Numeracy and Data Analysis: Mean, Median, Mode, and Forecasting

This report explores numeracy and data analysis techniques such as mean, median, mode, and linear forecasting model. It provides a case study on phone call data and explains how to calculate and interpret these values. The report also includes charts and a conclusion.

INDIVIDUAL PROJECT

TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................3
MAIN BODY..................................................................................................................................3
1. Data..........................................................................................................................................3
2. Presentation on Charts.............................................................................................................3
3. Calculation...............................................................................................................................4
4. Linear forecasting model.........................................................................................................7
CONCLUSION................................................................................................................................9
REFERENCES..............................................................................................................................10

INTRODUCTION
Numeracy and Data Analysis is the use of statistical data and formulas to analyse the data
and interpret it accordingly (Morley, 2017). The current report will evaluate the mean, median
and mode of the collected data and also use the linear forecasting model to forecast the relevant
data.
MAIN BODY
1. Data
S. No. Date Number of phone calls/ Day
1 11th August, 2020 6
2 12th August, 2020 4
3 13th August, 2020 5
4 14th August, 2020 9
5 15th August, 2020 4
6 16th August, 2020 8
7 17th August, 2020 6
8 18th August, 2020 2
9 19th August, 2020 10
10 20th August, 2020 4
2. Presentation on Charts
The above data can be pictorially represented on charts in following manner:
Column Chart:
3

Line Chart:
3. Calculation
i. Mean
S. No. Date Number of phone calls/ Day
1 11th August, 2020 6
2 12th August, 2020 4
4

3 13th August, 2020 5
4 14th August, 2020 9
5 15th August, 2020 4
6 16th August, 2020 8
7 17th August, 2020 6
8 18th August, 2020 2
9 19th August, 2020 10
10 20th August, 2020 4
Sum of Phone Calls (∑x) 58
Total number of Observations (n) 10
Mean [(∑x)/ n] 5.8
Interpretation: The mean value of the phone calls i.e. average number of phone calls that have
been made on a daily basis is 5.8. The total number of phone calls made in the 10 day period was
divided by the total number of observations i.e. 10 and hence the mean value of 5.8 was
obtained.
ii. Median
Calculation of media is a two- step process:
Step 1: Arrangement of data in ascending manner:
S. No. Date Number of phone calls/ Day
1 18th August, 2020 2
2 12th August, 2020 4
3 15th August, 2020 4
4 20th August, 2020 4
5 13th August, 2020 5
6 11th August, 2020 6
7 17th August, 2020 6
8 16th August, 2020 8
9 14th August, 2020 9
10 19th August, 2020 10
5

Step 2: Application of the formula (n+1)/ 2
No. of observations 10
Median = (10+1)/2 5.5
Value = (5+6)/2 5.5
Interpretation: First the median of 5.5 was obtained which indicated that the value at the
position of 5.5 is the median value but since 5.5 is not a definite position, the 5th and 6th value
between which the position 5.5 lies was selected and their average was calculated accordingly
(Fisher and Marshall, 2019). The average came out to be 5.5.The median value for the total of 10
observations was 5.5 i.e. this is the middle value of the data set.
iii. Mode
S. No. Date Number of phone calls/ Day
1 11th August, 2020 6
2 12th August, 2020 4
3 13th August, 2020 5
4 14th August, 2020 9
5 15th August, 2020 4
6 16th August, 2020 8
7 17th August, 2020 6
8 18th August, 2020 2
9 19th August, 2020 10
10 20th August, 2020 4
Mode 4
Interpretation: Mode indicates the maximum number of times a value is repeated within a set of
observation. Since the maximum number of times for which phone call is made per day is 4, the
mode value is therefore, 4.
iv. Range
Range can be calculated by obtaining the largest and the smallest value amongst the set of
observation:
6

