Answer to Question #223415 in Statistics and Probability for Ratul

Question

SN Height (inch) SN Height (inch) SN Height (inch) SN Height (inch)

1 70 26 56 51 70 76 60

2 23 27 21 52 60 77 64

3 48 28 67 53 48 78 64

4 70 29 69 54 70 79 67

5 68 30 72 55 68 80 69

6 64 31 73 56 64 81 66

7 65 32 70 57 65 82 75

8 66 33 56 58 66 83 70

9 56 34 59 59 56 84 61

10 64 35 61 60 64 85 71

11 64 36 71 61 56 86 62

12 67 37 62 62 66 87 67

13 69 38 67 63 67 88 65

14 66 39 65 64 69 89 65

15 75 40 59 65 72 90 70

16 60 41 68 66 73 91 60

17 48 42 67 67 70 92 60

18 66 43 65 68 56 93 70

19 68 44 54 69 59 94 70

20 69 45 43 70 61 95 60

21 66 46 70 71 71 96 53

22 66 47 66 72 51 97 70

23 61 48 64 73 52 98 64

24 66 49 66 74 60 99 56

25 64 50 65 75 54 100 96

Please find an appropriate measure of central tendency for the data and explain why the measurement is appropriate.

Answer 1

Solution:

First, let's arrange this data in ascending order:

21, 23, 43, 48, 48, 48, 51, 52, 53, 54, 54, 56, 56, 56, 56, 56, 56, 56, 59, 59, 59, 60, 60, 60, 60, 60, 60, 60, 61, 61, 61, 61, 62, 62, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 65, 65, 65, 65, 65, 65, 65, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 67, 67, 67, 67, 67, 67, 67, 68, 68, 68, 68, 69, 69, 69, 69, 69, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 71, 71, 71, 72, 72, 73, 73, 75, 75, 96.

We found that it is right skewed distribution.

The median is the most informative measure of central tendency for skewed distributions. 

Now, n=100 (even)

Median$=(\dfrac{100}{2})^{th}$ term = 50^th term = 65