Download Chapter 4 Part 3 Notes: Displaying Quantitative - peacock

Chapter 4 Part 3 Notes: Displaying Quantitative Data
When describing distributions, we need to discuss _____________________,
___________________ and ______________________. How we measure the center and
spread of a distribution depends on its ___________________________. The center of a
distribution is a “typical” value. If the shape is unimodal and symmetric, a “typical” value is
in the _________________.If the shape is skewed, however, a “typical” value is not
necessarily in the middle.
A measure of central tendency for a collection of data values is a number that is meant to
convey the idea of ___________________ or _____________ of the data set. The most
commonly used measures of central tendency for sample data are the: ___________,
____________, and ___________.
Calculate Mean on TI-84 – Your Turn:
Raw Data:
548, 405, 375, 400, 475, 450, 412
375, 364, 492, 482, 384, 490, 492
490, 435, 390, 500, 400, 491, 945
435, 848, 792, 700, 572, 739, 572
_______________
Calculate Mean on TI-84 – Your Turn:
Frequency Table Data (same):
_______________
The mean:

is the arithmetic ________________________of the data values

is the ___________________________of a histogram

has the same ___________________________as the data

is _________________________to outliers

is given by the formula
The median:

is the ________________________data value (when the data have been
________________) that divides the histogram into two equal
_______________________

has the same _______________________as the data

is ________________________________to outliers (extreme data values)
Find the Mean and Median – Your Turn:
CO2 Pollution levels in 8 largest nations measured in metric tons per person:
2.3, 1.1, 19.7, 9.8, 1.8, 1.2, 0.7, 0.2
a. Mean = 4.6 Median = 1.5
b. Mean = 4.6 Median = 5.8
c. Mean = 1.5 Median = 4.6
Summary Measures of Center:
Effect of Skewed Distributions:
The figure below shows the relative positions of the mean and median for right-skewed,
symmetric, and left-skewed distributions.
_______________________
_____________________
______________________
To choose between the mean and median, start by looking at the distribution.

__________________ is used, for unimodal symmetric distributions, unless extreme
values (outliers) exist.

__________________ is used, for skewed distributions or when there are outliers
present, since the median is not sensitive to extreme values.
Class Problem:
Observed mean =2.28, median=3, mode=3.1. What is the shape of the distribution and why?
_____________________________________________________________________________
A measure of _____________________ for a collection of data values is a number that is
meant to convey the idea of spread for the data set.

The most commonly used measures of variability for sample data are the:

____________________________________

____________________________________

____________________________________
The interquartile range (IQR):

contains the _________________________of the data

is the difference between the _____________________and
___________________quartiles

is a____________________, NOT an _____________________

is _____________________ to outliers
Calculate IQR - Your Turn:
The following scores for a statistics 10-point quiz were reported. What is the value of the
interquartile range?
7, 8, 9, 6, 8, 0, 9, 9, 9, 0, 0, 7, 10, 9, 8, 5, 7, 9
___________________
The ________________________________ of a distribution reports its minimum, 1st quartile
Q1, median, 3rd quartile Q3, and maximum in that order. Obtain 5-number summary from
______________________________.
Calculate 5 Number Summary – Your Turn:
The grades of 25 students are given below : 42, 63, 47, 77, 46, 71, 68, 83, 91, 55, 67, 66, 63,
57, 50, 69, 73, 82, 77, 58, 66, 79, 88, 97, 86. Calculate the 5 number summary for the student’s
grades.
____________________________________________
Calculate 5 Number Summary – Your Turn:
A group of University students took part in a sponsored race. The number of laps completed is
given in the table.
Calculate the 5 number summary. _______________________________________
A more powerful measure of spread than the IQR is the _____________________________,
which takes into account how far each data value is from the mean. To calculate the standard
deviation you must first calculate the ___________________________.
The standard deviation:

measures the “typical” distance each data value is from the
________________________

Because some values are above the mean and some are below the mean, finding
the sum is not useful (positives cancel out negatives); therefore we first
______________________the deviations, then calculate an
_________________________. This is called the_____________________. This
statistics does not have the same units as the data, since we squared the deviations.
Therefore, the final step is to take the ___________________of the variance, which
gives us the _________________________.

is given by the formula

is ___________________to outliers, since its calculation involves the _______________
Calculate Standard Deviation – Your Turn:
The prices ($) of 18 brands of walking shoes: 90, 70, 70, 70 , 75, 70, 65, 68, 60, 74, 70, 95, 75,
70, 68, 65, 40, 65. Calculate the standard deviation.
____________________________
Calculate Standard Deviation – Your Turn:
During 3 hours at Heathrow airport 55 aircraft arrived late. The number of minutes they were
late is shown in the grouped frequency table.
Calculate the standard deviation for the number of minutes late.
______________________________
Standard Deviation – Properties

The value of s is always ___________________.

s is ______________ only when all of the data values are the same number.

_________________ values of s indicate _________________ amounts of variation.

The units of s are the _______________ as the units of the original data. One reason s is
preferred to __________________.

Measures spread about the _________________.

_____________________ (like the mean), s can increase dramatically due to
___________________.
The range:

is the difference between the ________________________value and the
_____________________value

is a __________________________, NOT an _____________________

is ______________________to outliers
For symmetrical distributions, use the ________________________to determine the
_____________________of the distribution and the ________________________to describe
the ____________________________of the distribution.
For skewed distributions, use the ___________________________to determine the
____________________of the distribution and the ______________________to describe the
______________________of the distribution.
Find the mean and standard deviation of the average number of hours spent watching TV per
week for this class.
____________________________
How to Describe a Quantitative Distribution:
In any graph, look for the ______________________ and for striking _____________________
from that pattern.
Describe the overall pattern of a distribution by its:
•
S_____________
•
O_____________
•
C_____________
•
S_____________
Don’t forget your ____________________________!
Describe the Distribution – Your Turn:
The table and dotplot below displays the Environmental Protection Agency’s estimates of
highway gas mileage in miles per gallon (MPG) for a sample of 24 model year 2009 midsize
cars. Describe the shape, center, and spread of the distribution. Are there any outliers?
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
Describe the Distribution – Your Turn:
Smart Phone Battery Life:
Here is the estimated battery life for each of 9 different smart phones in minutes. Describe the
distribution.
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
Assignment: Watch the all 3 Chapter 4 videos.