Question

Ages of Presidents at Inauguration

57 61 57 57 58 57 61 54 68 51 49 64 50 48 65 52 56 46 54 49 51 47 55 55 54 42 51 56 55 51 54 51 60 62 43 55 56 61 52 69 64 46 54 47

Create a frequency table using the data above

Use 7 classes

Show the relative and cumulative frequencies

   List the class boundaries and class mid-points

   What is the modal class?

Answer 1

Smallest value = 42

Highest value = 69

Difference = Highest value - smallest value

Difference = 69 - 42

Difference = 27

Class width = (Highest value - Lowest Value) / Number of classes

Class width = (69 - 42) / 7

Class width = 27 / 7 = 3.86 4

Mid point = (UCL + LCL) / 2

For first class = (42 + 45)/2 = 43.5

For second class = (46 + 49)/2 = 47.5

simillarly solve for others..

Relative Frequency = Frequency / No. of observation

For first class interval, it would be = 2/44 = 0.05

For second class interval, it would be = 7/44 = 0.16

simillarly solve for others....

Class Boundaries:

Class boundaries = (UCL of one class + LCL of next class) / 2

Class boundaries = (UCL of one class + LCL of next class) / 2

Class boundaries = (45 + 46) / 2 = 91 / 2 = 45.5

For second class

Class Boundaries = (49 + 50) / 2 = 49.5

simillary solve for others......

Construct a table with six column, and then write the data groups or class intervals in the first column. The size of each group is 4. So, the groups will start at, 42, 46, 50, 54, 58, 62 and 66 to include all of the data.

Frequency Distribution Table:

Class Interval	Frequency	Mid points	Cumulative Frequency	Relative Frequency	Class boundaries
42 - 45	2	43.5	2	2/44 = 0.05	41.5 - 45.5
46 - 49	7	47.5	2 + 7 = 9	7 / 44 = 0.16	45.5 - 49.5
50 - 53	8	51.5	9 + 8 = 17	8 / 44 = 0.18	49.5 - 53.5
54 - 57	16	55.5	17 + 16 = 33	16 / 44 = 0.36	53.5 - 57.5
58 - 61	5	59.5	33 + 5 = 38	5 / 44 = 0.11	57.5 - 61.5
62 - 65	4	63.5	38 + 4 = 42	4 / 44 = 0.09	61.5 - 65.5
66 - 69	2	67.5	42 + 2 = 44	2 / 44 = 0.05	65.5 - 69.5
Total	44			Total = 1

Modal class = The class having maximum frequency

Maximum frequency is 16, and corresponding class interval is 54 - 57

Therefore, Modal class = 54 - 57