Question

For the data in Data Set #1, generate a Frequency Distribution with an interval size of 10, a lower apparent limit value as a multiple of 10, the largest interval size place on the top of the distribution, and use this distribution to answer questions 11-18.

54 67 88 109 26 33 92 97 32 55 75 81 83 45 21 86 94 100 78 62

What is the midpoint of the lowest interval?

What is the relative frequency of the second lowest interval?

What is the cumulative percentage of the second highest interval?

What is the cumulative frequency of the third lowest interval?

What is the cumulative relative frequency of the third highest interval?

What is the frequency of the highest interval?

For Data Set #1, what would the number of intervals be if you wanted an interval size of 4?

For Data Set #1, what would the interval size be if you wanted 11 intervals?

Answer 1

Class Interval	Mid- point	Frequency	Relative Frequency	Cumulative frequency	Cumulative relative frequency
20 - 30	25	2	0.1	2	0.1
30- 40	35	2	0.1	4	0.2
40 - 50	45	1	0.05	5	0.25
50 - 60	55	2	0.1	7	0.35
60 - 70	65	2	0.1	9	0.45
70 - 80	75	2	0.1	11	0.55
80 - 90	85	4	0.2	15	0.75
90 - 100	95	3	0.15	18	0.9
100-110	105	2	0.1	20	1
	Total	20

i)

The lowest interval is 20 -30

The midpoint of the lowest interval

ii)

Total number of frequency = 20

The second lowest interval is 30 - 40

Frequency of the second lowest interval = 2

The relative frequency of the second lowest interval

iii)

The second highest interval is 90 - 100

Cumulative frequency of the second highest interval =18

Total frequency = n = 20

cumulative percentage = (cumulative frequency ÷ n) x 100

The cumulative percentage of the second highest interval

iv)

The third lowest interval is 40 - 50

The cumulative frequency of the third lowest interval = 5

v)

The third highest interval is 80 - 90

The cumulative relative frequency of the third highest interval = 0.75

vi)

The highest interval is 100 - 110

The frequency of the highest interval = 2

vii)

Range = Maximum value - minimum value

= 109 - 21

= 88

Interval size = 4

Now,

Number of Interval = Range / Interval size

= 88 / 4

= 22

viii)

Given

number of interval = 11

Now,

Interval size = Range / number of interval

= 88/ 11

= 8