Interpretation and Use of Financial Statistics

This article covers exploratory data analysis, discrete probability distributions, continuous probability distributions, central limit theorem, confidence intervals, hypothesis tests, correlation and regression in financial statistics.

Running head: INTERPRETATION AND USE OF FINANCIAL STATISTICS
Interpretation and Use of Financial Statistics
Name
Course Number
Date
Faculty Name

INTERPRETATION AND USE OF FINANCIAL STATISTICS 2
Interpretation and Use of Financial Statistics
Exploratory Data Analysis
1) Quality of bank service
a) On average, the business account holders had a higher rating of the bank services
compared to the private holders. Similarly, the variation of their responses was not
widely dispersed from the mean as compared to the private account holders. Both the
distribution of bank rating between the private and business account holders are
slightly skewed to the left – showing that the means are less than their respective
median rating scores. Therefore, most of the customers had ratings less than the
average value.
b) Symmetric distribution means that there are no extreme values in the data which
affect the skewness of the distribution. This is evident in the slight variation between
the means and median values. Also, the boxplots do not show any cases of outliers
and the 50th percentile is approximately in the middle region of the plots. Similarly,
the stem and leaf show that most of the values were concentrated on the centre.
c) The standard deviation of 1.336 of the private account holders means that their ratings
on the quality of bank services they receive differ from the average value by 1.336.
d) The standard error of business account holders
se ( Business Account Holders )= 0.941
√30 =1.1718
e) 90% CI true mean of Business account holders
C . I of mean=8.323± 1.64∗1.1718
[6.401;10.245]
The 90% confidence interval shows that the true mean of business account holders on the
bank services would lie between 6.401 and 10.245 assuming that the sample is obtained
from the same population distribution.

INTERPRETATION AND USE OF FINANCIAL STATISTICS 3
2) Choice of tutorials
a) Based on the measures of central location and variation, a tutor based method of
studying had the best results. This is because the first quartile had at least 66.25
compared to the on-online type who had 61 and self who had 46. Further, the median
and the mean marks for tutor based tutorial were significantly higher compared to the
other two groups.
b) Skewed data means that the median and the mean statistic are not significantly equal.
Further, it shows that there are extreme values which are affecting the distribution.
For, tutor based marks distribution, the mean is not equal to the median and we can
conclude that the data is skewed to the right – which means that there were students
who had higher marks as compared to the general sample.
c) The tutor based group has an interquartile range of 7.25 showing the different the 75th
and 25th percentiles.
d) Tutor based group has the highest average followed by online the self-placed.
However, on-line based groups have a very large standard deviation and interquartile
range compared to the other two groups.
e) 95% confidence interval of the self-placed group
¿ 55.76 ±1.96∗1.01
¿ 55.76 ±1.9796
[53.7804 ;57.7396]
At 95% confidence level, the true mean of the performance of the self-placed group will
lie between 53.78% and 57.74%, assuming that the observation is selected from the same
population distribution.
3) Government funding
a) On average, the number of students in a class is around 22 students using the
arithmetic mean and 24 using the median statistic. Although some of the classes have
ratios above 26 students per teacher, there are many classes with less than 16 students
per teacher, pulls the average ratio. The distribution is slightly skewed to the left, due
to the high dispersion of classes with a small student to teacher ratio.

INTERPRETATION AND USE OF FINANCIAL STATISTICS 4
b) Mean is not the best measure of central location because there are some classes with
over 26 students per teacher. Therefore, the median is the best measure because of the
skewness.
c) Interquartile range
IQR=26.65−17.1=9.55
d) Standard deviation explains the variation of the students to teacher ratio – which is
more of the distribution of the observation and the standard error is the standard
deviation of the mean statistic distribution.
e) The confidence interval of the mean explains the range to which the average of
students to teacher ratio will lie at 95% confidence level when other samples are
selected from the same population distribution.
Discrete probability distributions
1) Number of cars
a) P(cars sold in a week = 2) = 0.2
b) P(cars sold in a week >=2) = 0.2+0.1 = 0.3
c) E ( x )=∑ xf ( x )=0∗0.4+ 1∗0.3+2∗0.2+3∗0.1=1
The average number of cars to be sold in any given week will be 1.
d) Std=Var ( x )=E ( x2 )− [ E ( x ) ]2
E ( x2 )=∑ x2 f ( x ) =02∗0.4+12∗0.3+22∗0.2+32∗0.1=2
Var ( x )=2−12=1
Std= √1=1
2) Number of absentees
a) P(number of absentee≥1)=0.4+0.2+0.1=0.7
b) P ¿

INTERPRETATION AND USE OF FINANCIAL STATISTICS 5
c) E ( x )=0∗0.3+1∗0.4+2∗0.2+3∗0.1=1.1
E ( x2 )=02∗0.3+12∗0.4+22∗0.2+ 32∗0.1=2.1
Std= √ 2.1−1.12 =0.943
3) E ( x )=xf ( x )
E ( x )=50000∗0.002+25000∗0.01+12500∗0.1=1600
Therefore, the premium to be paid should be $ 1600+$ 500=$ 2100 to realize a $500
profit
Continuous Probability Distributions
4) The ordinary shares annual rate average is 15% with a standard deviation of 10%
a) Z−Statistic= X−mean
standard deviation= 30−15
10 =1.5
Probability=0.0668
b) Z−Statistic= 0−15
10 =−1.5
The probability of the returns being negative is 0.0668
c) Z−Statistic= 2.5−15
10 =−1.25
The probability of re-investment is 0.8944
d) Return= (−1.64∗10 ) +15=−1.4 %
5) Retail store
a) Z−Statistic= 2.5−2
0.25 =2

INTERPRETATION AND USE OF FINANCIAL STATISTICS 6
The probability that the sales will exceed 2.5 million dollars is 0.02275
b) 1.8−2
0.25 <Z < 2.2−2
0.25
0.78814−0.21186=0.57626
The probability of the sales lying within 10% of the expected sales is 0.57626
c) Z−Statistic=1.45−2
0.25 =−2.2
The probability of exceeding the break-even value of 1.45 is 0.9861
d) sales= ( 1.64∗0.25 ) +2=2.41
6) Mean=$250,000; Standard deviation=$75,000
a) Z−Statistic= 385000−250000
75000 =1.8
The probability that the property is less than $385,000 is 0.96407
b) Z−Statistic at half a million= 500000−250000
75000 =3.33
The probability of the property being less than half a million dollars is 0.99957
The probability of the property is between $385000 and half a million
¿ 0.99957−0.96407=0.0355
c) Minimum value of top10 %of the market= ( 1.64∗75000 )+250000=$ 373,000

INTERPRETATION AND USE OF FINANCIAL STATISTICS 7
Central Limit Theorem and Confidence Intervals
7) Mean = 4days and Standard deviation of 0.5 days
a) 90 %CI of themean=4 ± 1.64∗0.5
√ 100
4 ± 0.082
[3.918; 4.082]
The 90% confidence interval shows that the average number of days an individual’s
loans are processed will lie between the two values assuming that the sample is
selected from the same population distribution.
b) The confidence intervals calculation uses the standard normal score to determine the
margin of error. Therefore, without assuming that the observations follow a normal
distribution means that the interval estimate of the statistic does not qualify to be
calculated using the normal standard scores.
c) Decreasing the sample size means that the error is widened, hence increase of the
confidence interval.
8) Mean waiting time=4 minutes and standard deviation of 0.5.
a) 95 % CI =4 ± 1.96∗0.5
3
4 ± 0.327
[3.673; 4.327]

INTERPRETATION AND USE OF FINANCIAL STATISTICS 8
If other samples are selected from the same population distribution, the true mean will
lie within 3.673 and 4.327 confidence intervals at 95% confidence level.
b) First, we assume that the sample comes from a normally distributed population.
Secondly, the observations should be identically and independently selected.
c) If the waiting times were not varying, it means that the confidence intervals are fixed
and only change as a result of changing the confidence interval or the sample size.
Hypothesis Tests
1) P=0.3 use of a new product
Estimated proportion (p^) of using the new product is 147
420 =0.35
a) Z−Statistic= p− p
√ pq
n
0.35−0.3
√ 0.3∗0.7
420
=2.24
The p-value= 0.01255
The p-value is less than the significance level, we conclude that the new product is
financially viable.
b) n=1.962∗0.3∗0.7
0.052 =322.7
The sample size should be approximately 323 participants.

INTERPRETATION AND USE OF FINANCIAL STATISTICS 9
Correlation and Regression
2) House selling price
a) Size of the house has the highest correlation with selling – a coefficient of 0.849.
b) The relationship is positive.
c) This means that as the size of a house increases, so does the selling price.
d) Land and size of a house have the least correlation.
e) In real estates, small land can accommodate a storey house, hence the negative
correlation between these two variables.
3) Business account holders
a) Costs=−1.97+ 1.19Usage
The usage for business account holders should be used to predict or estimate the
account costs.
b) The slope coefficient indicates that increasing the business account usage by one
increases its costs by 1.19.
The costs of the account will be /1.97 assuming that the usage is zero.
c) This is a good model because the usage explains 50.3% of the variation of the account
costs. Also, the model is statistically significant at 95% confidence level because the
p-value is less than 0.05.
d) The standard error of the regression is approximately 0.935, indicating that the
standard distance between the points is 1.87%. This is means that this is a good model
because the standard variation of the estimate is less than the significance level.
e) The null hypothesis of the t-test

INTERPRETATION AND USE OF FINANCIAL STATISTICS 10
Null hypothesis: The coefficient estimates = 0