Services 2 1 3 8 7 5 3 4 2 2 1 5 5 5 1 3 4 6 7 4 2 4 2 7 6 5 8 4 5 4 4 3 5 4 3 6 2 4 3 4 6 5 7 8 4 0 5 Debit Interest 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 City 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 0 1 Balance 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 Descriptives Balance Branch1 Branch2 748 1756 1501 2125 1886 1995 1593 1526 1474 1746 1913 1616 1218 1958 1006 1675 343 1885 1494 2204 580 2409 1320 1338 1784 2076 1044 2375 890 1125 1708 1989 2156 Branch1 Branch2 Mean 1499.867 Mean 1281.375 Mean Standard E 77.06009 Standard E 118.5792 Standard E Median 1604.5 Median 1397 Median Mode #N/A Mode #N/A Mode Standard D 596.9049 Standard D 474.3168 Standard D Sample Var 356295.5 Sample Var 224976.4 Sample Var Kurtosis -0.140727 Kurtosis -0.685929 Kurtosis Skewness -0.616401 Skewness -0.487078 Skewness Range 2525 Range 1570 Range Minimum 32 Minimum 343 Minimum Maximum 2557 Maximum 1913 Maximum Sum 89992 Sum 20502 Sum Count 60 Count 16 Count FREQUENCY TABLE ` $0 $430 $860 $1,290 $1,720 $2,150 Classes up to up to up to up to up to up to Midpoint Frequency $430 $215 #REF! 860 $645 #REF! 1290 $1,075 #REF! 1720 $1,505 #REF! 2150 $1,935 #REF! 2580 $2,365 #REF! 0 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 4 4 4 4 4 4 4 4 4 4 4 4 4 Total #REF! Histogram of bala 70.00 60.00 50.00 40.00 30.00 20.00 10.00 0.00 0 430 860 1290 a) They were 16 customers from branch 1, 17 from branch 2, 14 from b presented in above and the distribution for each branch is presente We observe that the highest frequency is observed in $1720-$2150 Thus, we could say that a typical customer has a median balance equ Furthermore, the midpoint of 1720-2150 class is less than 2000$, in Thus, approximately 27% of the customers have more than 2000$ in Boxplot of Balance 2500 2000 Balance 6 4 3 4 7 7 4 4 3 9 7 5 4 1500 1000 500 0 1 2 3 City 0 1 2 3 City In the above boxplots, we observe that the distribution of balance se branch 2 has a significantly greater median balance of approximately except for branch 4 which seems to be more symmetric. Finally, in the Frequency table above we see that most of the balanc b) The mean and median values for each branch are presented in the fo something we have already observed in the previous boxplots. We o indicating that the distributions of these branches are skewed. More we conclude that their distributions are negatively (left) skewed. Bra we will use the median balance for the comparisons, since it is a mo we conclude that there is a difference among branches: branch 1 ha approximately 1500$ median balance. The highest median balance i to the other three branches. Branch c) Mean Median 1 1281.4 1397 2 1879.6 1958 3 1359.4 1504.5 4 1423.5 1487 The standard deviation of the balance is 596 our data. Thus, we observe that there is a huge variation in the balan there is a great gap between these two values. Also, the standard de A high standard deviation, as in this case, shows that the data are wi The 3rd quartile is 1946.8$ indicating that 75 balance lower than 1121.3$.The skewness coefficient is -0.616, indic the median are more than balance values lower than the median. In in the right side of the x-axis. However, since the skewness value is g is approximately normal. Q3= Q1= #REF! #REF! Branch3 Branch4 1831 1622 740 1169 1554 2215 137 167 2276 2557 2144 634 1053 789 1120 2051 1838 765 1735 1645 1326 1266 1790 2138 32 1487 1455 Branch2 Branch3 Branch4 1879.647 Mean 1359.357 Mean 1423.462 85.10007 Standard E 182.6685 Standard E 196.7028 1958 Median 1504.5 Median 1487 #N/A Mode #N/A Mode #N/A 350.8766 Standard D 683.4829 Standard D 709.2219 123114.4 Sample Var 467148.9 Sample Var 502995.8 -0.086475 Kurtosis -0.061941 Kurtosis -0.821611 -0.513741 Skewness -0.797171 Skewness -0.125212 1284 Range 2244 Range 2390 1125 Minimum 32 Minimum 167 2409 Maximum 2276 Maximum 2557 31954 Sum 19031 Sum 18505 17 Count 14 Count 13 NCY TABLE Cumulative Percent Frequency Percent #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! k=6 (2^6>60) i>= 420.8333 width=430 #REF! Histogram of balance 430 860 1290 1720 2150 from branch 2, 14 from branch 3 and 13 from branch 4. The frequency table of the balances in the sample (N=60) is r each branch is presented in the following boxplots. The boxplots were created in Minitab. observed in $1720-$2150 class. However, there is also a very high frequency in the $1290-$1720 class. has a median balance equal to 1600$. Also, we see that 58% of the customers have a balance less than 1720$. lass is less than 2000$, indicating that approximately an extra 15% of the customers also have less than 2000$ in their balance. s have more than 2000$ in their account. plot of Balance 2 3 City 4 2 3 4 City distribution of balance seems to be different across the branches. The median balance of branches 1, 3 and 4 are closer to 1500$ , wh balance of approximately 2000$. All distributions seem to be negatively skewed, since the median is not in the center of the box, re symmetric. e that most of the balances are concentrated between 1290$ and 2150$. A total of 34 balances (56.7%) are within this range. nch are presented in the following table. We observe that there is a difference in the mean and median values across the braches, e previous boxplots. We observe that the mean and median values for branches 1, 2 and 3 are not very close, anches are skewed. More specifically, since the median values are greater than the respective mean values for branches 1, 2 and 3, gatively (left) skewed. Branch 4 seems to have a more symmetric distribution. Since not all four distributions are symmetric, mparisons, since it is a more representative measure of location. Thus, by observing the medians, ng branches: branch 1 has the lowest median balance of approximately 1400$, followed by branches 3 and 4 who have highest median balance is observed in branch 2 with a value of approximately 2000$, which is quite higher compared tion of the balance is 596.9$ and the range is equal to R=Largest value-smallest value=2557-32=2525. These two values measure the sp huge variation in the balance. In our sample, there is a minimum value of balance of 32$ and a maximum of 2557$; ues. Also, the standard deviation is quite large. The standard deviation is the square root of the variance. hows that the data are widely spread around the mean. 946.8$ indicating that 75% of the sample has balance lower than 1946.8. The 1 st quartile is 1121.3$ indicating that 25% of the sample coefficient is -0.616, indicating that the distribution is negatively skewed, meaning that balance values greater than ower than the median. In other words, the median balance is greater than the mean balance and the balances are concentrated ce the skewness value is greater than -1, we conclude that the skewness is not significant and the distribution of balances $ in their balance. 4 are closer to 1500$ , whereas he center of the box, within this range. s across the braches, or branches 1, 2 and 3, are symmetric, two values measure the spread of g that 25% of the sample has es are concentrated of balances