Ch. 12 Notes Pages 25P25 12.4: Standard Deviation

Measures of Central Tendency

Mean, median, and mode:98, 95, 99, 97, 89, 92, 97, 62, 90

Box-and-Whisker Plot

Upper Extreme

Lower Quartile

Upper QuartileLower

ExtremeMedian

Average temperatures of water in each month in Pensacola, FL (over 13 months)

Jan: 56 Apr: 71 Jul: 84 Oct: 74

Feb: 58 May: 78 Aug: 86 Nov: 73

Mar: 63 Jun: 84 Sept: 82 Dec: 65

Jan: 58

Box-and-Whisker Plot

***List the data from least to greatest

56, 58, 58, 63, 65, 71, 73, 74, 78, 82, 84, 84, 86

Median of lower part (Q1) = 60.5

Median of data set (Q2) = 73

Median of upper part(Q3) = 83

Standard Deviation

Range: The difference between the greatest and least values

Interquartile Range (IQR): The difference between the 3rd and 1st quartiles (Q3-Q1)

Standard Deviation: How much the values in a data set vary from the mean

***The smaller the standard deviation, the closer all of the numbers are to the mean

Standard Deviation

Finding Standard Deviation:

1. Find the mean of the data set:

2. Find the difference between each value and the mean:

3. Square each difference:

4. Find the average of these squares:

5. Take the square root to find standard deviation:

x

xx

2xx nxx

2

nxx 2)(

Standard Deviation

48.0, 53.2, 52.3, 46.6, 49.9

Finding Standard Deviation with the Calculator

Step 1: Enter data into L1

Step 2: Use the CALC menu of STAT to access the 1-Var Stats option

Daily Energy Demand during Weekends in August

Ch. 12 Notes Page 26P26 12.5: Working with Samples

Samples and Populations

Sample – gathers info from only part of a population

Sample Proportion – the ratio , where x is the number of times an event occurs in sample size n

Random Sample – all members of a population are equally likely to be chosen (so this is a good representation of the population)

n

x

Ex: Students and international travel

Sample: 350 students; 284 haven’t traveled internationally

Sample proportion:

Bias

A news program reports on a proposed school dress code. The purpose of the program is to find out what percent of the population in its viewing area favors the dress code. Identify the bias in each sampling method:

1. Viewers are invited to call the program and express their preferences.

“self-selected”

2. A reporter interviews people on the street near the local high school.

“convenience”

3. During the program, 300 people are selected at random from the viewing area.

“random”

Margin of Error

When a random sample of size n is taken from a large population, the sample proportion has a margin of error of about .

***The larger the sample, the smaller the margin of error!

We use margin of error to give us an interval that is likely to contain the true population proportion

n

1

Using the Margin of Error

A recent poll of 75 people at the mall reported that 64 would rather shop at American Eagle than Eddie Bauer.

1. Sample Proportion

2. Margin of Error

3. Interval likely to contain the true population proportion

12.5 Working with Samples