Problems of Frequency Tables and Charts

Exercise 1

Classify the following variables

1. Daily hours of exercise.
2. Nationality.
3. Blood pressure.
4. Severity of illness.
5. Number of sport injuries in a year.
6. Daily calorie intake.
7. Size of clothing.
8. Subjects passed in a course.

Exercise 2

The number of injuries suffered by the members of a soccer team in a league were

0 1 2 1 3 0 1 0 1 2 0 1 1 1 2 0 1 3 2 1 2 1 0 1

Compute:

1. Construct the frequency distribution table of the sample.
2. Draw the bar chart of the sample and the polygon.
3. Draw the cumulative frequency bar chart and polygon.

Solution

Injuries	$n_i$	$f_i$	$N_i$	$F_i$
0	6	0.2500	6	0.2500
1	11	0.4583	17	0.7083
2	5	0.2083	22	0.9167
3	2	0.0833	24	1.0000

3.

Exercise 3

A survey about the daily number of medicines consumed by people over 70 shows the following results:

3 1 2 2 0 1 4 2 3 5 1 3 2 3 1 4 2 4 3 2 3 5 0 1 2 0 2 3 0 1 1 5 3 4 2 3 0 1 2 3

1. Construct the frequency distribution table of the sample.
2. Draw the bar chart of the sample and the polygon.
3. Draw the cumulative relative frequency bar chart and polygon.

Solution

Medicines	$n_i$	$f_i$	$N_i$	$F_i$
1	8	0.200	13	0.325
2	10	0.250	23	0.575
3	10	0.250	33	0.825
4	4	0.100	37	0.925
5	3	0.075	40	1.000

3.

Exercise 4

In a survey about the dependency of older people, 23 persons over 75 years were asked about the help they need in daily life. The answers were

B D A B C C B C D E A B C E A B C D B B A A B

where the meanings of letters are:

A No help. B Help climbing stairs. C Help climbing stairs and getting up from a chair or bed. D Help climbing stairs, getting up and dressing. E Help for almost everything.

Construct the frequency distribution table and a suitable chart.

Solution

Help	$n_i$	$f_i$	$N_i$	$F_i$
A	5	0.2174	5	0.2174
B	8	0.3478	13	0.5652
C	5	0.2174	18	0.7826
D	3	0.1304	21	0.9130
E	2	0.0870	23	1.0000

Exercise 5

The number of people treated in the emergency service of a hospital every day of November was

15 23 12 10 28 7 12 17 20 21 18 13 11 12 26 30 6 16 19 22 14 17 21 28 9 16 13 11 16 20

1. Construct the frequency distribution table of the sample.
2. Draw a suitable chart for the frequency distribution.
3. Draw a suitable chart for the cumulative frequency distribution.

Solution

People	$n_i$	$f_i$	$N_i$	$F_i$
[5,10]	4	0.1333	4	0.1333
(10,15]	9	0.3000	13	0.4333
(15,20]	9	0.3000	22	0.7333
(20,25]	4	0.1333	26	0.8667
(25,30]	4	0.1333	30	1.0000

3.

Exercise 6

The following frequency distribution table represents the distribution of time (in min) required by people attended in a medical dispensary.

$$ \begin{array}{|c|c|c|c|c|} \hline \mbox{Time} & n_{i} & f_{i} & N_{i} & F_{i}\newline \hline \left[ 0,5\right) & 2 & & & \newline \hline \left[ 5,10\right) & & & 8 & \newline \hline \left[ 10,15\right) & & & & 0.7 \newline \hline \left[ 15,20\right) & 6 & & &\newline \hline \end{array} $$

1. Complete the table.
2. Draw the ogive.

Solution

$$ \begin{array}{|c|c|c|c|c|} \hline \mbox{Time} & n_{i} & f_{i} & N_{i} & F_{i}\newline \hline \left[ 0,5\right) & 2 & 0.1 & 2 & 0.1 \newline \hline \left[ 5,10\right) & 6 & 0.3 & 8 & 0.4 \newline \hline \left[ 10,15\right) & 6 & 0.3 & 14 & 0.7 \newline \hline \left[ 15,20\right) & 6 & 0.3 & 20 & 1\newline \hline \end{array} $$

Exercise 7

The following table represents the frequency distribution of the yearly uses of a health insurance in a sample of clients of a insurance company.

Draw the box plot. Study the symmetry of the distribution.

Solution

Exercise 8

The box plots below correspond to the age of a sample of people by marital status.

1. Which group has higher ages?
2. Which group has lower central dispersion?
3. Which groups have outliers?
4. At which group is the age distribution more asymmetric?