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5) The following is a set of data from a sample of n = 5. 5 11 9 8 6 2 a. Compute the mean, median, and mode. b. Compute the range, variance, standard deviation, and coefficient of variation. c. Compute the Z scores. Are there any outliers? d. Describe the shape of the data set. a. The sample mean is the sum of the values divided by the number of values. b. The range of a set of data is equal to its largest value minus its smallest value. Since the largest value is 11 and the smallest is 5, the range is 6. c. For a particular value, the corresponding Z score is the difference of that value and the mean, divided by the standard deviation. d. The shape of a set of data is related to the set's mean and median. If the mean is less than the median, the set of data is negative (left-skewed); if it is greater than the median, the set of data is positive (right-skewed); and if it is equal to the median, the set of data is symmetrical.

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

A sample of size 40 yields the following sorted data. Note that I have x-ed out x(39) (the second largest number). This fact will NOT prevent you from answering the questions below.

(a) Calculate range, IQR, and median of these data.

(b) Given that the mean of these data is 63.50 (exactly) and the standard deviation is 12.33, what proportion of the data lie within one standard deviation of the mean?

(c) How does your answer to (b) compare to the empirical rule approximation?

(d) Ralph decides to delete the smallest observation, 14.1, from these data. Thus, Ralph has a data set with n = 39. Calculate the range, IQR, and median of Ralph’s new data set.

(e) Refer to (d). Calculate the mean of Ralph’s new data set.

 

 For these situations, state which measure of central tendency -mean, median, or mode-should be shed.

a. The most typical case is desired Mode.

b. The distribution is open-ended Median 

c. There is an extreme value in the data set. Median 

d. The data are acategorical. Mode.

e. Further statistical computations will be needed. Mean 

f. The values are to be divided into two approximately equal groups containing the larger values and one containing the smaller values.

You are interested in how much time students spend on the internet each day. Here are data on the time spent on the internet (in minutes) for a particular day reported by a random sample of 30 students at a large college:

a) Make a histogram of these data. Is the shape symmetric or skewed?

b) Find the 5 number summary and P65.

c) Find the mean and sample standard deviation.

d) Are there any outliers? Justify your answer.

e) Would it be better to use the mean and standard deviation or the median and IQR to describe the centre and spread of this distribution? why?

 

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