Largest Value 10
Smallest Value 2
Range = Largest value - Smallest value 8
Interpretation: Range basically indicates the maximum and minimum value within which the
phone calls lies. The table clearly indicates that the range of the phone call data set is calculated
to be 8 by subtraction of the smallest value 2 by the largest value 10.
v. Standard Deviation
S. No. Date Number of phone calls/ Day (X) X2
1 11th August, 2020 6 36
2 12th August, 2020 4 16
3 13th August, 2020 5 25
4 14th August, 2020 9 81
5 15th August, 2020 4 16
6 16th August, 2020 8 64
7 17th August, 2020 6 36
8 18th August, 2020 2 4
9 19th August, 2020 10 100
10 20th August, 2020 4 16
Total 58 394
Standard Deviation = Square root of [(∑X2 / N) – (∑X / N)2]
= square root of [(394 / 10) – (58 / 10)2]
= square root of [(39.4) – (33.64)]
= square root of 5.76
= 2.4
Interpretation: The implementation of formula clearly indicates that the standard deviation was
obtained as 2.4 after square root of 5.76. This value indicates that how much deviation occurs of
the data from the mean value (Stamler and et.al., 2015).
4. Linear forecasting model
7

Date X Number of phone calls/ Day (Y) X*Y X2
11th August, 2020 1 6 6 1
12th August, 2020 2 4 8 4
13th August, 2020 3 5 15 9
14th August, 2020 4 9 36 16
15th August, 2020 5 4 20 25
16th August, 2020 6 8 48 36
17th August, 2020 7 6 42 49
18th August, 2020 8 2 16 64
19th August, 2020 9 10 90 81
20th August, 2020 10 4 40 100
Total 55 58 321 3025
Y= mX + c
i. Calculation of m
m = [(n*ΣXY) – (ΣX*ΣY)] / [(n*ΣX2) – (ΣX)2]
m = [(10 * 321) – (55 * 58)] / [(10 * 3025) * (55)2]
m = [3210 - 3190] / [30250 – 3025]
m = [20] / [27225]
m = 0.0007
ii. Calculation of c
c = (ΣY – m * ΣX) / n
c = (58 – 0.0007 * 55)/ 10
c = (58 – 0.0385)/ 10
c = 57.9615/ 10
c = 5.79
iii. Forecast of the number of calls for 12th and 14th day
Using the equation Y = mX + c, the forecasted value for 12th and 14th day can be ascertained in
following manner:
8

Forecasting phone calls per
day for 12th day
Y = mX + c
Here,
X = Day 12
Y = 0.0007 (12) + (5.79)
Y = 0.0084 + 5.79
Y = 5.7984
Forecasting for 14th day
Y = mX + c
Here,
X = Day 14
Y= 0.0007 (14) + (5.79)
Y = 0.0098 + 5.79
Y = 5.7998
Interpretation: The calculation of the above forecasted results helps in clearly indicating that
the value of m was calculated to be 0.0007 and the value of c was ascertained as 5.79 by the
input of the respective formulas (Bertrand and Goupil, 2020). Then, the equation Y = mX + c
was used to forecast the phone calls for 12th and 14th day as 5.7984 and 5.7998 respectively.
CONCLUSION
The report above helps in clearly concluding that the implementation of the different
formulas can be used to obtain different values and every result can be interpreted in its own
context and manner.
9

REFERENCES
Books and Journals
Bertrand, P. and Goupil, F., 2020. Descriptive statistics for symbolic data. In Analysis of
symbolic data (pp. 106-124). Springer, Berlin, Heidelberg.
Fisher, M. J. and Marshall, A. P., 2019. Understanding descriptive statistics. Australian Critical
Care. 22(2). pp.93-97.
Morley, P., 2017. An analysis of large-Scale numeracy assessment data in Australia (Doctoral
dissertation, Monash University).
Stamler, J. and et.al., 2015. INTERMAP: background, aims, design, methods, and descriptive
statistics (nondietary). Journal of human hypertension. 17(9). pp.591-608.
10

11