BABS Numeracy and Data Analysis Report: Forecasting Techniques

This report presents a comprehensive analysis of numerical data using various statistical and mathematical tools. It begins by organizing expense data over ten days into tables and charts, followed by the computation of descriptive statistics including mean, median, mode, range, and standard deviation. The analysis provides interpretations for each statistical measure, highlighting how the data is assessed. Furthermore, the report employs a linear forecasting model to predict expenses for days 15 and 20, demonstrating the application of historical data to forecast future trends. The conclusion summarizes the findings, indicating a downward trend in expenses and emphasizing the usefulness of statistical tools for identifying patterns and predicting future values. The report references relevant sources to support its analysis.

Numeracy and Data Analysis

INTRODUCTION......................................................................................................................3
1. Arranging the data into table..............................................................................................3
2. Presenting data in chart form.............................................................................................3
3. computing descriptive statistics.........................................................................................4
4. Using the linear forecasting model for predicting the value for 15 and 20 day.................8
CONCLUSION........................................................................................................................10
REFERENCES.........................................................................................................................11

INTRODUCTION
Numeracy and data assessment involves the processing of mathematical and statistical
data to understand the patterns of hidden numerical values. The current study will emphasize
on various expenses that have been made for a period of 10 consecutive days. Moreover, it
will involve the use of various statistical and mathematical tools like mean, mode and median
to predict the changes effectively.
1. Arranging the data into table
Number
of Days Date Expenses
1
1st April
2020 300
2
2nd April
2020 400
3
3rd April
2020 600
4
4th April
2020 250
5
5th April
2020 300
6
6th April
2020 450
7
7th April
2020 500
8
8th April
2020 820
9
9th April
2020 750
10
10th April
2020 200
2. Presenting data in chart form
Line graph

Column graph
3. computing descriptive statistics
i. Mean
Number
of Days Date Bill payment
1 1st April 2020 300
2 2nd April 2020 400
3 3rd April 2020 600

4 4th April 2020 250
5 5th April 2020 300
6 6th April 2020 450
7 7th April 2020 500
8 8th April 2020 820
9 9th April 2020 750
10 10th April 2020 200
total of
expenses 4570
No. of
observation 10
Mean 457
Interpretation- From the above data it can be interpreted that the total expenses done
incurred to 4570. Therefore, in order to calculate the mean data, all the expenses are added
and then divided by the total observations (Zheng and et.al., 2017). Thus, the resulted mean
came up to 457.
ii. Median
Step 1: Arranging data in ascending order
Number
of Days Date
Data in relation
to payment of
bill
1
10th April
2020 200
2
4th April
2020 250
3
1st April
2020 300
4
5th April
2020 300
5
2nd April
2020 400
6
6th April
2020 450
7
7th April
2020 500
8
3rd April
2020 600
9
9th April
2020 750
10 8th April 820

2020
No. of
observation 10
Median
observation= (10+1)/2 5.5
Median= (400+450)/2 425
Interpretation- Median can be defined as the value that separates the higher half from
the lower half in an observation. From the above data, it can be assessed that the median
value obtained for 10 days is 425 (Peleg, 2019). It is important to arrange the data from
ascending to descending order and then by applying the formulae, (n+1)/2 where n means
total no. of observations. The resulted answer is considered to be the median.
iii. Mode
Date Expenses
1st April
2020 300
2nd April
2020 400
3rd April
2020 600
4th April
2020 250
5th April
2020 300

6th April
2020 450
7th April
2020 500
8th April
2020 820
9th April
2020 750
10th April
2020 200
Mode = 300
Interpretation- It is represented as the highest number of data that appears in an
observation. From the above set of data, it can be interpreted that the value of mode is
calculated to be 300 (George and Mallery, 2016). It is evitable that the bill amount of 300
was paid on both 1st and 5th April therefore the modal value is 300.
iv. Range
Particulars Formula Amount
Maximum 820
Minimum 200
Range
Largest value-Smallest
value 620
Interpretation- The above table reflects that the highest bill payment was for 820
whereas the minimum was 200. Thus, in order to calculate range lowest no. was reduced
from the highest no. which gave the result 620.
v. Standard deviation
Date
Bill
payment X^2
1st April
2020 300 90000
2nd April
2020 400 160000
3rd April
2020 600 360000

4th April
2020 250 62500
5th April
2020 300 90000
6th April
2020 450 202500
7th April
2020 500 250000
8th April
2020 820 672400
9th April
2020 750 562500
10th April
2020 200 40000
Total 4570 2489900
Standard deviation= Square root of ∑x^2 / N – (∑x / n) ^ 2
= SQRT of (2489900 / 10) – (4570 / 10) ^ 2
= SQRT of 248990 – 208849
= SQRT of 40141
= 200.35
Interpretation- From the above assessment, it can be interpreted that standard
deviation equals to 200.35. The value was calculated by working out the mean and then
reducing it from the square root result (Sarkar and Rashid, 2016). In the end, the mean of
squared differences is computed with square root of difference value.
4. Using the linear forecasting model for predicting the value for 15 and 20 day
iii. Forecast for day 15 and 20
Date X Bill payment (Y) X*Y X^2
1st April
2020 1 300 300 1
2nd April
2020 2 400 800 4
3rd April
2020 3 600 1800 9
4th April
2020 4 250 1000 16
5th April
2020 5 300 1500 25
6th April
2020 6 450 2700 36
7th April
2020 7 500 3500 49

8th April
2020 8 820 6560 64
9th April
2020 9 750 6750 81
10th April
2020 10 200 2000 100
Total 55 4570 26910 385
m = NΣxy – Σx Σy / NΣ x^2 – (Σx)^2
Y = mX + c
m = 10 (26910) - (55 * 4570) / (10 * 385) – (55)^2
m = (269100 – 251350) / (3850 – 3025)
m = 17750 / 825
m = 21.51
c = Σy – m Σx / N
c = 4570 – (21.51 * 55) / 10
c = (4570 – 1183.33) / 10
c = 3386.667 / 10
c = 338.667
Computing value of Y by making use of m and c value
For 12 days-
Y = mX + c
= 21.51(12) + (338.667)
= 258.18 + 338.667
= 596.84
For 14 days -
Y = mX + c
= 21.51(14) + (338.667)

= 301.21 + 338.667
= 639.87
Interpretation- The major objective of linear forecasting model is to forecast the
demand by using historical data. From the above data it can be interpreted that the bill
expenses for 12 days were computed to be 596.84 and for 14 days 639.87. The values were
obtained after multiplying x with m and then by adding c. Thus, It helped in predicting the
value for day 15 and 20.
CONCLUSION
From the above study it can be concluded that mean, mode and median are an important tool
of statistics and they can be really helpful in identifying current and future trends. The above
study predicted a downward trend in the bill expenses. In the beginning, the bill expenses
fluctuated but towards the end there was a downward shift which means that the bill expenses
reduced gradually as the days proceeded.

REFERENCES
Books and journals
George, D. and Mallery, P., 2016. Descriptive statistics. In IBM SPSS Statistics 23 Step by
Step (pp. 126-134). Routledge.
Peleg, M., 2019. Beta distributions for particle size having a finite range and predetermined
mode, mean or median. Powder Technology. 356. pp.790-794.
Sarkar, J. and Rashid, M., 2016. Visualizing mean, median, mean deviation, and standard
deviation of a set of numbers. The American Statistician. 70(3). pp.304-312.
Zheng, S and et.al., 2017. The relationship between the mean, median, and mode with
grouped data. Communications in Statistics-Theory and Methods. 46(9). pp.4285-4295.