1. Data In Table Format

In this task of data analysis technique, we have to collect the number of phone calls making per day for ten consecutive days. After collecting data we have to arrange it in a table form.

Days	Number of Calls Made
Day 1	14
Day 2	15
Day 3	8
Day 4	10
Day 5	15
Day 6	9
Day 7	7
Day 8	8
Day 9	12
Day 10	12
n=10	xi=110

 

 

2. Data Arranged In Column Chart

In this, we are going to arrange the data collected in 10 days in the form of a chart. In the column chart given below, there are two columns. The column in blue colour shows the day on which data is collected and the green colour column represents the number of phone calls made on that day.

3. Data Arranged In Scatter Plot

4. Calculating Mean

In mathematics, mean is the average which is calculated by dividing the sum of a set of numbers by the count of numbers available in a particular data set. In this case, we have 10 days and each day have a unique number so we have to add them up and divide it by 10.

14

15

8

10

15

9

7

8

12

12

 

n = Number of Days

xi=Sum of calls made in 10 days

= 11

 

5. Calculating the Median

Median is the middle value of the given data list. It is also known as the central term of the data table. It is very easy to calculate median, just we have to arrange the values of the data in ascending or descending order. If the number of terms is even then two terms are used to calculate the median and if the number of terms is odd we can easily get the middle one.

 

Day	Phone Calls Made	Sequence of Phone Calls Made
1	14	7
2	15	8
3	8	8
4	10	9
5	15	10
6	9	12
7	7	12
8	8	14
9	12	15
10	12	15

 

Formula = n2+n2+1Term2 =  Median

10+122=11

So 11 is the median o our collected data

 

6. Calculating the Mode

The mode is the value which occurred the most number of time in our data.

Day	Phone Calls Made
1	14
2	15
3	8
4	10
5	15
6	9
7	7
8	8
9	12
10	12

 

After analysing the phone calls made column we found that 8, 12, and 15 came twice in the data. But still, there is not a single number which occurs the most times. So here  all together 8, 12, and 15 are the mode of our collected data

7. Calculating the Range

Range in statistics is the value we get after subtracting the smallest value from the biggest value of the data. In other words, the difference between the biggest and smallest value is called range.

In the given data of Phone calls Made, the biggest number is 15 and the smallest number is 7

Range = Smallest Number- Smallest Number

Range=  15 – 7 = 8

8. Calculating Standard Deviation

Standard deviation is used to find the difference between the mean value and set value in a given data. For calculating standard deviation there is a formula and steps to calculate it as shown below.

Standard Deviation = ∑(xi - x)2n

Steps-

• Find the mean
• For each data point, we have to find its square and difference to the mean
• Sum all the obtained values from the above step
• Divide it by number of data points
• Take its square root

xi = I point of data

n = total number of data

 x= Mean of our Dataset

x	xi - x	xi - x	(xi - x)2
14	14-11	3	9
15	15-11	4	16
8	8-11	-3	9
10	10-11	-1	1
15	15-11	4	16
9	9-11	-2	4
7	7-11	-4	16
8	8-11	-3	9
12	12-11	1	1
12	12-11	1	1
			82

 

Standard Deviation = ∑(xi - x)2n = 8210= 8.2.=2.8635

 

9. Linear Forecasting Model

Now here we have to use linear forecasting model our collected data of phone calls made in 10 days which will help us in forecasting the calls made in the upcoming day.

The Linear Forecasting Model Is y = mx +c

So here first we will calculate the value of m

 

Calculation Of M Value

Given Equation = y=mx+c

Calculation of M value

x	y
1	14
2	15
3	8
4	10
5	15
6	9
7	7
8	8
9	12
10	12
∑x=55	∑y=110

 

Calculation of = mx= 5510=5.5

Calculation of = my= 11010=11

Here we will calculate the value of m with the help of SS and SP method.

In the table given below x- mx is calculated in first column and y- my is calculated in the second column. In the third column, we will calculate the square root of x- mx and in last column we will find the product of x- mx and y- my.

 

x- mx	y- my	(x- mx)2	(x- mx)(y- my)
-4.5	3	20.25	-13.5
-3.5	4	12.25	-14
-2.5	-3	6.25	7.5
-1.5	-1	2.25	1.5
-0.5	4	0.25	-2
0.5	-2	0.25	1
1.5	-4	2.25	-6
2.5	-3	6.25	-7.5
3.5	1	12.25	3.5
4.5	1	20.25	4.5
		∑SS = 82.5	∑SP = -25

 

The total value of the third column is SS = 82.5

The total value of the fourth column is SP = -25

For calculating m value, we have to find (x- mx)2 and (x- mx)(y- my)

So,

Sum of x = 55

Sum of y = 110

Mean x = 5.5

Mean y =11

 

Sum of sequences (x- mx)2 = 82.5

Sum of products (SP) = -25

Regression equation y=mx+c

M = (sp)(ss)= -2582.5=-0.30

Value of M = -0.30

 

Calculating the value of C

After getting the value of m its easy to calculate the value of c.Just we have to put the value of my and subtract from the value of m.mx

 

C = my-m.mx

C= 11 – (-0.30 x 5.5)

C= 12.65

 

10. The Calculation for Phone Calls Made on Day 12 and Day 14

As above we have already calculated the value of m and c so putting the values in the equation we can get the number of calls made on day 12 and day 14 as follow-

Given Equation = y=mx+c

Put values in equation = y=-0.30x+12.65

Forecast for day 12

Put x value also = y=-0.30×12+12.65

y=9.05

Phone Calls made on  12^th day  = 9.05

Forecast for day 14

Put x value also = y=-0.30×14+12.65

y=8.45

References

[1]       Luo, D., Wan, X., Liu, J., and Tong, T., 2018. Optimally estimating the sample mean from the sample size, median, mid-range, and/or mid-quartile range. Statistical methods in medical research, 27(6), pp.1785-1805.

[2]       Scheffe, H. (1959). The Analysis of Variance, John Wiley, New-York.Begun, J. M. and Gabriel, K. R. (1981). "Closure of the Newman-Keuls Multiple Comparisons Procedure", Journal of the American Statistical Association, 76, page 374

[3]       Statistics Canada (2017). North American Industry Classification System (NAICS) Canada 2017 Version 3.0: classification structure - 312130 - Wineries.  https://www.statcan.gc.ca/eng/subjects/standard/naics/2017/v3/index

[4]       Zheng, S., Mogusu, E., Veeranki, S.P., Quinn, M., and Cao, Y., 2017. The relationship between the mean, median, and mode with grouped data. Communications in Statistics-Theory and Methods, 46(9), pp.4285-4295.