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

### Algebra 1Box and Whisker Plots

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 #.

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

- 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

- 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

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

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

Examples

- 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

- 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)

- 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

- 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}

Interquartile Range (IQR)

- 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.

Measures of Central Tendency

- 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(s)

- 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)

Example

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}

Example

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

- Misleading Graphs
- Matrices
- Percents
- Random Sample
- Frequency Distributions

Examples

- 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.

Sampling

Vocabulary

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.

Vocabulary

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.

Vocabulary

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.

Vocabulary

- 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

- 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..)

Drill

- Determine the mean and median prices for 7 different cars shown below:
- Which measure of central tendency best represents the average price? (Why)

Matrices

- 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

Sampling

- 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

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

Example

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

Examples

- 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.

Examples

- 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}

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

- 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

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

Median (Quartiles)

- 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.

Drill

- 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

- 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.

Example

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

Try to create a stem and leaf plot:

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

Example #2

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

Example #3

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.

DRILL

- 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

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

Review For Test 2

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

- 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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