if his grade was below a “B”, should Sam be worried? Explain.

  • Which measure of central tendency would give Sam the best grade possible?

  • Which measure of central tendency best reflects Sam’s actual test performance?

  • Are there any outliers in his test scores?


Practice on your own
Practice – On your own

  • A statistician randomly selected 12 7th grade students and asked them how much time they spend each night on homework. The responses were:

    • 0 mins 20 mins 15 mins

    • 1 hour 30 mins 45 mins

    • 15 mins 0 mins 15 mins

    • 30 mins 1 hour 1 hr & 10 mins


Practice on your own1
Practice – On your own

  • What is the average amount of time these students spent on homework?

  • Explain how you determined your answer.

  • Does your answer reflect the mean, the median, or the mode? Explain how you know.

  • If you had found a different measure of central tendency, would you expect your answer to be the same or different? Explain.

  • If a 7th grader spends 15 hours per day at home, what percent of home time does the “average” student spend on homework?


Measures of variability
Measures of Variability

  • Attempt to describe the clustering seen in a set of numbers.

  • The two most common measures of variability are:

    • Range (easy)

    • Interquartile Range (complicated)

  • Range is used quite often, interquartile range is really only seen when creating a box-and-whisker plot


Range
Range

  • Range is quite simply the difference between the largest value and smallest value in a numerical data set.

  • Code word: difference = subtraction

    • EX. 12, 15, 19, 21, 41, 67

    • The range is the largest value (67) minus the smallest value (12), which equals 55.


Interquartile range
Interquartile Range

  • Yes, it is as complicated as it sounds.

  • First, what is a quartile?

    • Think quad, which means four.

  • Ok, so 4 of what?

    • Quartile refers to one of 3 numbers that can break a set of data into 4 even sections.

  • Quartile – a number that creates 4 equal sections of numbers in a distribution


Interquartile range1
Interquartile Range

  • Lets see these quartiles in action!

    • Step 1: Put a set of numbers in order

      • 13, 15, 16, 18, 22, 25, 26

    • Step 2: Find the median

      • 13, 15, 16, 18, 22, 25, 26

      • This separates the data into two sections, exclude the median

      • [13, 15, 16] 18 [22, 25, 26]

      • The median is now called the Second Quartile or Q2.


Interquartile range2
Interquartile Range

  • Step 3: Find the median of the set of numbers less than Q2.

    • [13, 15, 16] 18, 22, 25, 26

    • 13, 15, 16

    • This number is now called the First Quartile or Q1.

  • Step 4: Find the median of the set of numbers greater than Q2.

    • 13, 15, 16, 18, [22, 25, 26]

    • 22, 25, 26

    • This number is now called the Third Quartile or Q3.


  • Interquartile range3
    Interquartile Range

    • Step 5: Find the distance between the Third Quartile and the First Quartile

      • (Q3 – Q1)

        • 13, 15, 16, 18, 22, 25, 26

          Q1 Q2 Q3

          (25 – 15) = 10

          This value is the interquartile range!


    Interquartile range4
    Interquartile Range

    • So why did we do all of that work?

      • What does a range tell us?

        • All values fall between the smallest and largest value……..well duh!!!

      • What does the interquartile range tell us?

        • Half (50%) of all values fall between the first and third quartile.

        • The interquartile range reflects the real “heart” of the data set.


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