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Statistics Notes
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12.3 Analyzing Data
Scores:
Mean –
Median –
Mode –
Outlier and its effects–
Quartile –
Group work on Mean, Median, Mode –
1. Find Q1, Q2, and Q3 of the scores from the warm-up.
Box and Whisker Plot -
2. Make a box and whisker plot of the scores from the warm-up.
Range –
3. Find the range of the scores from the warm-up.
Interquartile Range (IQ Range)–
4. Find the interquartile range of the scores from the warm-up.
Your Turn
5. Use the given ACT scores and answer the questions.
Scores:
12.4 and 12.7 Standard Deviation and Normal Distribution
Intro Activity:
Measures of Variation –
Normal Distribution (Draw in the curve and label the parts)-
Standard Deviation –
If the standard deviation of one set of data is 2.8 and another is 2.5 of a second set of
data, how will the distributions compare?
Example 1:
Example 2:
Example 3:
a)
b)
Conclusions:
Other Distributions
Football Means:
Negatively Skewed/Skewed Left (Draw a picture)–
How do the mean and median compare?
Positively Skewed/Skewed Right (Draw a picture)-
How do the mean and median compare?
c)
Finding Standard Deviation
*Calculate your own height in inches. _______________________
*Write the list of heights of students according to your gender in the first column of the
chart below.
Step 1) Find the mean of your list: x
-> Write this number in every box of the second column of the chart below.
Step 2) Find the difference between each value and the mean: x  x
->Take the number in the first column minus the number in the second column to
get the third column. Do this for each row. (some numbers will be negative)
Step 3) Square each difference: (x  x)2
-> Take each number in the third column and square it to get the number in the
fourth column. Do this for each row.
 (x  x)
Step 4) Find the average (mean) of these squares:
2
-> Total up all numbers in the last column
n
-> Take the total and divide by the number of rows
Step 5) Take the square root to find the standard deviation:  
x



2
n
x  x 2
xx
x
 (x  x)

Total
________________________
Standard Deviation ________________________________
Now, sketch the normal curve for this distribution, labeling the x-axis with the values that
are one, two, and three standard deviations from the mean.
Find the mean and the standard deviations for the values: 10, 15, 16, 11, 13
x
x
xx
(x  x)2
Given the standard deviation and the mean draw a number line displaying 3
standard deviations. (   standard deviation and x  the mean)
1.   4.5, x  65
2.   2.3, x  40
3.   3.4, x  89
4.   8, x  116
All together:
With your calculator, find the mean and the standard deviations for the
values: 2, 3, 4, 6, 7, 9, 10, 12, 13, 14