3.4 Stats
The 10th percentile of the weight of males 36 months of age in a certain city is 12.0 kg.
10% of 36-month-old males weigh 12.0 kg orless, and 90% of 36-month-old males weigh more than 12.0 kg
Violent crimes include rape, robbery, assault, and homicide. The following is a summary of the violent-crime rate (violent crimes per 100,000 population) for all states of a country in a certain year. Complete parts (a) through (d).
25% of the states have a violent-crime rate that is 273.8 crimes per 100,000 population or less. 50% of the states have a violent-crime rate that is 388.5 crimes per 100,000 population or less. 75% of the states have a violent-crime rate that is 529.1 crimes per 100,000 population or less. IQR = 255.3 (The middle 50% of all observations have a range of 255.3 crimes per 100,000 population.)
Which of the accompanying boxplots likely has the data with the larger standard deviation? Why? ( you need the picture)
Boxplot II likely has the data with the larger standard deviation because the boxplot appears to have a greater spread, which likely results in a larger standard deviation.
Interquartile Range (IQR)=
Q3-Q1
Distribution Shape and Boxplot
Right Skewed: If the median is to the left of the center of the box, the right whisker is longer than the left one Symmetric: If the median is at or near the center of the box, the whiskers are of equal lengths Left Skewed: If the median is to the right of the center of the box, the left whisker is longer than the right one.
Explain the circumstances for which the interquartile range is the preferred measure of dispersion. What is an advantage that the standard deviation has over the interquartile range?
The interquartile range is preferred when the data are skewed or have outliers. An advantage of the standard deviation is that it uses all the observations in its computation.
The _______ represents the number of standard deviations an observation is from the mean.
Z-Score
5 number summary
min= Q1, median=Q2,max= Q3,
_______ divide data sets in fourths.
quartiles
In a boxplot, if the median is to the left of the center of the box and the right whisker is substantially longer than the left whisker, the distribution is skewed
right
z-score
the number of standard deviations a data score is from the mean
Interquartile Range (IQR)
the range of the middle 50% of the observations in a data set
z-score formula for a sample
z = (x - xbar)/s
z-score formula for a population
z = (x - μ)/σ
The 95th percentile of the length of newborn females in a certain city is 53.3 cm.
95% of newborn females have a length of 53.3 cm orless, and 5% of newborn females have a length that is more than 53.3 cm.
