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

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 values3 8 5 6 6 10 38

6.36 6

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

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.

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

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.

Example 4: Mode of a Data Set Find the mode of the data represented

by the bar graph below

02468101214

Purple Orange Red Green Blue

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

Assignment Page 862 – 863 Problems 1 – 17 (odd)

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

Measures of Spread Variability → spread of the data

6 6 5 6

7 7 7

8 5 8 1 9 8

9 1 9 9 9 1 5

10 1 5 9 10 1 5 9 10 1 3 5 7 9

11 1 9 11 11 5 9

12 5 12 1 9 12

13 13 13

14 14 5 14most least

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

Standard Deviation1) Find the mean2) Determine each individual deviation3) Square each individual deviation4) Find the average of those squared values▪ This gives you the variance (σ2)

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

Find the standard deviation for the data set: 2, 5, 7, 8, 101)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 = 6.4

4.4, 1.4, 0.6, 1.6, 3.619.36, 1.96,

0.36, 2.56, 12.96

37.2/5 = 7.4437.2/4 = 9.3

σ ≈ 2.73

s ≈ 3.05

Using the calculator TI Calculators▪ Make a list (2nd, minus sign, edit)▪ Go into statistical functions (2nd, plus sign, Calc)▪ Choose “OneVar”

▪ Go into list (2nd, minus sign, names)▪ Choose the appropriate list

Casio Calculators▪ Menu (Stat – Menu item #2)▪ Make a list▪ Calc (F2)▪ 1Var (F1)

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 1-

2-3 standard distributions

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

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 (Q3 – Q1), which represents the spread of the middle 50% of data

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