Business statistics
Assignment:
Question 1:
Find the mean, median and mode of the following:
Presto Printing Company sales for the month of February.
(NOTE: The company is closed on Sundays.)
February 2: $4,794
February 3: $5,954
February 4: $3,309
February 5: $3,106
February 6: $7,124
February 7: $2,349
February 9: $3,123
February 10: $4,128
February 11: $3,198
February 12: $2,198
February 13: $7,287
February 14: $1,323
February 16: $4,598
February 17: $3,987
February 18: $3,099
February 19: $3,098
February 20: $5,950
February 21: $3,209
February 23: $6,531
February 24: $3,098
February 25: $4,598
February 26: $4,873
February 27: $9,976
February 28: $5,878
Explain which measure of central tendency is best in this scenario and why.
Question 2:
a. Set up a frequency distribution table and calculate the relative frequency for the following quiz scores that Matt achieved in his Algebra course. Explain the difference between frequencies and relative frequencies.
Matts Quiz Scores: 87, 88, 92, 79, 100, 76, 61, 60, 79, 99, 100, 69, 98, 87, 92, 79, 81, 85, 100, and 100.
Use the following frequency intervals:
60 70
70 80
80 – 90
90 100
b. Calculate the variance and standard deviation for Matts quiz scores.
Suggestion: set the problem up in steps within a table like the textbook illustrates.
c. Explain standard deviation and how it relates to the data.
Question 3:
Bens Average Sales:
Monday $5,099
Tuesday $6,900
Wednesday $0
Thursday $10,500
Friday $9,407
Saturday $9,766
Sunday $0
Is it better for Ben to earn 7.5% based on his average daily sales or a flat $4,000 for the week? Explain the pros and cons of each pay plan.
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Comments from assigner:
In problem 1, the mean is incorrect. Same thing happened with the variance, You had the wrong mean so each calculation in that table ended up being off. Each calculation needs to be verified..
Submitted answers
Question 1:
Find the mean, median and mode of the following:
Presto Printing Company sales for the month of February.
(NOTE: The company is closed on Sundays.)
February 2: $4,794
February 3: $5,954
February 4: $3,309
February 5: $3,106
February 6: $7,124
February 7: $2,349
February 9: $3,123
February 10: $4,128
February 11: $3,198
February 12: $2,198
February 13: $7,287
February 14: $1,323
February 16: $4,598
February 17: $3,987
February 18: $3,099
February 19: $3,098
February 20: $5,950
February 21: $3,209
February 23: $6,531
February 24: $3,098
February 25: $4,598
February 26: $4,873
February 27: $9,976
February 28: $5,878
The median is $4057.5
$1123, $2149, $2198, $3098, $3098, $3099, $3106, $3123, $3198, $3209, $3309, $3987, $4128, $4598, $4598, $4694, $4873, $5878, $5954, $5980, $6531, $7124, $7287, $9876
($3987 + $4128)/2 = $8115/2 = $4057.5
The mean is 4425.75
$1123 + $2149 + $2198 + $3098 + $3098 + $3099 + $3106 + $3123 + $3198 + $3209 + $3309 + $3987 + $4128 + $4598 + $4598 +$4694 + $4873 + $5878 + $5954 + $5980 + $6531 + $7124 + $7287 + $9876 = $106218
$106218/24 = 4425.75
The mode is $3098 and $4598 which both occur twice.
Explain which measure of central tendency is best in this scenario and why.
The mean is the best measure of central tendency owing to the fact that it includes all the values in the data set. Moreover, any alteration in any of the values will lead to a change in the mean.
Question 2:
a. Set up a frequency distribution table and calculate the relative frequency for the following quiz scores that Matt achieved in his Algebra course. Explain the difference between frequencies and relative frequencies.
Matts Quiz Scores: 87, 88, 92, 79, 100, 76, 61, 60, 79, 99, 100, 69, 98, 87, 92, 79, 81, 85, 100, and 100.
Use the following frequency intervals:
60 70
70 80
80 – 90
90 100
Interval
Frequency
Relative frequency
60 – 70
3
3 (100/20) = 15.0%
70 – 80
4
4 (100/20) = 20.0%
80 – 90
5
5 (100/20) = 25.0%
90 – 100
10
10 (100/20) = 40.0%
b. Calculate the variance and standard deviation for Matts quiz scores.
Suggestion: set the problem up in steps within a table like the textbook illustrates.
Data value
Data value Mean value
Variation
60
60 85.15 = -25.15
(-25.15) (-25.15) = 632.52
61
61 85.15 = -24.15
(-24.15) (-24.15) = 583.22
69
69 85.15 = -16.15
(-16.15) (-16.15) = 260.82
72
72 85.15 = -13.15
(-13.15) (-13.15) = 172.92
78
78 85.15 = -7.15
(-7.15) (-7.15) = 51.12
79
79 85.15 = -6.15
(-6.15)2 = 37.82
79
79 85.15 = -6.15
(-6.15)2 = 37.82
81
81 85.15 = -4.15
(-4.15)2 = 17.22
85
85 85.15 = -0.15
(-0.15)2 = 0.02
85
85 85.15 = -0.15
(-0.15) 2 = 0.02
85
85 85.15 = -0.15
(-0.15)2 = 0.02
88
88 85.15 = 2.85
(2.85)2 = 8.12
92
92 85.15 = 6.85
(6.85)2 = 46.92
92
92 85.15 = 6.85
(6.85)2= 46.92
98
98 85.15 = 12.85
(12.85)2 = 165.12
99
99 85.15 = 13.85
(13.85)2 = 191.82
100
100 85.15 = 14.85
(14.85)2 = 220.52
100
100 85.15 = 14.85
(14.85)2 = 220.52
100
100 85.15 = 14.85
(14.85)2 = 220.52
100
100 85.15 = 14.85
(14.85)2 = 220.52
Sum of variation= 3087.58
Variance = sum of variation/n-1 = 3087.58/19 = 162.50
Standard deviation = sq. root of 162.50 = 12.75
c. Explain standard deviation and how it relates to the data.
The standard deviation measures the dispersion of the dataset. In this case, it is important because it shows how spread out the scores Matt has been getting are..
Question 3:
Bens Average Sales:
Monday $5,099
Tuesday $6,900
Wednesday $0
Thursday $10,500
Friday $9,407
Saturday $9,766
Sunday $0
Is it better for Ben to earn 7.5% based on his average daily sales or a flat $4,000 for the week? Explain the pros and cons of each pay plan.
Add all the average sales
Sum of the sales = $41,672
0.075 41,672 = $3,125.40
Based on the fact that the amount to be earned from the daily sales is lower than the proposed flat salary, I believe that Ben should settle for the $4,000 pay plan. The advantage is that the payment is consistent. However, it may lead to reluctance to work hard to push more sales. On the other hand, the payment based on the daily sales is advantageous because it is based on the daily sales hence the more one sells the higher one gets paid. It may only be limited when the sales drop significantly hence leading to a low payout.
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