Math week 5
c. What shape would you expect for the distribution?
The distribution would probably be symmetric because the distribution of monthly sales of sunglassessunglasses has its peak in the summersummer months becausebecause of theof the needneed forfor sunglassessunglasses thenthen.
c. What shape would you expect for the distribution?
The distribution would probably be left-skewed because many of the students got an A, and very few got a C.
c. What shape would you expect for the distribution?
The distribution would probably be right-skewed because there is a clear minimum amount of rainfall but no obvious maximum amount.
In my data set of 10 exam scores, the median turned out to be the score of the person with the third highest grade. No two people got the same score.
This does not make sense because the median value should be between the fifth and sixth highest scores.
b. Make a sketch of the distribution. Choose the correct answer below.
left-skewed (peak on the right)
medianequals=7474, meanequals=7272, low scoreequals=1717, high scoreequals=80
left-skewed; high variation
What are outliers? Describe the effects of outliers on the mean, median, and mode.
An outlier in a data set is a value that is much higher or much lower than almost all other values. An outlier can change the mean of a data set, but does not affect the median or mode.
What do we mean when we say that a distribution is symmetric? Give simple examples of a symmetric distribution, a left-skewed distribution, and a right-skewed distribution.
A single-peaked distribution is symmetric if its left half is a mirror image of its right half.
b. Make a sketch of the distribution. Choose the correct answer below.
right-skewed (peak on left side)
b. Make a sketch of the distribution. Choose the correct answer below.
symmetric single peak
Give a simple example of a symmetric distribution. Choose the correct answer below.
The heights of a sample of 100 women is a symmetric distribution.
The individual weights of oranges in a 5-pound bag.
The mean because there are likely to be few outliers.
Define and distinguish among mean, median, and mode. Choose the correct description of the mean below.
The mean is the sum of all the values divided by the number of values. It can be strongly affected by outliers.
Per capita earnings in New York City.
The median because it is unaffected by outliers.
Choose the correct description of the median below.
The median is the middle value in a data set. It is not affected by outliers.
Choose the correct description of the mode below.
The mode is the most common value in a data set. It is not affected by outliers.
Give a simple example of a right-skewed distribution. Choose the correct answer below.
The number of books read during the school year by fifth graders is a right-skewed distribution.
Give a simple example of a left-skewed distribution. Choose the correct answer below.
The speed of cars on a road where a visible patrol car is using radar to detect speeders is a left-skewed distribution.
I made a distribution of 15 apartment rents in my neighborhood. One apartment had a much higher rent than all of the others, and this outlier caused the mean rent to be higher than the median rent.
The statement makes sense because an outlier with a large value increases the mean, but does not affect the median.
In a data set of 10 exam scores, in which no two people got the same score, the mean was equal to the score of the person with the third highest grade.
The statement makes sense because the data could be skewed towards the higher scores, causing the mean to be equal to the third highest grade.
d. What variation would you expect in the distribution?
The variation would probably be large because many students got an A, some got a B, and a small number got a C, and so the data are not clustered.
d. What variation would you expect in the distribution?
The variation would probably be large because there would likely be several cities with very different amounts of rainfall.
d. What variation would you expect in the distribution?
The variation would probably be large because there would likely be several months with very different numbers of sunglassessunglasses sold.
Consider the distribution of exam scores (graded from 0 to 100) for 7878 students when 3636 students got an A, 2424 students got a B, and 1818 students got a C. Complete parts (a) through (d) below. how many peaks would you expect for the distribution?
There would probably be one peak because there are no obvious reasons why the exam scores would form different groups.
Consider the distribution of the annual rainfall in 113113 cities selected randomly throughout the United States. Complete parts (a) through (d) below. a. How many peaks would you expect for the distribution?
There would probably be one peak because there are no obvious reasons why the values of the annual rainfall would form different groups.
Consider the distribution of the monthly sales of sunglassessunglasses over a one-year period at a store in Orlando comma FLOrlando, FL (the distribution will look best if you start from JanuaryJanuary). Complete parts (a) through (d) below. a. How many peaks would you expect for the distribution?
There would probably be one peak corresponding to the summersummer months.
