Q. 23 - Elementary Statistics

Question

Busy Bank Tellers. The Prescott National Bank has six tellers available to serve customers. The data in the following table provide the number of busy tellers observed during 25 spot checks.

6	5	4	1	5
6	1	5	5	5
3	5	2	4	3
4	5	0	6	4
3	4	2	3	6

a. Use single-value grouping to organize these data into frequency and relative frequency distributions.

b. Draw a relative-frequency histogram for the data based on the grouping in part (a).

c. Identify the modality of the distribution of these numbers of busy tellers.

d. State whether the distribution is (roughly) symmetric, right-skewed, or left-skewed.

e. Construct a dot plot for the data on the number of busy tellers.

f. Compare the dot plot that you obtained in part (e) to the relative frequency histogram that you drew in part (b).

Step-by-Step Solution

Answer

Ans:  

(a)   Related frequencies of the number of busy counters detected during the 25-spot test are,  

$0.04, 0.08, 0.08, 0.16, 0.20, 0.28, and 0.16$.

(b)

(c)  From the histogram of the related frequency above, we can see that the distribution status of the number of busy calculators employed during the 25-spot test has been left to chance. Therefore, the given data set for the number of busy enumerators follows the standard distribution. 

(d)   The distribution of the number of busy narrators follows a crooked distribution; as the shape of the histogram of the frequency appears to be the left tail longer than its right tail. 

(e)  According to the dot plot, here is the number of busy tellers following the left-skewed distribution. 

(f)  From both diagrams, a dot diagram related to the dot structure, we can see that the number of busy counters follows the twisted distribution on the left.

Step 1. Given information.

given data,

6	5	4	1	5
6	1	5	5	5
3	5	2	4	3
4	5	0	6	4
3	4	2	3	6

Step 2. (a) Single-value grouping,

Bulk data collection is the use of classes where each category represents a potential value, such categories are called single-value classes and this method of collecting bulk data is called a single-value collection.

Using one collection method, the classes collected the numbers of busy narrators identified during the 25-spot test by $0,1,2,3,4,5, and 6$.

We need to create a frequency distribution of the number of busy counters employed during the 25-area survey.

The general distribution of the number of busy counters detected during the 25-spot test can be found below.

Category	Frequency
0	1
1	2
2	2
3	4
4	5
5	7
6	4

Thus, the frequencies for the number of busy tellers observed during 25 spot checks are $1, 2, 2, 4, 5, 7, and 4$ .

Step 3. We need to build a frequency distribution value for the number of busy calculators detected during the 25-site survey.

The distribution frequency associated with the number of busy counters detected during the 25-spot test can be found below.

Category	Relative frequency
0	0.04
1	0.08
2	0.08
3	0.16
4	0.20
5	0.28
6	0.16

Related frequencies of the number of busy counters detected during the 25-spot test are, $0.04, 0.08, 0.08, 0.16, 0.20, 0.28, and 0.16$

Step 4. (b) We have to construct a relative frequency histogram for the number of busy tellers,

The relative frequency histogram for the above frequency table is given below,

 

Step 5. (c) Identify the modality,

From the histogram of the related frequency above, we can see that the distribution status of the number of busy calculators employed during the 25-spot test has been left to chance. Therefore, the given data set for the number of busy enumerators follows the standard distribution.

Step 6. (d) State whether the distribution is (roughly) symmetric, right-skewed, or left-skewed.

The distribution of the number of busy narrators follows a crooked distribution; as the shape of the histogram of the frequency appears to be the left tail longer than its right tail.

Step 7. (e) Construct a dot plot for the data on the number of busy tellers.

Using MINITAB software, the dot plot for the number of busy tellers is drawn below.

 

According to the dot plot, here is the number of busy tellers following the left-skewed distribution.  

Step 8. (f) Compare the dot plot that is found in part (a),

From both diagrams, a dot diagram related to the dot structure, we can see that the number of busy counters follows the twisted distribution on the left.