National Park rangers keep data on the bears that inhabit their park. Below is a histogram of the weights of bears measured in a recent year.
Which statement below is correct?
(a) The median will lie in the interval (), and the mean will lie in the interval ().
(b) The median will lie in the interval (), and the mean will lie in the interval ().
(c) The median will lie in the interval (), and the mean will lie in the interval ().
(d) The mean will lie in the interval (), and the median will lie in the interval ().
(e) The mean will lie in the interval (), and the median will lie in the interval ().
The correct statement is that the median will lie in the interval and the mean will lie in the interval i.e., correct option is (a).
We are given with the histogram of the weights of bears measured in a recent year and we have to find out the mean and median interval.
Now, as we know that in this histogram the distribution is skewed towards right because the lowest bars in the histogram are towards right and A right skewed distribution has the property that mean is larger than median.
So, in this median lies in the interval of highest bars and that is why will contain the median.
As the mean is larger than median thus it should be right to the median and this is the bar which have a mid point at and thus we can expect mean in .
Hence, the correct statement is option (a) i.e., The median will lie in the interval (), and the mean will lie in the interval ().
You can find the Excite Poll online at poll.excite.com. You simply click on a response to become part of the sample. The poll question for June , was “Do you prefer watching first-run movies at a movie theater, or waiting until they are available on home video or pay-per-view?” In all, people responded, with only people) saying they preferred theaters. You can conclude that
(a) American adults strongly prefer home videos or pay-per-view.
(b) the high nonresponse rate prevents us from drawing a conclusion.
(c) the sample is too small to draw any conclusion.
(d) the poll uses voluntary response, so the results tell us little about all American adults.
(e) American adults strongly prefer seeing movies at a movie theater.
Dropping out You have data from interviews with a random sample of students who failed to graduate from a particular college in years and also from a random sample of students who entered at the same time and did graduate. You will use these data to compare the percentages of students from rural backgrounds among dropouts and graduates.
Which of the following is false?
(a) A measure of center alone does not completely describe the characteristics of a set of data. Some measure of spread is also needed.
(b) If the original measurements are expressed in inches, the standard deviation would be expressed in square inches.
(c) One of the disadvantages of a histogram is that it doesn’t show each data value.
(d) Between the range and the interquartile range, the IQR is a better measure of spread if there are outliers.
(e) If a distribution is skewed, the median and interquartile range should be reported rather than the mean and standard deviation.
42. Long words Mary was interested in comparing the mean word length in articles from a medical journal and an airline’s in-flight magazine. She counted the number of letters in the first words of an article inthe medical journal and in the first words of an article in the airline magazine. Mary then used Minitab statistical software to produce the histograms shown.
The power takeoff driveline on tractors used in agriculture is a potentially serious hazard to operators of farm equipment. The driveline is covered by a shield in new tractors, but for a variety of reasons, the shield is often missing on older tractors. Two types of shields are the bolt-on and the flip-up. It was believed that the bolt-on shield was perceived as a nuisance by the operators and deliberately removed, but the flip-up shield is easily lifted for inspection and maintenance and may be left in place. In a study initiated by the U.S. National Safety Council, random samples of older tractors with both types of shields were taken to see what proportion of shields were removed. Of tractors designed to have bolt-on shields, 35 had been removed. Of the 136 tractors with flip-up shields, 15 were removed. We wish to perform a test of f versus where pb and pf are the proportions of all tractors with the bolt-on and flip-up shields removed, respectively. Which of the following conditions for performing the appropriate significance test is definitely not satisfied in this case?
(a) Both populations are Normally distributed.
(b) The data come from two independent samples.
(c) Both samples were chosen at random.
(d) The counts of successes and failures are large enough to use Normal calculations.
(e) Both populations are at least 10 times the corresponding sample sizes
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