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.