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Drill. Put these numbers in order from least to greatest: {-2, 6, 3, 0, -5, 1, -8, 8} b) Add the #’s together c)Subtract the smallest # from the largest #. Algebra I Statistics Mean, Median, Mode. Day 2. Visual Memory. Mean.

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Drill
Drill

Put these numbers in order from least to greatest: {-2, 6, 3, 0, -5, 1, -8, 8}

b) Add the #’s together c)Subtract the smallest # from the largest #.


Algebra i statistics mean median mode

Algebra IStatisticsMean, Median, Mode

Day 2



Mean

  • The mathematical average, the number you get when you add up all the numbers in the sample space and divide the sum by the amount of numbers there are.


Median
Median

  • After the numbers are put in numerical order the median is the middle #.

  • If two numbers are in the middle you take the mean of those two #’s.


Mode

  • The number that appears the most in the sample space. If more then one number appears the most then they are both the mode.

  • If all numbers appear the same amount of times we say that ALL #’s are the mode.


Range
Range

  • The difference between the largest and smallest numbers. {2, 4, 6, 7, 10}

  • The Range of this set is 8. because 10 – 2 = 8


Find the mean median mode and range for these two sets of s
Find the mean, median, mode and range for these two sets of #’s

{2, 4, 4, 7, 9, 10, 11, 15}

{1, 2, 6, 6, 9, 9, 25, 30}


Examples
Examples #’s

  • Jed’s test scores so far are 86, 95, 78, 87, and 92. What is Jed’s mean score? What is his median score?

  • An article in the newspaper states that the median price of a home in your neighborhood is $275,000 and the mean price is $389,000. Explain what might cause such a large difference in the two measures of central tendency.


Example hsa
Example HSA #’s

  • The newspaper printed the high temperatures for last week, but the temperature for Saturday was smudged. If the mean high temperature for last week was 84 , what was the temperature for Saturday?

Day Sun Mon Tues Wed Thurs Fri Sat

Temp. 78 82 83 80 84 80 **


Outlier s
Outlier(s) #’s

  • An outlier is a number that is far away from the rest of the data.

  • Ex: (2, 4, 5, 8, 10, 13, 48)

  • Ex: (3, 28, 31, 36, 39, 43, 46)


Mean vs median
Mean vs. Median #’s

  • When you have an outlier it can drastically effect the mean. The median will roughly stay the same.

  • When you have an outlier you should use median for the measure of central tendency.

  • When you do not have an outlier you should use the mean.


Find the mean and median for each set of data and determine which measure of central tendency is better.

  • {20, 21, 24, 27, 29, 30, 31, 35}

    b){12, 14, 16, 19, 22, 23, 30, 73}


Example
Example which measure of central tendency is better.

  • Create a box and whisker plot for this set of data:

    {12, 8, 21, 16, 9, 11, 18, 22, 24, 17}


Interquartile range iqr
Interquartile Range (IQR) which measure of central tendency is better.

  • The interquartile range of a set is the difference between the lower and upper quartiles.(Q3 – Q1 = IQR)

  • Find the IQR for the last problem we did.


Algebra 1 which measure of central tendency is better.Statistics(Measures of Central Tendency)Obj: SWBAT determine which measure of central tendency is best for describing the data.


Measures of central tendency
Measures of Central Tendency which measure of central tendency is better.

  • Mean, Median, Mode and Range are all measures of central tendency, because they give us an average of all the values in a data set.

  • (They find the “center” of the set)


Outlier s1
Outlier(s) which measure of central tendency is better.

  • An outlier is a number that is far away from the rest of the data.

  • An outlier can dramatically change the value of the mean and range. (Non-Resistant)

  • But it will not drastically change the median or mode. (Resistant)


Example1
Example which measure of central tendency is better.

Which one(s) of these numbers would be considered an outlier? (If any)

A) {2, 24, 25, 36, 38, 40, 42, 44, 90}

B) {1, 5, 7, 9, 11, 14, 16, 20, 25}


Example2
Example which measure of central tendency is better.

Which measure of central tendency would best describe this set of data? (Why)

{2, 4, 5, 6, 8, 10, 12, 13, 14, 50}


Extra stat topics
Extra Stat Topics which measure of central tendency is better.

  • Misleading Graphs

  • Matrices

  • Percents

  • Random Sample

  • Frequency Distributions


Examples1
Examples which measure of central tendency is better.

  • Find the mean, median, mode and range then state which measure of central tendency is the best one to use.

    {2, 4, 4, 8, 10,12, 15, 15, 20, 88}

Mean: 17.8 Median: 11 Mode: 4, 15 Range: 86

We should choose the median since there is an outlier.


Unit B which measure of central tendency is better.

Sampling


Vocabulary
Vocabulary which measure of central tendency is better.

Sample: A sample is a portion of a larger group, called the population.

If all units in a population are included, then it is called a census.


Example3
Example which measure of central tendency is better.


Vocabulary1
Vocabulary which measure of central tendency is better.

A random sample of a population is selected so that it is representative of the entire population.

A simple random sample must be selected so that every individual in the population has an equal chance of being selected.


Vocabulary2
Vocabulary which measure of central tendency is better.

A stratified random sample is when the population is divided into smaller similar groups. Then a simple random sample is selected from each group.

In a systematic random sample, the items are selected according, to a specific time or item interval.


Vocabulary3
Vocabulary which measure of central tendency is better.

  • All random samples are unbiased.

  • A Biased Sample is when one group or portion of the population is more likely to be picked then another.


Types of bias
Types of Bias which measure of central tendency is better.

