1. (12) students were asked their SAT Math scores:
Warm – Up
(12) students were asked their SAT Math scores:
600, 650, 505, 520, 800, 480,
740, 540, 630, 590, 400, 550
Construct And Describe the Histogram :
HI! I’m SKEWED. …RIGHT?
FREQUENCY
S.A.T. MATH SCORES

2. Hey! I’m Approximately SYMMETRIC. HI! I’m SKEWED to the LEFT
Warm – Up
COMPARE these two distributions:
Hey! I’m Approximately SYMMETRIC.
HI! I’m SKEWED to the LEFT
FREQUENCY
FREQUENCY
S.A.T. MATH SCORES
S.A.T. VERBAL SCORES
SAT Math scores have a higher center than Verbal scores. They both have equal spread.
MATH VERBAL
Center: 700 > 600
Unusualness: Nothing Nothing
Spread: = 480

3. Chapter 5 Describing Distributions Numerically

4. I. CENTER
MEAN = Average.
n = number of observations in data set
MEDIAN = Middle. The Median of a distribution is the MIDDLE number after all ‘n’ observations have been ordered from smallest to largest.
-If n is odd the Median is the center.
-If n is Even the median is the mean of the two center observations.
MODE = Most. The observation with the highest Frequency.

5. II. MEASURING SPREAD QUARTILES
One way to measure spread of a data set is by the Range = difference between Largest and Smallest observations. But there is a better way…
QUARTILES
Quartiles are values used to examine the variability or spread of a set of data.
There are three Quartiles (After the data set is arranged from smallest to largest):
Q1 = The Middle of the First Half of the Data. 25%
Q2 = The Middle or Median of the Data. 50%
Q3 = The Middle of the Second Half of the % Data.

6. Inter-Quartile Range (IQR) = Q3 – Q1
EXAMPLE: 25, 26, 27, 35, 39, 41, 46
Q1 = ? Q2 or Median = ? Q3 = ? 26 35 41
IQR = 15
EXAMPLE: 25, 26, 27, 35, 39, 41, 46, 50
Q1 = ? Q2 or Median = ? Q3 = ?
26.5 37
43.5
IQR = 17
Inter-Quartile Range (IQR) = Q3 – Q1
(The middle 50%)

7. Measure of Spread (continued):
The Standard Deviation = s or sx
The standard deviation measures the spread of a distribution by examining the average difference (deviation) between each observations and the mean.
s2 = Variance

8. Find the Standard Deviation for the following data set: 5, 12, 22
The Mean = 13 and n = 3 so…

9. PAGE 91: 3-7

13. Since the Standard Deviation is the square root of variance then…

14. Find the Standard Deviation for the following data set: 4, 5, 5, 7, 9
The Mean = 6 and n = 5 so…
Find the Standard Dev.
11.5, 12, 14.1, 25.2, 22, 15.8, 28.3, 47.5, 18