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Essential Question: What are the different graphical displays of data?

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Presentation on theme: "Essential Question: What are the different graphical displays of data?"— Presentation transcript:

1 Essential Question: What are the different graphical displays of data?

2  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  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  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  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  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  Example 4: Mode of a Data Set  Find the mode of the data represented by the bar graph below

8  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  Assignment  Page 862 – 863  Problems 1 – 17 (odd)

10 Essential Question: What are the different graphical displays of data?

11  Measures of Spread  Variability → spread of the data mostleast

12  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

13  Standard Deviation 1) Find the mean 2) Determine each individual deviation 3) Square each individual deviation 4) Find the average of those squared values ▪ This gives you the variance ( σ 2 ) 5) 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

14  Find the standard deviation for the data set:  2, 5, 7, 8, 10 1) Find the mean: 2) Find each individual deviation: 3) Square each individual deviation: 4) Find the variance: a)Population? Average n: b)Sample? Use n – 1: 5) Take square root of each: a)Population standard deviation: b)Sample standard deviation: 32 / 5 = , 1.4, 0.6, 1.6, , 1.96, 0.36, 2.56, / 5 = / 4 = 9.3 σ ≈ 2.73 s ≈ 3.05

15  Using the calculator  TI Calculators ▪ Make a list (2 nd, minus sign, edit) ▪ Go into statistical functions (2 nd, plus sign, Calc) ▪ Choose “OneVar” ▪ Go into list (2 nd, minus sign, names) ▪ Choose the appropriate list  Casio Calculators ▪ Menu (Stat – Menu item #2) ▪ Make a list ▪ Calc (F2) ▪ 1Var (F1)

16  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  What is cool (but not necessary) to know:  68% - 96% - 99% of population within standard distributions

17  Box & Whisker Plot  Need five pieces of data: minimum, Q 1, median, Q 3, maximum  Box is drawn, with the Q 1 and Q 3 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

18  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, Q 1, is the median of the lower half ▪ The third quartile, Q 3, is the median of the upper half  The interquartile range is the difference between the two quartiles (Q3 – Q1), which represents the spread of the middle 50% of data

19  Assignment  Page 862 – 863  Problems 19 – 37 (odd)


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