JV Stats HW & Test # 2

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JV Stats HW &amp; Test # 2. OUTLIER FORMULAS BOX PLOTS HISTOGRAMS DESCRIBING A DISTRIBUTION (C.U.S.S.) STANDARD DEVIATION AND VARIANCE. Test #1. Splitting Stems was used in these stemplots. Per 4. Per 2. Period 2 test scores. Find the Median, also called Q 2. 69. Period 2 test scores.

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JV Stats HW & Test # 2
• OUTLIER FORMULAS
• BOX PLOTS
• HISTOGRAMS
• DESCRIBING A DISTRIBUTION (C.U.S.S.)
• STANDARD DEVIATION AND VARIANCE
Test #1

Splitting Stems was used in these stemplots

Per 4

Per 2

Period 2 test scores

Find the Median, also called Q2

69

Period 2 test scores

Find Q1 which is median below the Median

59

Find Q3 which is median above the Median

79

Period 2 test scores

Give the 5-# summary which is

Min, Q1 , Q2 , Q3 , Max

41,59,69,79,97

IQR is the interquartile range

IQR = Q3 – Q1

20

Period 2 test scores

Checking for Outliers. We have formulas to check high and low numbers

TO CHECK for a LOW OUTLIER

Q1 – 1.5(IQR) any # smaller is an outlier

TO CHECK for a HIGH OUTLIER

Q3 + 1.5(IQR) any # larger is an outlier

Create a box plot

Outliers

Min, Q1 , Q2 , Q3 , Max

Create a box plot of your test scores
• Start with a number line below your box plot
• Make your increments consistent
• Draw the box accurately
Period 4 test scores

Find the Median, also called Q2

69

Period 4 test scores

Find Q1 which is median below the Median

59

Find Q3 which is median above the Median

83

Period 4 test scores

Give the 5-# summary which is

Min, Q1 , Q2 , Q3 , Max

41,59,69,83,97

IQR is the interquartile range

IQR = Q3 – Q1

24

Period 4 test scores

Checking for Outliers. We have formulas to check high and low numbers

TO CHECK for a LOW OUTLIER

Q1 – 1.5(IQR) any # smaller is an outlier

TO CHECK for a HIGH OUTLIER

Q3 + 1.5(IQR) any # larger is an outlier

Create a box plot

Outliers

Min, Q1 , Q2 , Q3 , Max

Create a box plot of your test scores
• Start with a number line below your box plot
• Make your increments consistent
• Draw the box accurately
C.U.S.S.
• This acronym is used to compare two or more distributions(graphs)

C: center……give the mean and median

U: unusual features……are there outliers?

S: shape……skewed left, skewed right, fairly symmetric….etc

S: spread……..give the range….(max – min)

Period 2 has a mean of 69.5 and period 4 has a mean of 69.7. Both classes have a median of 69. There are no outliers for either class. Both distributions are fairly symmetric. Both classes had a min score of 41 and a max score of 97.

Find the 5 # Summary and check for outliers

{3,5,2,6,5,1,9,7,4,2,3,23}

If you need to, put them in order

1,2,2,3,3,4,5,5,6,7,9,23

5 # Summary {1,2.5,4.5,6.5,23}

Mystery box plot
• Here is the 5 # summary of a distribution of a set of 12 numbers

{1,7,9,13,22}

a) Is it possible that there is no number 9 in the set of numbers? Explain.

Yes, since there is an even number of numbers in the set, there is no exact middle number.

Example. {1,2,7,8,8,10,10,13,19,22}

Mystery box plot
• Here is the 5 # summary of a distribution of a set of 23 numbers

{1,7,9,13,22}

a) Is it possible that there is no number 9 in the set of numbers? Explain.

No, since there is an odd # of numbers in the set, the median must be a number in the set.

Create your set of data
• Create a set of data with 20 numbers.
• Make sure there are 2 low outliers and 2 high outliers.
• Show your outlier formulas to prove that your set meets these requirements.
• Create a box plot of your data.
Quartiles
• A Box Plot is made up of Q1, Q2, and Q3.
• These are called quartiles because they split the box plot into 4 parts.

1

2

3

4

Q1

Q2

Q3

Each of the 4 parts contain 25% of the data

Standard Deviation & Variance
• Consider the following set of numbers

{1,1,2,2,3,4,5,6,7,9}

Find the Mean.

Find the distance each # is from your mean, square all those distances and add them up

Divide that sum by (n-1)…..this is the Variance

Take the square root of the Variance. Now you have the Standard Deviation

What is standard deviation
• It is the average distance the set of numbers are from the mean.
• It is a measure of spread.
• Lower standard deviation means that the numbers in the set are grouped closely around the mean
• High standard deviation means that the numbers in the set are widely spread and may possibly have outliers

Find the 5 # Summary {0,16,32,53,73}

• Check for Outliers

Q1 – 1.5(IQR)…….16 – 1.5(37) = -39.5

Q3 + 1.5(IQR)…….53 + 1.5(37) = 108.5

There are NO OUTLIERS

• Draw the Box Plot
• Describe the distribution(C.U.S.S.)

The mean is 34.3 and the median is 32. There are no outliers. The distribution is fairly symmetric and the range is from 0 to 73.

Histograms
• How many times did you go out to eat over the weekend?
• Before we create our histogram we need to make a frequency table.
Different types of histograms

Bars are centered on the numbers

Bars are for a given range

Your data will help you decide which type is better

Outfiers affect Range, Mean, Variance, and Standard Deviation. An outlier causes all these to increase or decrease

Outliers do not affect the median and IQR.

Coin in a cup activity

Given 3 minutes for your strong hand and 3 minutes for your weak hand. How many quarters can you bounce in a cup? Is your strong hand better than your weak?

To reduce bias student flipped a coin to determine whether they would use their strong or weak hands for the first 3 minutes. This is done because students may learn how to bounce their coins and get better the second time around.

Compare the Strong and Weak

C.U.S.S.

The median of the strong is 3.5 and the median of the weak is 2. The mean of the strong is 4.1 and the mean of the weak is 3.5. There are no outliers. Both distributions are skewed to the right. The strong ranges from 0 to 12 and the weak ranges from 0 to 10.

Check for outliers

1,25,23,38,45,45,48,53,67,72,76

Check for outliers

1,25,23,38,45,45,48,53,67,72,76

Create a boxplot

1,25,23,38,45,45,48,53,67,72,76

Times(seconds) to Text Phrase

Boys

(25,31.5,40,45,120

Girls

(22,29,34,48,78)

Per 2

BOYS

GIRLS

Describe the Distribution(C.U.S.S.)

Also use this to compare multiple distributions

Times(seconds) to Text Phrase

Boys

(31,40,42,53,53)

Girls

(25,34,40.5,46.5,66)

Per 4

BOYS

GIRLS