Transcript Data Analysis: Part 2

Data Analysis: Part 2
Lesson 7.1 & 7.2
1/11-12/12
Data Analysis: Part 2
• MM2D1. Using sample data, students will
make informal inferences about population
means and standard deviations.
• a. Pose a question and collect sample data
from at least two different populations.
• b. Understand and calculate the means and
standard deviations of sets of data.
• c. Use means and standard deviations to
compare data sets.
Data Analysis: Part 2
• d. Compare the means and standard deviations of
random samples with the corresponding
population parameters, including those
population parameters for normal distributions.
• Observe that the different sample means vary
from one sample to the next.
• Observe that the distribution of the sample
means has less variability than the population
distribution.
Data Analysis: Part 2
Solve for the mean, median, mode, range,
quartile for the following data set.
71, 70,68,74,73,67,66,75,74,68,70,75,73,73,72,
67, 68,63, 72, 70
**Homework/Answers**
Data Analysis: Part 2
EQ: What is a variance? What is standard
deviation?
Today you will begin to learn about data analysis
as we learn about variance and standard
deviation!!
Data Analysis: Part 2
How to create a box and whisker plot
Step 1: Place the elements of the data set in numerical order
Step 2: Find median of the entire set (Q2)
Step 3: Find the median of lower quartile (Q1) and median of
upper quartile (Q3)**If the number of data in the data set
is EVEN include the middle values to compute the Q1 & Q3
medians; If data set id ODD DO NOT include the middle
value for the entire data set***
Step 4: Identify the range value (maximum and minimum
elements) of data set
**The box provides you with the central value of the data set;
The whiskers represents the minimum and maximum
values of the data set**
Data Analysis: Part 2
Subjective vs. Random Sample
Example: Height, Age, Food
Data Analysis: Part 2
Examples: Create a box and whisker plot for
following data sets
Data set: 16, 25, 40, 72, 53, 84, 66, 42, 51, 22,
35, 17, 26, 48, 36, 59, 60, 64, 29, 71
Data set: 5.2, 9.1, 4.5, 1.3, 5.9, 8.4,
6.7,4.2,6.0,9.0, 10.5, 2.8, 4.7, 5.5, 4.5
Data Analysis: Part 2
RANDOM NUMBER GENERATOR- a machine or
program that will generate random numbers
Ex: Random Number Table, Random Number
Option on Calculator
Data Analysis: Part 2
Steps to find a Random Numbers using TI-30XIIS
Calculator:
Press PRB
Use R arrow until come to RANDI
Press Enter
Press number want to start with comma number
want to stop with **Values will be include within
parenthesis and to get comma press 2nd close
parenthesis button**
Data Analysis: Part 2
Examples:
Example#1
Random numbers for the interval [1, 100]
Example #2
Random numbers for the interval [5, 20]
Example #3
Random numbers for the interval (20, 40)
Example #4
Random numbers for the interval (18, 36)
Data Analysis: Part 2
Fact: The distribution a set of data can be
measured using the population distribution or
a sample distribution
Fact: The population distribution is categorized
by the mean and standard deviation
Data Analysis: Part 2
• VARIANCE- the value that is the average squared
distance between the mean and each data point of the
data set.
𝑁
(𝑥ᵢ − 𝑥)²
𝑖=1
Formula: **you must divide the summation by N-1**
N= the number of data points
X= the mean of data set
xᵢ = the ᵢth data point
Data Analysis: Part 2
• STANDARD DEVIATION-this is the value that
represents the square root of the variance
𝑁
(𝑥ᵢ − 𝑥)²
𝑖=1
Formula: **you must divide the summation by
N-1**
Data Analysis: Part 2
IMPORTANT FACT:
The mean, variance, and standard deviation of a
random sample can fairly accurately characterize
the whole population!!!!!!!!!!!
Data Analysis: Part 2
Calculate the variance and standard deviation of
the following data set
Example #1 Prices of cars at a dealership:
12,000 14,500 22,000 17,750 13,450 16,875
56,000 12,750 13,650 14,735
Data Analysis: Part 2
Calculate the variance and standard deviation of
the following data set
Example #1 Plant Heights (in centimeters)
10 14 11 12 10 13 13 12 13 12
Data Analysis: Part 2
Calculate the variance and standard deviation of
the following data set
Example #1 Scores on an English test:
54 68 53 75 42 48 70 58 64 63
Data Analysis: Part 2
Homework: Skills pg. 463-467
Problem Set #1 (2-5)
(7-10)
(12-22)
Data Analysis: Part 2
Activation: Solve for the mean, median, mode, range,
quartile for the following data set.
71, 70,68,74,73,67,66,75,74,68,70,75,73,73,72,
67, 68,63, 72, 70
Instruction: Notes on Box and Whisker Plot, Variance, and
Standard Deviation
Work: Complete Guided Examples on Box and Whisker
Plot, Variance, and Standard Deviation
Assessment: Unit 4 Test
Summary: Write the definition of variance and standard
deviation