Grouped Data- The Frequency Distribution
The approximate number of classes can be determined from a formula given by Sturges,
No. of classes=1+3.322(Log10 n )
h. It is necessary to find the lowest and highest values of the data, and arrange the data into classes or (class interval).
Class limit or class interval = range / No. of classes
Determine the number of individuals belonging to each class is called the class frequency.
Relative frequency = frequency / total frequencies
Exercises
2.3.3 : Ellist et al. (A-3) conducted a study to explore the platelet imipramine binding characteristics in manic patients and to compare the results with equivalent data for healthy controls and depressed patients. As part of the study the investigators obtained maximal receptor binding (Bmax) values on their subjects. The following are the values for the 57 subjects in the study who had a diagnosis of unipolar depression.
1074 392 286 179
372 475 511 530
473 319 147 446
797 301 476 328
385 556 416 348
769 300 528 773
797 339 419 697
485 488 328 520
334 1114 1220 341
670 761 438 604
510 571 238 420
299 306 867 397
333 80 1657
303 607 790
768 1017 479
(a) Use these data to construct
A frequency distribution
A relative frequency distribution
A cumulative relative frequency distribution
A histogram
A frequency polygon
(b) What percentage of the measurement are less than 500?
(c) What percentage of the measurement are between 500 and 999 inclusive?
(d) What percentage of the measurement are greater than 749?
(e) Describe these data with respect to symmetry and skewness.
(f) How many of the measurements are less than 1000?
ANSWER
(a)
cumulative
Class Relative cumulative relative
interval frequency frequency frequency frequency
--------------------------------------------------------------------------------------
0 - 249 4 .0702 4 .0702
250-499 29 .5088 33 .5790
500-749 11 .1930 44 .7720
750-999 8 .1404 52 .9124
1000-1249 4 .0702 56 .9826
1250-1499 0 .0000 56 .9826
1500-1749 1 .0175 57 1.0000
---------------------------------------------------------------------------------------
Total 57 1.0000
(b) 50.88 (c) 33.34 (d) 22.8 (e) Skewed right (f) 52
2.3.5 The following table shows the number of hours 45 hospital patients slept following the administration of a certain anesethetic.
7 10 12 4 8 7 3 8 5
12 11 3 8 1 1 13 10 4
4 5 5 8 7 7 3 2 3
8 13 1 7 17 3 4 5 5
3 1 17 10 4 7 7 11 8
(a) From these data construct:
A frequency distribution A histogram
A relative frequency distribution A frequency polygon
(b) Describe these data relative to symmetry and skewness .
ANSWER
(a)
Class Relative
Interval Frequency frequency
----------------------------------------------------------------------
0 - 2 5 .1111
3 - 5 16 .3556
6 - 8 13 .2889
9-11 5 .1111
12-14 4 .0889
15-17 2 .0444
-----------------------------------------------------------------------
Total 45 1.0000
(b) Skewed right