Report on Numeracy and Data Analysis: Station Usage over 10 Years

This report presents a comprehensive analysis of Castle Bar Park station usage data over a 10-year period, employing various numeracy and data analysis techniques. It begins with a tabular representation of the data and visualization through bar and line charts. The report then delves into descriptive statistics, calculating the mean, median, mode, range, and standard deviation to understand the central tendencies and dispersion of the data. Furthermore, it applies a linear forecasting model (Y=mx+c) to predict station usage for the 12th and 15th years. The calculations for 'm' and 'c' values are detailed, along with the forecasted values. The conclusion highlights the importance of data analysis and numeracy in decision-making, emphasizing the significance of graphical presentation and statistical methods. The report is supported by relevant references.

NUMERACY AND DATA
ANALYSIS

TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................1
1. Data in tabular aspect..............................................................................................................1
2. Data in chart form ..................................................................................................................1
3. Extracting mean, mode, median, range and standard deviation..............................................2
4 . Use of linear forecasting model.............................................................................................5
Calculating m value....................................................................................................................5
Calculating c value......................................................................................................................5
Forecasting for 12th and 15th year.............................................................................................5
CONCLUSION................................................................................................................................6
REFERENCES................................................................................................................................7

INTRODUCTION
Numeracy is considered as ability for reasoning and application of simple concepts of
numbers. It is very significant for individuals for developing logical thinking and strategies in
regular activities. Data analysis is considered as procedure to systematic apply for describing and
illustrating, recapping and evaluating data. The present report is all about Castle Bar park station
usage with use of descriptive analysis such as parameters like mean, median, mode, standard
deviation and range. Apart from this, it has stated implication of linear regression equation of
Y=mx+c for predicting 12th and 15th year.
1. Data in tabular aspect
Year Castle Bar park station usage
1 10
2 111
3 12
4 63
5 66
6 70
7 80
8 14
9 30
10 29
2. Data in chart form
Bar Chart
1

Line chart
3. Extracting mean, mode, median, range and standard deviation
Steps for mean
It is replicated as average which is used for measuring central tendency of the entire data
set. The detailed steps for calculating mean are stated below:
2

 At the initial step, identifying the set of values average should be considered and ensuring
about using real numbers but not variables.
 Listing every numbers and then aggregate should be considered (Sullivan and Brown,
2015).
 In the same series, every number which is aggregated there count should be taken along
with identical values as well.
 Further, the outcome of step 2 must be divided by step 3 gives final result of average.
Particulars Amount
Sum 485
N 10
Mean Total/N
Mean 48.5
Steps for median
It is one of the important measure of central tendency as this separates higher half from
lower half of the data set. The median with the odd number of sequences is easy to find. For the
set of values with even number of values, median is calculated by taking the average of the two
middle values. The detailed steps for calculating median are stated below:
 After identification, the data set must be arranged in increasing order and then
determining about even or odd data set (Vives‐Mestres, Martín‐Fernández and Kenett,
2016).
 If it is even, then set of middle value's count must be considered.
 The above outcome's amount will be divided by 2 and its result will be replicated as
median of data set.
Particulars Amount
Median (5th and 6th)/2
(30 + 63) / 2
Median 46.5
Steps for mode
3

Mode is also one of tendency measure as in simple words, highest repetitive frequency
number is mode. After tracing the count of every number, it has been observed that no number is
repeating twice as well. Thus, there is absence of mode in Castle bar park station usage over past
10 consecutive years.
Steps for range
It is a a descriptive statistic which is area of variation among upper and lower limit of
specific scale. The steps for finding the outcome of range are stated below:
 The numbers must be set in ascending order (Mean, Median, Mode, 2019).
 The identification of highest and lowest number or maximum and minimum within the
data set.
 To reach at final stage, the minimum must be excluded by maximum amount as range
within the data set of station usage.
Particulars Amount
Minimum 10
Maximum 111
Range Maximum – Minimum
111 – 10
101
Steps for standard deviation
It is a statistics which measures dispersion of dataset on basis of mean and this is the
number which helps in representing about measurements of spread from the mean or expected
value. The steps for extracting standard deviation are stated below:
 This is continuous steps after mean is stated as X bar.
 On basis of other step, each number must be subtracted from X bar and then its outcome
will be squared.
 The aggregate of squared outcome must be undertaken which will be divided through n-1
as 9 as variance of station usage (Federici, Skaalvik and Tangen, 2015).
 At the final phase, square root of variance should be considered as standard deviation.
Particulars amount
Variance [Sum of (X – X bar) ^ 2] / N - 1
4

N – 1 10 – 1
9
[Sum of (X – X bar) ^ 2] / 9 10604.50 / 9
Variance 1178.28
Standard deviation Square root (Variance)
34.33
In the above scenario, Its standard deviation is 34.33 which is far from mean so it has low
spread out of the data sets.
4 . Use of linear forecasting model
Year (x)
Castle Bar park station
usage XY X^2
1 10 10 1
2 111 222 4
3 12 36 9
4 63 252 16
5 66 330 25
6 70 420 36
7 80 560 49
8 14 112 64
9 30 270 81
10 29 290 100
55 485 2502 385
Calculating m value
Particulars Details
m NΣxy – Σx Σy / NΣ x^2 – (Σx)^2
(10 * 2502) – (55 * 485) / (10 * 385) – (55)^2
(25020 – 26675)/ (3850 – 3025)
5

m -2.01
Calculating c value
Particulars Details
c Σy - m Σx / N
(485 – (-2.01 * 55))/10
c 59.53
Forecasting for 12th and 15th year
Forecast of 12th year
Y = mX + C
Y -2.01 (X) – 59.53
X 12
Y -2.01 (12) – 59.53
35.46
Forecast of 15th year
Y = mX + C
Y -2.01 (X) – 59.53
X 15
Y -2.01 (15) – 59.53
29.44
CONCLUSION
From the above report it could be concluded that data analysis and numeracy plays very
important role for purpose of decision making and to interpret the numerical amount. It has
shown importance of graphical presentation along with significance of descriptive statistics.
Moreover, it had articulated significance of linear forecasting model of station usage over past 10
6

consecutive years with use of y = mx + b. Thus, it has also predicted with this equation for 12th
and 15th year as 35.46 and 29.44 respectively.
7