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0-12: Measures of center, variation, and position

0-12: Measures of center, variation, and position. 0-12: Center, Variation, and Position. Quantitative Data : Data that has units and can be measured (numerical) Ex: Times for a race, ages of people, Distances Qualitative Data : Data that can be organized into categories

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0-12: Measures of center, variation, and position

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  1. 0-12: Measures of center, variation, and position

  2. 0-12: Center, Variation, and Position • Quantitative Data: Data that has units and can be measured (numerical) • Ex: Times for a race, ages of people, Distances • Qualitative Data: Data that can be organized into categories • Favorite color, hair color, phone numbers

  3. 0-12: Center, Variation, and Position • Mean: • Use the mean to describe the middle of a set of data that DOES NOT have an outlier. An outlier is a data value that is much higher or lower than the other data values in the set. • Median: Middle value in the set when the numbers are arranged in order. • If a set has an even number of values, the median is the average of the two middle numbers. • Use the median to describe the middle of a data set that DOES have an outlier. • Mode: The data item that occurs the most times • Can have 0, 1, or more than one modes

  4. 0-12: Center, Variation, and Position • Example 1: The table shows the number of hits Marcus made for his baseball team. Find the mean, median and mode. • Mean • 26 hits in 6 games • 26/6 ≈ 4.3 hits • Median • Put numbers in order: 2, 3, 3, 5, 6, 7 • Average two middle numbers • 3 + 5/2 = 8/2 = 4 hits • Mode • Number that shows up most often • 3 hits

  5. 0-12: Center, Variation, and Position • Variation: A measure of spread that shows how widely data values vary • Range: Largest value minus smallest value of a set • Example 2: It took Olivia 18, 15, 15, 12, and 14 minutes to walk to school each day. Find the range. • Range = biggest – smallest • = 18 – 12 = 6 minutes

  6. 0-12: Center, Variation, and Position • Quartiles: A measure of position that divides data into four equal sized groups. • The median marks the second quartile (Q2) • The lower quartile (Q1) is the median of the lower half • The upper quartile (Q3) is the median of the upper half • Five-number summary: The minimum, three quartiles, and maximum of a data set.

  7. 0-12: Center, Variation, and Position • Example 3 • The number of boxes of donuts sold for a fundraiser each day for the last 11 days were 22, 16, 35, 26, 14, 17, 28, 29, 21, 17, and 20. Find the five-number summary of this data set. • Put all numbers in order • 14, 16, 17, 17, 20, 21, 22, 26, 28, 29, 35 • Find the median of the data set • Use the data to the left/right of the median to find the lower/upper quartiles • Find the minimum/maximum • The minimum is 14, the lower quartile is 17, the median is 21, the upper quartile is 28 and the maximum is 35

  8. 0-12: Center, Variation, and Position • The difference between the upper and lower quartile is called the interquartile range • 14, 16, 17, 17, 20, 21, 22, 26, 28, 29, 35 • The interquartile range is 28 – 17 = 11 • Outlier: An extremely high or extremely low value when compared with the rest of the set. Outlier data will be more than 1.5 times the interquartile range.

  9. 0-12: Center, Variation, and Position • Example 4: Finding an outlier • Students taking a make-up test received the following scores: 88, 79, 94, 90, 45, 71, 82, 88 • Identify any outliers • Determine Q1 and Q3 • 45, 71, 79, 82, 88, 88, 90, 94 • Interquartile range: 89 – 75 = 14 • Any outliers will be smaller than Q1 – 1.5(IQR) or bigger than Q3 + 1.5(IQR) • 75 – 1.5(14) = 54 • 89 + 1.5(14) = 110 • The outlier is 45 (because it’s smaller than 54) Q3 = 89 Q1 = 75 Q2 = 85

  10. 0-12: Center, Variation, and Position • Assignment • Page P39-P40 • 1 – 17, odds

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