Question

1. (a) A recent study of home technologies reported (as per the following table) the number of hours of personal computer usage per week for a sample of 60 persons.

9.3	5.3	6.3	8.8	6.5	0.6	5.2	6.6	9.3	4.3
6.3	2.1	2.7	0.4	3.7	3.3	1.1	2.7	6.7	6.5
4.3	9.7	7.7	5.2	1.7	8.5	4.2	5.5	5.1	5.6
5.4	4.8	2.1	10.1	1.3	5.6	2.4	2.4	4.7	1.7
2.0	6.7	1.1	6.7	2.2	2.6	9.8	6.4	4.9	5.2
4.5	9.3	7.9	4.6	4.3	4.5	9.2	8.5	6.0	8.1

1. Construct a frequency distribution [4 marks]
2. Construct the histogram corresponding to the frequency distribution [3 marks]

1. (b) A research physician conducted a study on the ages of people with diabetes. Construct the stem and leaf diagram for the following data that were obtained for the ages of a sample of 35 diabetics: [ 3 marks]

48	41	57	83	41	55	59
61	38	48	79	75	77	7
54	23	47	56	79	68	61
64	45	53	82	68	38	70
10	60	83	76	21	65	47

Answer 1

(i) CONSTRUCTED FREQUENCY DISTRIBUTION:

We type the given value from A1:J6 in the Excel Sheet

9.3	5.3	6.3	8.8	6.5	0.6	5.2	6.6	9.3	4.3
6.3	2.1	2.7	0.4	3.7	3.3	1.1	2.7	6.7	6.5
4.3	9.7	7.7	5.2	1.7	8.5	4.2	5.5	5.1	5.6
5.4	4.8	2.1	10.1	1.3	5.6	2.4	2.4	4.7	1.7
2	6.7	1.1	6.7	2.2	2.6	9.8	6.4	4.9	5.2
4.5	9.3	7.9	4.6	4.3	4.5	9.2	8.5	6	8.1

C .I	f
0 - 1.5	5
1.5 - 3.0	11
3.0 - 4.5	6
4.5 - 6.0	15
6.0 - 7.5	10
7.5 - 9.0	6
9.0 - 10.5	7
TOTAL	60

After typing the given values; Make the Class Interval by finding Minimum and Maximum Values. After that with the command we will get the frequencies for the class intervals.

=COUNTIFS($A$1:$J$6,">=0",$A$1:$J$6,"<1.5") with this we will get the frequency for the first class interval 0 - 1.5

=COUNTIFS($A$1:$J$6,">=1.5",$A$1:$J$6,"<3.0"); with this we will get the frequency for the second class interval 1.5 - 3.0

.......................... =COUNTIFS($A$1:$J$6,">=9.0",$A$1:$J$6,"<10.5"); We will get the frequency for the last class interval.

(ii) HISTOGRAM:

HISTOGRAM 16 15 14 10-1.5 12 11 10 1.5-3.0 10 3.0 -4.5 8 7 6 4.5-6.0 6 6 10 16.0 -7.5 4 7.5-9.0 2 9.0 -10.5 0 0-1.5 1.5 -3.0 3.0-4.5 4.5-6.0 6.0 - 7.5 7.5 -9.0 9.0 -10.5

(b) STEM & LEAF:

STEM	LEAF
0	7
1	0
2	13
3	88
4	1157788
5	345679
6	0114588
7	056799
8	233