3.6 #5) Robust Measures = 1.5 IQR.
It's possible, all values between q1 and q2, would have to be equal. It's possible that they're all sevens. The resulting boxplot would just be a line.
c) Mean is larger than q3? when set is heavily skewed right.
d) mean is smaller than q1? when set is heavily skewed left.
e) median smaller than q1? impossible.
f) Q3 cannot be smaller than c1, but can be equal.
3.6 #9) Organize them in descending order, find the median (observations 5 and 6), find q1 (observation 3), find q3 (observation 8).
3.6 #31) 10 calories, 50% of the cereals are within 10 calories of each other.
Quantitative data uses mean and median.
Asterisks in a Minitab produced graph denote an outlier.
3.4 Measures of Position (Z-Scores)
What are the measures of spread? range, IQR, five number summary, standard deviation.
What is the best measure of spread? Standard deviation, tells you the average distance an observation is from the mean.
Percentile - Percentage of the data is below a given number. E.G. 95% of people are below this score, 5% of people are above this score.
Median = 50th percentile.
Q1 = 25th percentile.
Q3 = 75th percentile.
Simply a relative measure of position.
To find the observation corresponding to a percentile:
Example for 85th percentile of 12 observations: i = (85/100)12
i=10.2. The 85th percentile is found in the 11th box, because if we rounded down to 10 it would not reflect the 85th percentile.
Z-Score - Standardized Measure (score) used to compare unlike distributions.
SAT
Maximum score: 2400
Mean score: 1500
Standard deviation: 150
ACT
Maximum score: 36
Mean score: 24
Standard deviation: 2.5
Bob scored a 1700 on the SAT.
Sandy scored a 27 on the ACT.
Who scored higher? We cannot tell directly since SAT and ACT are measured on different scales. How do we find out? We use Z-scores to determine how many standard deviations away from the mean each person is.
Z-score formula for a parameter from a population:
Z-score formula for a statistic from a sample:
Z-score value = (observed value - expected value (mean)) /standard deviation
Bob: (1700-1500)/150 = 1.33 standard deviations above the mean.
Sandy: (36-24)/2.5 = 1.2 standard deviations above the mean.
Knowing this, who performed better on the standardized tests? Bob
Example from p. 129.
Mean blood level for lead poisoning: 31.4 micrograms/deciliter
Standard deviation of blood level for lead poisoning: 14.2 micrograms/deciliter
Ryan: 78.26 μg/dl
Megan: 1.58 μg/dl
Kyle: 55.54 μg/dl
Calculate the z-score for each person.
Ryan: 3.3, Megan: -2.1, Kyle: 1.7
If you are unclear on any of this please watch this video
No comments:
Post a Comment