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Numeracy and Data Analysis Related to Weather

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  • Unit No: N/A
  • Level: High school
  • Pages: 9 / Words 2307
  • Paper Type: Assignment
  • Course Code: N/A
  • Downloads: 793
Question :

Questions- This assessment will cover the following questions:

  • Calculate the mean, median, mode, range and standard deviation through following steps.
  • Demonstrate the steps of calculation of m value and c value and forecast the humidity for day 15 and day 20.
Answer :

INTRODUCTION

Numerical and data analysis involves the practical use of statistical or mathematical calculations to data approximate data of upcoming trend. Mainly, this method is used for estimation of data related to weather report while maintaining the reasonable as accurate as possible (Noh, 2019). The current assignment is going to estimate the data about humidity of London in upcoming days, on the basis of past data of current month. For this purpose, statistical methods like average, median and mode including range and standard deviations are used for further analysis of numerical data.

Main Body

For forecasting the upcoming humidity of London the past data from 1st Dec. to 10th Dec. 2019 is taken (Past Weather in London, England, United Kingdom – December 2019). These data are further represented in both tabular and graphical form to analyse the numerical data in systematic manner –

1. Table Format

Report of Humidity in atmosphere of London from last consecutive days is gathered (Past Weather in London, England, United Kingdom – December 2019. As mentioned below -

Days

Humidity (At 12pm)

1

94%

2

85%

3

86%

4

80%

5

98%

6

84%

7

72%

8

80%

9

74%

10

76%

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2. Graphical representation of weather report

Humidity in London atmosphere from last few days

Days

Humidity (At 12pm)

1

94%

2

85%

3

86%

4

80%

5

98%

6

84%

7

72%

8

80%

9

74%

10

76%

3. Calculation

Calculation for Humidity in percentage

Days

Humidity (At 12pm)

1

94%

2

85%

3

86%

4

80%

5

98%

6

84%

7

72%

8

80%

9

74%

10

76%

total

829%

mean

82.90%

median

82%

mode

80%

standard deviation

0.083592929 = 8%

Calculation -

For understanding the humidity of London and getting a detailed information of the same, the data of past ten days is taken (Eyre, English and Forsythe, 2019). These observations are then converted into the central tendencies, which include arithmetic mean, median of data, mode, range as well as standard deviation is calculated in following manner –

Arithmetic Mean:

This central tendency can be defined as the average of entire data, that is calculated by dividing the sum of all observation from the number of observations, using below formula -

[ Arithmetic Mean/ Average = ∑x / n ]

here, ∑x depicts the total of all data points,

and, n represents the total frequency or number of observation

For present data,

Mean = (Total Sum of Observation) / Number of observation

= 829 / 10

= 82.90 %

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Median:

This term defines as the middle data point by dividing the total population into two equal parts. But before dividing the data, it is essential for statistician to synchronise the data from smallest to largest. Now to find median, following formulae is used –

If, no. of data points in total population is odd then,

[ Median Position = (No. of data + 1) / 2 ]

But if, no. of data points is even then

[ Median Position = No. of data / 2 ]

For present data,

Median position = (10 / 2)th observation

= 5th Observation

Now, present data for ten consecutive days is – 94%, 85%, 86%, 80%, 98%, 84%, 72%, 80%, 74% and 76%.

Therefore, arranging the data in serial order then median can be calculated as –

M = (84 + 85)/ 2

= 84.50%

Mode:

This kind of central tendency depicts the observation which is occurred in more frequent manner in a sample (Wang and et. al., 2019). For this purpose, term which has highest frequency conclude as mode of data.

For present data,

Mode = 80% (as this term is repeated in given data two times)

Also Read:- Use of Statistical Analysis in Management

Range:

This statistical method is calculated by determining the difference between maximum observation and minimum one in following way –

Range = Maximum observed data – Minimum observed data

For present humidity data,

Range = Max – Min

= 94 – 72

= 22%

Standard Deviations:

This one can be calculated by finding the variance of dispersed data in following way -

Variance2 = {∑(x – mean)2 / N}

[ Standard Deviation =(variance) ]

Table for calculating standard deviation and variance –

Date

Humidity (At 12pm)

(x-mean)

(x-mean)2

1

94.00%

11.1

123.21

2

85.00%

2.1

4.41

3

86.00%

3.1

9.61

4

80.00%

-2.9

8.41

5

98.00%

15.1

228.01

6

84.00%

1.1

1.21

7

72.00%

-10.9

118.81

8

80.00%

-2.9

8.41

9

74.00%

-8.9

79.21

10

76.00%

-6.9

47.61

 

Mean = 82.90%

 

628.9

Variance 2 = [ ∑(x – mean) 2 / N ]

= 628.90 / 10 = 62.89

Std Dev. = √variance

=√ 62.89 = 7.93%

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4. Liner-forecasting model

To estimate the percentage of humidity in upcoming days in December month of London, linear forecasting model can be used, by using following formula -

y = mx + c

in this linear equation, m indicates line’s slope of a line that shows the angular relationship among variables as -

m = Change in Y / Change in X

therefore, using the above humidity equation –

Days (X)

Humidity (At 12pm) (Y)

X2

∑XY

1

94.00%

1

94

2

85.00%

4

170

3

86.00%

9

258

4

80.00%

16

320

5

98.00%

25

490

6

84.00%

36

504

7

72.00%

49

504

8

80.00%

64

640

9

74.00%

81

666

10

76.00%

100

760

Total = 55

829.00%

∑X2 = 385

∑XY = 4406

1. Compute value of m as per above table -

m = N * ∑XY - ∑X * ∑Y /N * ∑X2 - (∑X)2

= 10 * 4406 – 55 * 829 / 10 * 385 – (55)2

= 44060 – 45595 / 3850 – 3025

= -1535 / 825 = -1.86 approx.

Now, c = ∑Y – m ∑x / N

= 829 – (-1.86) * 55 / 10

= 93.13

Taking the above value of m and c, humidity on coming days can be forecasted by -

For 15th day -

Y = m x + c

= (-1.86) * 15 + 93.13

= 65.23

so, forecasted value of humidity on 15th day of dec. is 65.23% approx.

similarly, on 20th day, it is

Y = m x + c

= (-1.86) * 15 + 93.13

= 55.93

so, forecasted value of humidity on 20th day of dec. is 55.93% approx.

CONCLUSION

It has been evaluated from this overall report, that to predict the future report from a number of statistical methods, central tendency refers to be the best method would help in determining the current trend as well as forecasting the upcoming data also. 

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