Question

n du Consider the data set below: 22 12 21 22 S = 19 45 20 30 37 34 44 23 26 33 70 54 40 48 23 17 22 56 38 17 21 16 33 41 84 43 27 65 34 19 100 34 48 29 54 16 43 33 8934 43 31 37 77 43 43 Problem 1 (a) Make a stem and leaf display of S. (b) Calculate the mean I = 2 (c) Calculate the 10%-trimmed mean I. Problem 2 (a) Find the range, the 1st and 3rd quartile, and the median of S (b) Make a bor and whiskers plot of S. (c) Use the formula below to calculate the inter-quartile mean 319M = 3 i= +1 Problem 3 (a) Create a frequency table for S. (b) Create a relative frequency histogram for S. (c) Find the deciles D, and label them on your histogram above.

Answer 1

Part a.

Using Minitab:

1. With the raw data entered in C1,

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select the Graph menu and highlight Stem-and-Leaf.

Select the data in C1 and press OK

2. Select the data in C1 and press OK.

Stem-and-Leaf Display: S Stem-and-leaf of S Leaf Unit = 1.0 N = 50 7 18 (12) 1 2 2667799 01122233679 013334444778 01333334588 446 20 07 38 49 wa 1 10 0

Part b.

Π = Στη

= 1910/50

=3820

Part c.

Consider the given data, (Sample size,n=50)

12   16   16   17   17   19   19   20   21   21   22   22   22   23   23   26   27   29   30   31   33   33   33   34   34   34   34   37   37   38   40   41   43   43   43   43   43   44   45   48   48   54   54   56   65   70   77   84   89   100  

The given data is already arranged from smallest to largest.

The trimmed mean, as the name suggests that we have to trim some of the observation from the given data. The percentage is given, we have to trimmed 10% of the data.

10% trimmed of the data is performed as,

trimmed percentage * sample size

11 10% * 50 = " + 50-5 100

it means, the 10% trimmed of the data will remove 5 observation from the bottom and 4 observation from the top of the data.

12   16   16   17   17   19   19   20   21   21   22   22   22   23   23   26   27   29   30   31   33   33   33   34   34   34   34   37   37   38   40   41   43   43   43   43   43   44   45   48   48   54   54   56   65   70   77   84   89   100  

So, the trimmed new data is, (Sample size, n=40)

19   20   21   21   22   22   22   23   23   26   27   29   30   31   33   33   33   34   34   34   34   37   37   38   40   41   43   43   43   43   43   44   45   48   48   54   54   56   65

and trimmed mean is,

- Στη 19 + 20 +... 56 + 65 1412 , = 35.3 12 40

Therefore, the 10% trimmed mean is 35.3

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