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Statistics and Data Analysis

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Organizing, Summarizing, &Describing Data

Probability

Summer

is about...

Displaying Data

Family of Distributions

Center

Spread

Shape

Slope Triangles

Standard Deviation

5 Number Summary & Box Plot

Histogram

Mean

Stem and Leaf Plot

When is it better to use a histogram than a boxplot?

What does standard deviation tell you?

How are the boxplot and histogram limited in what they can tell you about the data?

How do outliers influence the mean?

What does the spread tell you about the data?

Why can’t you make a histogram with categorical data?

When would you use a bar graph instead of a pie chart?

UNIT SELF-TEST QUESTIONS

Bill Gates makes $500 million a year. He’s in a room with 9 teachers, 4 of whom make $40k, 3 make $45k, and 2 make $55k a year. What is the mean salary of everyone in the room? What would be the mean salary if Gates wasn’t included?

Mean With Gates:

$50,040,500

Mean Without Gates:

$45,000

How do we determine if a number is an outlier

?

To find any outliers in a set of data, we need to find the 5 Number Summary of the data.

- Step 1 - Find the median: the middle value in a data set when you put the numbers in order.
18, 40, 50, 58, 59, 59, 61, 68, 69, 70, 70, 71, 80, 93, 100

68 is the median of this data set.

- Find the lower quartile.
- The lower quartile is the middle of the data set to the left of median.
(18, 40, 50, 58, 59, 59, 61), 68, 69, 70, 70, 71, 80, 93, 100

58 is the lower quartile

- Find the upper quartile.
- The upper quartile is the middle of the data set to the right of the median.
18, 40, 50, 58, 59, 59, 61, 68, (69, 70, 70, 71, 80, 93, 100)

71 is the upper quartile

- Find the maximum and minimum values in the set.
- The maximum is the greatest value in the data set.
- The minimum is the least value in the data set.
18, 40, 50, 58, 59, 59, 61, 68, 69, 70, 70, 71, 80, 93, 100

18 is the minimum and 100 is the maximum.

Find the Interquartile Range (IQR)

18, 40, 50, 58, 59, 59, 61, 68, 69, 70, 70, 71, 80, 93, 100

= 19.5

- Mark the upper and lower fence
- lower fence (LF):Q1 – 1.5×IQR
- Upper fence (UF): Q3 + 1.5×IQR
If LF and UF is within data set mark boundaries and Dot in outliers (otherwise keep max min marks)

18, 40, 50, 58, 59, 59, 61, 68, 69, 70, 70, 71, 80, 93, 100

30.5

90.5

The weights of 20 randomly selected juniors are recorded below:

a) Construct a boxplot of the data

b) Determine if there are any mild or extreme outliers.

Q1 = 130.5median = 138Q3 = 145.5

Min = 121Max = 213IQR = 15

UF = 168 LF = 108

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Weight

Quick Write: Compare these two boxplots

- If the median is at the center of the box and each horizontal line the data is symmetric
(mean is equal to the median)

- median is to the left of the center then data is skewed right
(mean is right of median)

- median is to the right of the center then data is skewed left (mean is left of median)