1 / 16

Statistics and Probability 13.2 Measures of Center and Spread

Essential Question: What are the different graphical displays of data?. Statistics and Probability 13.2 Measures of Center and Spread. 13.2 Measures of Center and Spread. Mean → Average Example 1: Mean Number of Accidents

dex
Download Presentation

Statistics and Probability 13.2 Measures of Center and Spread

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Essential Question: What are the different graphical displays of data? Statistics and Probability13.2 Measures of Center and Spread

  2. 13.2 Measures of Center and Spread • Mean → Average • Example 1: Mean Number of Accidents • A six-month study of a busy intersection reports the number of accidents per month as 3, 8, 5, 6, 6, 10. Find the mean number of accidents per month at the site. Solution: Add all the values, divide by the number of values

  3. 13.2 Measures of Center and Spread • Example 2, Mean Home Prices • In the real-estate section of the Sunday paper, the following houses were listed: • 2-bedroom fixer-upper: $98,000 • 2-bedroom ranch: $136,700 • 3-bedroom colonial: $210,000 • 3-bedroom contemporary: $289,900 • 4-bedroom contemporary: $315,500 • 8-bedroom mansion: $2,456,500 • Find the mean price, and discuss how well it represents the center of the data. $584,433.33

  4. 13.2 Measures of Center and Spread • Median → middle value of a data set • If the number of values is odd, the median is the number in the middle • If the number of values is even, the median is the average of the two middle numbers • Example 3: Median Home Prices • Find the median of the data set in example 2, and discuss how well it represents the center of data.

  5. 13.2 Measures of Center and Spread • Example 3: Median Home Prices • Find the median of the data set in example 2, and discuss how well it represents the center of data. • 2-bedroom fixer-upper: $98,000 • 2-bedroom ranch: $136,700 • 3-bedroom colonial: $210,000 • 3-bedroom contemporary: $289,900 • 4-bedroom contemporary: $315,500 • 8-bedroom mansion: $2,456,500 $249,950

  6. 13.2 Measures of Center and Spread • Mode → data value with the highest frequency • Most often used for qualitative data • Why? • If every value appears the same number of times, there is no mode • If two or more scores have equal frequency, the data is called bimodal (2 modes), trimodal (3 modes), or multimodal.

  7. 13.2 Measures of Center and Spread • Example 4: Mode of a Data Set • Find the mode of the data represented by the bar graph below

  8. 13.2 Measures of Center and Spread • Mean, Median, and Mode of a Distribution • Symmetric Distribution: mean = median • Skewed Left: mean is to the left of the median • Skewed Right: mean is to the right of the median

  9. 13.2 Measures of Center and Spread • Measures of Spread • Variability → spread of the data most least

  10. 13.2 Measures of Center and Spread • Standard Deviation → most common measure of variability • Best used with symmetric distribution (bell curve) • Measures the average distance of an element from the mean • Deviation→ individual distance of an element from the mean

  11. 13.2 Measures of Center and Spread • Standard Deviation • Find the mean • Determine each individual deviation • Square each individual deviation • Find the average of those squared values • This gives you the variance (σ2) • Take the square root of the variance • Denoted using the Greek letter sigma (σ) • Population versus Sample • When dealing with a sample of a population, divide by n-1 instead of n. The result is called the sample standard deviation, and is denoted by s. • As samples become larger, the deviation approaches the population standard deviation

  12. 13.2 Measures of Center and Spread • Find the standard deviation for the data set: • 2, 5, 7, 8, 10 • Find the mean: • Find each individual deviation: • Square each individual deviation: • Find the variance: • Population? Average n: • Sample? Use n – 1: • Take square root of each: • Population standard deviation: • Sample standard deviation: 32/5 = 6.4 4.4, 1.4, 0.6, 1.6, 3.6 19.36, 1.96, 0.36, 2.56, 12.96 37.2/5 = 7.44 37.2/4 = 9.3 σ ≈ 2.73 s = 3.05

  13. 13.2 Measures of Center and Spread • What is cool (but not necessary) to know: • 68% - 96% - 99% of population within 1-2-3 standard distributions • What I want you to know • What a standard deviation is • How to calculate it based on a population • How to calculate it based on a sample

  14. 13.2 Measures of Center and Spread • Assignment (Wed) • Page 862 – 863 • Problems 1 – 13 (odd) • Assignment (Thurs) • Page 862 – 863 • Problems 19 – 25, 35 & 37 (odds)

  15. 13.2 Measures of Center and Spread • Interquartile Range • Measure of variability that is resistant to extreme values • A median divides a data set into an upper & lower half • The first quartile, Q1, is the median of the lower half • The third quartile, Q3, is the median of the upper half • The interquartile range is the difference between the two quartiles, which represents the spread of the middle 50% of data

  16. 13.2 Measures of Center and Spread • Box & Whisker Plot • Need five pieces of data: minimum, Q1, median, Q3, maximum • Box is drawn, with the Q1 and Q3 representing the left and right sides of the box, respectively • Vertical line is drawn at the median • “Whiskers” are horizontal lines drawn from the left side of the box to the minimum, and right side to the maximum

More Related