Question

Section 3.1 Measures of Central Tendency Mode, Median, and Mean GUIDED EXERCISE 2 MEAN AND TRIMMED MEAN ican Colleges, 19th Edition, lists average class size for introductory lecture courses at each of the prof lor Ame introductory lecture courses to be sprofles of nctitutions A sample of 20 colleges and universities in Calformia showed dass szas for 1 20 20 20 20 35 35 35 4 4 42 50 0 25 30 30 30 Compute the mean for the entire sample. Add all the values and divide by 20 sx 71936.0 (a) Compute a 5% trimmed mean for the sample The data are already ordered. Since 5% of 20 is 1,we eliminate one data value from the bottom of the list and one from the top. These values are circled in the data set Then we take the mean of the remaining 18 entries. 5% trimmed mean x 625 -18-347 (d) Find the median of the original data set. Note that the data are already ordered. Median32.5 Find the median of the 5% trimmed data set. Does the median change when you trim the data? The median is still 32.5. Notice that trimming the same number of entries from both ends leaves the middle position of the data set unchanged. (d) e) is the trimmed mean or the original mean closer The trimmed mean is closer to the median. to the median? Minitab, Excel 2010, and TI-84Plus TI-83Plus/TI-nspire calculators all provide th mean and median of a data set. Minitab and Excel 2010 also provide the mode. T Tİ 84Plus TI 83Plus/TI nspre calculators sort data, so you can easily scan the sort data for the mode. Minitab provides the 5% trimmed mean, as does Excel 2010. All this technology is a wonderful aid for analyzing data. However, a mecasu ment is worthless if you do not know what it represents or how a change in data TECH NOTES ing the measures tell you a great deal about the measures. Even if you use a calcul tiral measures, pay attention to the information the form

Answer 1

a>

Sum all the numbers(14,20,20,......,80) and divide them with number of observations (count of 14,20,20,....80) which is 20

(14+20+20+...+80)/20 = 719/20 = 35.95

b>

First need to order the data.Here since data is already ordered,nothing to do.

Now 5% of 20 is 1.

Now we need to eliminate one observation from top (14) and from bottom (80) of the list.

After that need to calculate mean of remaining 18 observations

(719-(14+80))/18 = 34.72

c>

First need to order the data.Here since data is already ordered,nothing to do.

Here we have 20 number of observations which is even number.

So median would be mean of (20/2)=10 th observation which is 30 and (20/2)+1 = 11 the observation which is 35

(30+35)/2 = 32.5

d>

trimmed median would be same. Since we are removing same number of observation from each end.Hence the middle point of the series remain unchanged.

e>

original mean is 35.95

trimmed mean is 34.72

median is 32.5

Hence trimmed mean is closer to median.