Question

The data shown here represent the anxiety test scores of 36 random clients entered a mental health clinic. Construct a frequency distribution using 4 classes, analyze the distribution, and provide a frequency histogram graph, a frequency polygon, a cumulative frequency ogive, and a cumulative relative frequency ogive

7.75	0	10	5	5	0
8.25	4.5	8.75	5	7	8
4	7.25	7	6.25	7.5	0
9.5	4	6	0	6.25	8.25
6.25	8.25	3	7.5	9.25	7.75
3	7.25	7.25	7	11	0

Note: The complete frequency table should have 8 columns (relative frequency and cumulative relative frequency included). You can draw the graphs on a piece of paper and either scan it or take a photo of it and submit it with the other questions.

Answer 1

Class width =(maximum value-minimum value)/number of classes =(11-0)/4 =11/4 =2.75 - rounding it to next integer, class width =3​​​​​​

LCL =lower class limit; UCL =upper class limit; LCB =lower class boundary and UCB =upper class boundary.

LCB =LCL - 0.5 (here)

UCB =UCL+0.5 (here)

Mid point =(LCL+UCL)/2 Or Mid point =(LCB+UCB)/2

The complete frequency table:

Frequency histogram graph:

On X-axis: Classes

On Y-axis: Frequencies

So, the anxiety scores for half of the 36 random clients(i.e, 18) are between 5.5 and 8.5 (including 5.5 but excluding 8.5).

Frequency polygon:

Cumulative frequency ogive:

On X-axis: Classes

On Y-axis: Frequencies

Cumulative relative frequency ogive: