Statistical Analysis of Bike Hiring Trends in London | Desklib

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QUA4A5 Group Project – Assessment 3

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Task 1
A. Average number of bikes hired from the docks was evaluated to be 29279.92 or
approximately 29280 per day between July 2014 and August 2018. Standard deviation of
bikes hired from the docks was evaluated to be 11418.19 or approximately 11419 per day.
The number of observations in the sample is 1494
( n )
, which is also considered to be the
population (Anderson, Sweeney, Williams, Camm & Cochran, 2017).
The 95% confidence interval for population of bike hired is calculated as
x
¿
±Z0. 25∗ s
√ n = [ 29279 . 92−1 . 96∗11418 .19
√ 1494 ,29279 . 92−1 . 96∗11418 .19
√ 1494 ]= [ 28700 . 93 ,29585 . 91 ]
where
Z0. 25=1 . 96
.
Hence, with 95% confidence it is possible to say that average number of bikes hired from the
docks would be somewhere between 28701 and 29586 per day, between July 2014 and
August 2018.
Population of bikes for daily hires was analysed using descriptive statistics. Within the time
period of July 2014 to August 2018, a maximum of 63732 bikes and a minimum of 3593
bikes were hired per day. Number of daily hires has been plotted graphically using a Boxplot
and a frequency histogram (Newbold, Carlson & Thorne, 2012).

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Figure 1: Histogram and Boxplot of daily hires of bicycles
B. Figure 1 indicates that the median number of bikes was slightly less than 30000 bikes per
day. The exact value of median was evaluated as 28377.5 or approximately as 28378 bikes
per day. The median was slightly less than the mean number of bikes hired daily, which
indicated a little positive skewness in the distribution of number of bicycles hired daily. The
histogram of daily hired bikes also represents that the distribution is almost normal.
Approximately on 50% of the days, number of bikes hired was less than 28378 and on rest of
days more than 28378 bikes were hired. The first quartile is noted to be somewhere around
twenty thousand bikes per day
( Q1=21862 )
and the third quartile is pointed out to be just
above 35000 bikes
( Q3=36361 . 3 or 36362 )
. Hence, middle 50% of the demand of bikes by
customers varied between 21862 and 36362 bikes per day. The lowest 25% hiring of bikes
hired in day was below 21862, and top 25% hiring was above 36362 bikes.
C. In the statistical analysis, the characteristics of interest are always average or standard
deviation. Therefore, it is required to estimate the distribution of samples for mean. The
sample itself does not contain enough information to perform this operation. The shape and
form of the sampling distribution are always assumed to be normal (Ghasemi & Zahediasl,
2012).
The first known characteristic of the normal distribution is that, given the random and

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independent samples of N observations, the distribution of the sample mean is normal and
impartial, regardless of the size of N. Therefore, if we assume that the population is normal,
then it is always safe to make parametric assumptions about the distribution of the sample,
regardless of the size of the sample. The second known characteristic of the normal
distribution indicates that sample and variance of the sample are independent in random and
independent observations. Therefore, assuming that estimation of population mean and
variance are independent, the sample average and sample deviation are used to make these
estimates. So we assume that the population is normal.
Task 2
A. Three samples of size 10, 50 and 500 were randomly generated in Excel using
RANDBETWEEN function. First 10 observations for each of the three samples have been
presented in the following table. The formula used for the sample selection is “INDEX
($A$2:$A$15000, RANDBETWEEN (2, COUNTA ($A$2:$A$15000)), 1)”.
Table 1: First 10 observation of three samples
Number of
Bicycles_10
Number of
Bicycles_50
Number of
Bicycles_500
38131 29989 26520
55958 52787 34608
38243 20439 27301
27706 27071 58002
58531 15938 29047
39725 20919 28043
47524 48955 13612
45929 6242 37514
41468 42935 31436
18135 34115 15059
For the first sample with 10 observations,
Mean = 41135, Median = 40596.5, Standard deviation = 12087.50 and Mode = Does not
exist.
For the second sample with 50 observations,