  • Convenience: is when people or subjects in the population are simply picked due to the fact they are easy to contact.

  • Voluntary Response: is when the people is the sample are offering their time or choosing to give data. (Ex: phone calls, surveys mailed out, etc..)


Drill1
Drill which measure of central tendency is better.

  • Determine the mean and median prices for 7 different cars shown below:

  • Which measure of central tendency best represents the average price? (Why)


Algebra i matrices and sampling frequency distribution

Algebra I which measure of central tendency is better.Matrices and SamplingFrequency Distribution


Matrices
Matrices which measure of central tendency is better.

  • Matrices are simply used to organize and arrange data.

  • Example:

  • What is the total amount of tests taken by 9th graders?

9th 10th 11th

Tests

Quizzes

HW


9 which measure of central tendency is better.th 10th 11th

L

H

S

Tests

Quizzes

HW

9th 10th 11th

W

H

S

Tests

Quizzes

HW


Sampling
Sampling which measure of central tendency is better.

  • When taking a sample you want the sample to be random and each possible individual in the group must have an equal chance of being selected.


Frequency distribution charts
Frequency Distribution Charts which measure of central tendency is better.

  • A frequency distribution chart tells you how many “items” there are in each group.


Example4
Example which measure of central tendency is better.

  • Find the mean, median, mode and range for this set of data.


Examples2
Examples which measure of central tendency is better.

  • Think of two random ways of selecting 50 students in the school for a survey. Every student in the school must have an equal opportunity to be selected.

  • Make a frequency distribution chart with at least 20 total numbers and find the mean, median, mode and range for the set.


Examples3
Examples which measure of central tendency is better.

  • Find the mean, median, mode and range for each set of numbers.

  • {2, 4, 5, 5, 7, 7, 7, 9, 10, 15}

  • {10, 4, 8, 12, 4, 12, 16, 20, 22}


Algebra 1 box and whisker plots

Algebra 1 which measure of central tendency is better.Box and Whisker Plots

Objective: students will be able to construct a box and whisker plot after finding the five-number summary of a set of data.


Five number summary
Five-Number Summary which measure of central tendency is better.

  • The five number summary of a set of data consists of the median, the upper and lower quartiles and the upper and lower extremes.

  • LE, Q1 (LQ), MED, Q3 (UQ), UE


Extremes
Extremes which measure of central tendency is better.

  • The upper and lower extremes of a set of data are just the maximum and minimum numbers in the set.


Median quartiles
Median (Quartiles) which measure of central tendency is better.

  • The upper and lower quartiles are found by finding the median of the numbers larger then the median of the whole set and the median of the numbers lower then the median of the whole set.


Create a box and whisker plot
Create a Box and Whisker Plot which measure of central tendency is better.

{2, 4, 5, 8, 10, 14, 18}

LE (Min): LQ:

MED: UQ:

UE (Max):


Create a box and whisker plot1
Create a Box and Whisker Plot which measure of central tendency is better.

{8, 10, 14, 20, 24, 38, 42, 48}

LE (Min): LQ:

MED: UQ:

UE (Max):


Stem and leaf plots

Stem and which measure of central tendency is better.Leaf Plots


Drill2
Drill which measure of central tendency is better.

  • Create a Box and Whisker Plot for this set:

    {1, 2, 3, 3, 5, 7, 8, 10}

    Hint: Find Extremes, Quartiles, and the Median.


Stem and leaf plot
Stem and Leaf Plot which measure of central tendency is better.

  • A stem and leaf plot is another way of arranging data to make it easier to analyze.

  • The last digit in the number is known as the leaf and all other digits are known as the stem.


Example5
Example which measure of central tendency is better.

{31, 33, 36, 44, 58, 63, 67}


More examples
More Examples which measure of central tendency is better.

107

  • 10 is the Stem

  • 7 is the Leaf


Try to create a stem and leaf plot
Try to create a stem and leaf plot: which measure of central tendency is better.

{11, 14, 15, 17, 17, 21, 24, 28, 31, 40}


Solution
Solution which measure of central tendency is better.


Example 2
Example #2 which measure of central tendency is better.

11, 13, 14, 14, 32, 33, 27, 29, 10, 41, 25, 32, 39, 42, 35, 27, 19, 23, 47, 42, 20


Solution1
Solution which measure of central tendency is better.


Solution cont
Solution (Cont.) which measure of central tendency is better.


Example 3
Example #3 which measure of central tendency is better.

Best Buy: 30, 35, 40, 20, 25, 23, 45, 50, 55, 60, 43, 35, 32

Toys R Us: 32, 20, 15, 28, 35, 42, 34, 50, 35, 20, 26, 34

Find the mean, median,mode and range for each store.


Drill3
DRILL which measure of central tendency is better.

  • Write each percent as a decimal.

    a) 27% b) 9%

    2) Find Q3 for this set of numbers:

    {3, 5, 6, 8, 12, 15, 18, 20, 21, 22}


Frequency tables
Frequency Tables which measure of central tendency is better.

A frequency table is used to tell you how many of each number are contained in the data set.


Review for test 2
Review For Test 2 which measure of central tendency is better.

1) Box and Whisker Plots

2) (5 Number Summary)

3) Interquartile Range

4) Random Samples

5) Central Tendency

6) Mean, Median, Mode and Range

7) Misleading Graphs

8) Matrices

9) Stem and Leaf Plots


Homework
Homework which measure of central tendency is better.

  • Make 5 Sets of numbers that contain 10 values in each set, with no numbers repeating and create Box-and-Whisker plots for each set of data.

  • Also state the IQR for each set.


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