Transcript Standard Deviation

Ch. 12 Notes Pages 25
P25 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
Lower
Extreme
Lower
Quartile
Median
Upper
Quartile
Upper
Extreme
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
Median of
upper part(Q3)
Median of
lower part (Q1)
= 83
= 60.5
56, 58, 58, 63, 65, 71, 73, 74, 78, 82, 84, 84, 86
Median of
data set (Q2) =
73
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:
x
2. Find the difference between each value and the mean:
3. Square each difference:
x  x 
xx
2
4. Find the average of these squares:

x  x 
2
n
5. Take the square root to find standard deviation: 


( x  x) 2
n
Standard Deviation
48.0, 53.2, 52.3, 46.6, 49.9
Finding Standard Deviation with the Calculator
Daily Energy Demand during Weekends in August
Step 1: Enter data
into L1
Step 2: Use the
CALC menu of STAT
to access the 1-Var
Stats option
Ch. 12 Notes Page 26
P26 12.5: Working with Samples
Samples and Populations
Sample – gathers info from only part of a population
Sample Proportion – the ratio
an event occurs in sample size n
x
n,
where x is the number of times
Random Sample – all members of a population are equally likely
to be chosen (so this is a good representation of the population)
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
.

1
n
***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
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