The data set below is the cost (in cents) per 1-ounce serving for a sample of 13

Question

The data set below is the cost (in cents) per 1-ounce serving for a sample of 13 chocolate chip cookies. Complete parts (a) through (d) below 55 20 26 23 38 45 9 45 26 48 27 42 49 a. Compute the mean, median, and the mode. The mean is (Round to two decimal places as needed.) The median is[].(Type an integer or a decimal ) What is the mode? Select the correct choice below and, if necessary, fil in the answer box to complete your choice. O A. The mode(s) isare O B. There is no mode for this data set b. Calculate the variance, standard deviation, range, and Z scores. Are there any outliers? Explain. The variance is (Round to four decimal places as The standard deviation is (Round to three deornal places as needed.) The range is (Type an integer or a decinal.) Compute the Z scores for the first five values. (Type an integer or a decimal. Use a comma to separate answers as needed.) needed.) Daa Z Score 20 26 23 38 (Round to two decimal places as needed ) Compute the Z scores for the next five values. Data 45 Z Score 45 26 48

Explanation / Answer

solution in excel:

a) mean=34.84615 (=AVERAGE(data))

median=38 (=MEDIAN(data))

mode=26 (=MODE(data))

b)Variance=191.141 (=VAR(data))

Standard Deviation=13.82538 (=STDEV(data)

Range=46 (max-min)

data Z score

hence there is no outliers present in data because there is no Z scores that are less than -3.0 or greater than +3.0

The Z-score of an observation is defined as

Zi=YiY¯/s

with Y¯ and s denoting the sample mean and sample standard deviation, respectively. In other words, data is given in units of how many standard deviations it is from the mean.

Although it is common practice to use Z-scores to identify possible outliers, this can be misleading (partiucarly for small sample sizes) due to the fact that the maximum Z-score is at most (n1)/n

Iglewicz and Hoaglin recommend using the modified Z-score

Mi=0.6745(xix~)MAD

with MAD denoting the median absolute deviation and x~denoting the median.

These authors recommend that modified Z-scores with an absolute value of greater than 3.5 be labeled as potential outliers.

c) C

d)A

55 1.457743 20 -1.07383 26 -0.63985 23 -0.85684 38 0.22812 45 0.734436 9 -1.86947 45 0.734436 26 -0.63985 48 0.951428 27 -0.56752 42 0.517443 49 1.023758

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