This is a solution of Unit 2 Business Decision Making Assignment Help that describes about Developing business

Task 2

Data given: –

Amount Spent (£)No. of customers
10-2018
20-3020
30-4016
40-5014
50-6012
60-708
70-806
80-904
90-1002

i. Mean, Median and Mode (AC 2.1 & AC 2.2)

Mean:

Amount Spent (£)No. of customersMid-valuefx
10 – 201815270
20 – 302025500
30 – 401635560
40 – 501445630
50 – 601255660
60 – 70865520
70 – 80675450
80 – 90485340
90 – 100295190
1004120

(Marković, et. al., 2013)

Analysis:

Mean is termed as the average of the total data and get utilised as a base for decision making. In order to calculate the mean of above table the total sum of given data get divided by total number of customers such as:

Mean = 4120/ 100 = 41.20

£41.20 is the mean for the above table.(Marković, et. al., 2013)

Median:

Amount Spent (£)No. of customersCumulative
20-Oct1818
20-302038
30-401654
40-501468
50-601280
60-70888
70-80694
80-90498
90-1002100
100

(Majumdar, 2014)

Analysis:

It also calculates the average of the given data but it renders closed value to the central point. It get preferred over the mean due to its qualitative results and utilised as an base for decision making.

Media = 100/ 2 = 50

50 lie in the group of 30-40

= 30 + {(50-38)/16} * 10 = 37.50(Majumdar, 2014)

Median for the above table is 37.50

Mode:

Unit 2 Business Decision Making Assignment HelpAnalysis: It is also another form of calculating average and in order to calculate the average the highest value in the frequency table is considered as mode. The value rendered by mode is considered as the benchmark and utilised in decision making for the purpose of comparison with others. In the given data mentioned as above the highest frequency is 20 and it is termed as mode for the data gathered(Majumdar, 2014).

ii. Range and Standard Deviation. (AC 2.3)

Range: It is effective technique which get utilised in order to calculate maximum variations and it renders by measures of dispersion. In order to calculate the range lowest value gets deducted from the highest value. Below is the calculation made such as:

 Range = (maximum value – minimum value)

= 20 – 2 = 18

18 customers become the range.(Majumdar, 2014)

Standard deviation:

Amount Spend  (in £)No of ordersMid-valuedx (x – 40 ÷ 10)F x dxDx
10-201815-4-72288
20-302025-3-60180
30-401635-2-3264
40-501445-1-1414
50-601255000
60-70865188
70-8067521224
80-9048531236
90-1002954832
100-138646

(Djokovic, 2013)

Standard deviation: {[646 / 138] – [138 *138 / 100 *100]} * 10

= {4.68 – 1.9044) *10

= 27.75

The standard deviation is £27.75 as there may be increase or decrease of £27.75 in the customer spending. This information is utilized for the decision making purpose.(Djokovic, 2013)

iii. 25th Percentile (Lower Quartile) and 75th Percentile (Upper Quartile) and explain the use of Percentile (AC 2.4)

Percentile is a measure which get utilised under statistics where value below percentage is observed. Such as 25th percentile (lower quartile) are 3,5,6,8,9 in this 6 customers is lower quartile.

75th (upper quartile) are 12, 13, 16, 18, 21 in this 16 customers is the upper quartile.(Djokovic, 2013)

iv. Inter-quartile range. (AC 2.4)

= Upper quartile – lower quartile

Upper quartile = 16

Lower quartile = 6

Inter- quartile range = 16 – 6 = 10 customers.(Zabukovec & Jaklic, 2015)

v. Calculate correlation coefficient using the additional information provided below and discuss its advantages to a business. (AC 2.4)

Data given:

Sales (units)Discount
201
404
506
556
6010
7012
8013
9014
10015
56581

Correlation with sales and discount is as discussed below such as:

Sales (units) xDiscount yxyx2y2x2y2
201204001400
40416016001625600
50630025003690000
556330302536108900
60106003600100360000
70128404900144705600
8013104064001691081600
9014126081001961587600
100151500100002252250000
565816050405259236209700

(Zabukovec & Jaklic, 2015)

X2 = 319,225

Y2 = 6,561

Correlation of coefficient = {n * ∑ xy – ∑x * ∑y) / SQRT (n * ∑x2 –(∑x) 2) * (n * ∑y2–(∑y) 2}

= [9 * 6050 – 565 * 81) / SQRT(9 * 40525 – 319225) * (9 * 923 – 6561)

= [54450 – 45765] / SQRT (45500) * (1746)

= 8685/ 8913.08

= 0.9744106(Zabukovec & Jaklic, 2015)

Correlation of coefficient = 0.9744106

Correlation of coefficient: It is termed as decision making tool and business management make use of it in their decision making purpose. It get utilised in order to build effective relationship among two variables and in the above calculation there is effective relationship is analysed among sales and discounts(Zabukovec & Jaklic, 2015).

Advantages of correlation of coefficient are:

  • It is an effective technique which get utilised in order to make predictions related to the correlation.
  • As if there is correlation among two variables then effective predictions get made for one variable by using second one.
  • Effective relation is evaluating with the use of this technique.

(Zabukovec & Jaklic, 2015)

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