XYZ National Bank A statistical data analysis was conducted regarding the checking accounts of the clients of XYZ National Bank. It encompasses tables and graphs representing the checking account balances in peso and the distribution of it among the four branches. It also includes characteristics of the accounts in terms of number of ATM transactions in the month, number of other bank services used, clients who have debit card and those who don’t have, clients who receive interest on the account and those who don’t.

It was determined that the balance of a typical customer based on the data of the account balances in peso per client given is 149,986.67. It was also determined that twelve out of the said number of clients have more than P200,000 in their accounts.

Using the frequency distribution we found out that Makati, Manila, Quezon City and Pasig City branches have sixteen, eighteen, thirteen and thirteen clients respectively. Thus, there is a difference in the distribution of the accounts among the four branches. For the mean and the median of the account balances for the said branches, the Makati branch has a mean of 128, 137.50 and a median of 139,700. On the other hand, Manila branch has a mean and a median of 187964.71 and 195800 respectively. It is discovered that the Quezon City branch has a mean of 135935.71 and a median of 150450, while the Pasig City branch has a mean and median of 149,986.67 and 148,700.

For the standard deviation of the said branches, it is computed that Makati has 47431.675, Manila has 35087.66, Quezon City has 68348.29 and Pasig City has 70922.195 for their Standard Deviation. This is based on the calculated results in standard deviation.

I.

1) Table that shows the checking balances

*TABLE 1.1*

This table shows the checking account balances and its respective frequency.

|Checking Account Balance |Frequency |
|243200-263199 |2 |
|223,200 – 243,199 |4 |
|203,200 – 223,199 |6 |
|183,200 – 203,199 |8 |
|163,200 – 183,199 |10 |
|143,200 – 163,199 |8 |
|123,200 – 143,199 |5 |
|103,200 – 123,199 |6 |
|83,200 – 103,199 |1 |
|63,200 – 83,199 |5 |
|43,200 – 63,199 |1 |
|23,200 – 43,199 |1 |
|3,200 – 23,199 |3 |

*Figure 1.1*

The graph represents the illustration of the checking account balances and the frequency of each.

[pic]

2) Balance of a typical customer.

The balance of a typical customer is 149,986.67. This was determined by computing the mean of each of the following accounts.

2) How many customers have more than 200,000?

There are 12 customers who have more than 200,000 in their accounts. This is obtained by the record of each of the customers frequency.

3) Does it appear that there is a difference in a distribution of the accounts among four branches?

Yes, there is a difference in the distribution of the accounts among the four branches, whereas Makati, Manila, Quezon City and Pasig City have sixteen, seventeen, fourteen and thirteen clients respectively.

Frequency Distribution

*TABLE 1.2*

This table shows the frequency of each of the following branches and its corresponding percent, valid percent and cumulative percent.

|Branches |Frequency |Percent |Valid Percent |Cumulative percent |
|Makati |16 |26.67 |26.67 |26.67 |
|Manila |17 |28.33 |28.33 |55.0 |
|Quezon City |14 |23.33 |23.33 |78.33 |
|Pasig City |13 |21.67 |21.67 |100 |
|TOTAL: |60 |100 |100 | |

*FIGURE 1.2*

The illustration corresponds to the histogram of the frequency of the branches.

4) Around what value do the account balances tend to cluster?

*TABLE 1.3*

|X6 |Mean |Frequency |Standard Deviation |
|Makati |128137.50 |16 |47431.675 |
|Manila |187964.71 |17 |35087.657 |
|Quezon City |135935.71 |14 |68348.289 |
|Pasig City |142346.15 |13 |70922.195 |
|TOTAL: |149986.67 |60 |59690.491 |

II.

1. Determine the mean and median of the checking account balances.

The mean of the checking account balances are as follows: Makati branch has 128,137.50, Manila Branch has 187964.7059, Quezon City branch has 135935.7143 and Pasig City branch has 142,346.15. On the other hand the median of the checking account balances are as follows: Makati(n=16) has 139,700, Manila(n=17) has 195800, Quezon City(n=14) has 150450 and Pasig City(n=13) has 148,700. These are obtained by sorting the sets in numerical order and getting its middle number.

2. Compare the mean and the medians. Is there a difference among the balances?

Yes, there is a difference among the balances as shown in table 2.1.

*TABLE 2.1*

This table indicates the mean, median and standard deviation of each of the following branches.

| |
| | |MAKATI |MANILA |QUEZON CITY |
|Median |139700.0000 |195800.0000 |150450.0000 |148700.0000 |
|Standard Deviation |47431.67542 |35087.65704 |68348.28913 |70922.19464 |

*FIGURE 2.1*

The graph illustrates the mean, median and the mode of the branches Makati, Manila, Quezon City and Pasig City.

[pic]

3. What is the standard deviation of the balances?

The standard deviation of the balances is 59690.491. This is determined by getting the summation of Fx, whereas Fx is equal to frequency multiplied by the class limit.

Other Relevant Graphs

Figure 3.1

This graph shows the number of clients who have debit card and those who don’t.

[pic]

I. ANOVA

Research Question

Is there a significant difference between distributions of the accounts in all four branches in terms of their customer’s account balances?

Hypothesis

There is a significant difference between distributions of the accounts in all four branches in terms of their customer’s account balances.

