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Prob & Stat 1.1-1.4
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Stand tall The heights of the 25 students in Mrs. Navard’s statistics class have a mean of 67 in. and a standard deviation of 4.29 in. Find the standardized score (z-score) for Boris, a member of the class who is 76 in. tall.
2.1
Estimate and interpret the 60th percentile of this distribution.
60%
What is the percentile for a lamp that lasted 900 hours?
40th
Asher’s height is at the 88th percentile of the distribution. Interpret this value in context. How tall is Asher?
Asher’s height is larger than 88 percent of the 25 students in Mrs. Navard’s statistics class. (0.88)(25) = 22, so Asher is taller than 22 of the 25 students. A
Find the percentile for Lynette, the student who is 65 in. tall.
36th
Make a boxplot to display the data.
min=43, Q1=82, Med = 87.75, Q3 = 93, Max=98, 43 & 45= outliers
Identify any outliers in the distribution
no outliers
Calculate and interpret the standard deviation.
5.4 mg/dec
Find the interquartile range. Interpret this value in context.
5 pairs
Find the range of the distribution.
55 min
Which measure of center better describes a typical birthrate? Explain.
The median better summarizes the center of the distribution because the birth rate distribution is skewed to the left.
Explain how the mean and median would compare.
The mean will be less than the median because the mean is pulled toward the long tail in this left- skewed distribution.
Calculate Joey’s mean quiz grade. Show your work.
84
Find and interpret the median.
83
Describe the shape of the distribution.
The histogram of average travel times, in minutes, is fairly symmetric with one major peak from 22-25. There are gaps in the 16 to <17 interval, the 19 to <20 i
In what percent of states is the average travel time at least 20 min?
84.3%
Make a histogram that displays the distribution of IQ scores effectively.
histogram
Make a steam plot
steam plot
Which value appears to be an outlier? Give the stemplot a key using this value.
84°
Describe the shape of the distribution.
slightly left-skewed with a single peak on the 105 - 109 stem and a gap from 84 to 93.
What’s wrong with Herschel’s dotplot?
stacked in one tall column
What percent of its games did the 2012 U.S. women’s team win?
84%
Explain what the dot above –1 represents.
lost one game by 1 goal.
How fuel efficient? Here are the EPA estimates of city gas mileage in miles per gallon (mpg) for the sample of 21 model year 2014 midsize cars.19 Make a dotplot of these data.
dot plot.
Make a relative frequency bar chart for these data. Describe what you see.
Bar chart
Explain how this graph is misleading.
Based on the heights of the people, it appears that the peak of social media use is ages 50-64, but really it is ages 19-29.
Would it be appropriate to make a pie chart of these data? Explain.
Yes b/c %
Make a bar chart to display the data. Describe what you see
For vehicles sold worldwide in 2014, white (29%) and black (19%) were the most popular colors while green (1%) was the least popular color.
What percent of vehicles would fall in the “Other” category?
2%
What is the relative frequency of January?
17.5%
What is the frequency of June?
5
What is the relative frequency of October?
2.5%
What is the frequency of April?
6
Which sections are Categorical?
State, gender, marital status.
Which sections are Quantitative?
Time (minutes), box office sales (dollars).
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