Proof

The whole study shows that there is a significant difference between the distributions of the accounts in all four branches. This is in accordance with the number of clients of the four branches Makati, Manila, Quezon City and Pasig City. Each of them has 16, 17, 14 and 13 clients respectively. Whereas, every client in each branch has different account balances. This is seen through a mere observation of the frequency of each of the customer’s account balances. With this, it is said that 10 out of 60 customers, which is equivalent to 16.67% have an account balance between the ranges of 163,200 to 183,199. On the other hand, there is only one out of 60 clients, which is equal

to 1.67% for each of the ranges between 83,200 to 103,199, 43,200 to 63,199 and 23,200 to 43,199. From the highest down to the lowest percent of the number of clients for the checking account balances, there is said to have a difference of 15%. This only shows that

there’s a significant difference between the distributions of the accounts in all four branches in terms of their customer’s account balances.

|Descriptives |
|X1 |
| |
|X1 |
|Levene Statistic |df1 |df2 |Sig. |
|2.961 |3 |56 |.040 |

The second table from the ANOVA output, or the Test of Homogeneity of Variances provides the Levene’s Test to check the assumption that the variances of the four branches are significantly different. Thus, the assumption of homogeneity of variance is met.

|ANOVA |
|X1 |
| |
| |
| | |Levene's Test for |t-test for Equality of Means |
| | |Equality of | |
| | |Variances | |
| |
| |Cases |
| |Valid |Missing |Total |
| |
|Branches |Observed N |Expected N |Residual |
|MAKATI |16 |15.0 |1.0 |
|MANILA |17 |15.0 |2.0 |
|QUEZON CITY |14 |15.0 |-1.0 |
|PASIG CITY |13 |15.0 |-2.0 |
|Total |60 | | |

Using this method, we figured out the expected frequencies is 15 for each of the branches. Obviously, there are discrepancies between the four branches. The null hypothesis states that there is no significant difference between the expected and observed frequencies. The alternative hypothesis states they are different. The level of significance (the point at which you can say with 10% confidence that the difference is NOT due to chance alone) is set at .05 (the standard for most science experiments.)

|Branches |o |e |o-e |(o-e) 2 |(o-e) 2/e |
| | | | | | |
|Makati |16 |15 |1 |1 |0.07 |
|Manila |17 |15 |2 |4 |0.27 |
|Quezon City |14 |15 |-1 |1 |0.07 |
|Pasig City |13 |15 |-2 |4 |0.27 |

X2=0.68
|Test Statistics |
| | | |X6 |X3 |
|Chi-Square |.667a |31.667b |
|Df |3 |9 |
|Asymp. Sig. |.881 |.000 |
|Monte Carlo Sig. |Sig. |.880c |.000c |
| |10% Confidence Interval |Lower Bound |.876 |.000 |
| | |Upper Bound |.884 |.001 |

In this situation, the rejection of the null hypothesis means that the differences between the expected frequencies and the observed frequencies are not due to chance. Meaning, there is a real difference between them. This is because, the calculated chi-square value of 0.68 is equal to or greater than that of the table value which is 0.667. That is why the null hypothesis must be rejected. Thus there is a significant difference in all four branches in terms of other bank services.

IV. REGRESSION

Regression analysis is a statistical tool for the investigation of relationships between variables. Usually, the investigator seeks to ascertain the causal effect of one variable upon another—the effect of a price increase upon demand, for example, or the effect of changes in the money supply upon the inflation rate. To explore such issues, the investigator assembles data on the underlying variables of interest and employs regression to estimate the quantitative effect of the causal variables upon the variable that they influence. The investigator also typically assesses the “statistical significance” of the estimated relationships, that is, the degree of confidence that the true relationship is close to the estimated relationship regression analysis includes any techniques for modelling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables.

Table IV. A
|Variables Entered/Removed |
|Model |Variables Entered |Variables Removed |Method |
|1 |X3, X2a |. |Enter |
|a. All requested variables entered. |

Table IV. B
|Model Summary |
|Model |

As seen in table IV. B, the ATM transactions and account balances affect each other in the manner of increasing action. This is observed because of the positive R.

The ATM transactions tend to increase (due to positive R) the account balances of the customers. We can assume that 55% of the account is dependent to the number of ATM transactions and other bank services used by the clients.

Table IV. C

|Coefficientsa |
|Model |

The table IV.C tells that the value of ATM transaction is significant and the coefficient is positive indicating that ATM transactions are related to higher account balances. Other bank services used have the same effect.

V. CORRELATION

Correlation is basically the test of measurement when the degree of relationship is measured. It means that two variables tend to vary together; the presence of one indicates the presence of the other; one can be predicted from the presence of the other.

Research Problem

Is there a significant relationship between the account balances and ATM transactions and also on the number of other bank services used?

Hypothesis (Null)

There is no significant relationship between the account balances and ATM transactions and also on the number of other bank services used.

Hypothesis (Alternative)

There is a significant relationship between the account balances and ATM transactions and also on the number of other bank services used.

|Correlations |
| |

Based on the correlation test, it showed a significant relationship among the variables x1 and x2, x1 and x3. The said values are below the significance level of correlation of alpha = 0.01.

Business Statistics

CASE STUDY

SUBMITTED BY:

Alpe, Christian John

Arce, Julie Ann

Cariaga, Gwynett

Marquez, Jetro Paulo

Simbahan, Kiel Charl

SUBMITTED TO:

MANUELITO BENGO