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Lesson Example Discussion Quiz: Class Homework

Step-2

Title: Mean Absolute Deviation, Standard Deviation, Percentages

Grade: 1400-a Lesson: S4-L5

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Calculate the Mean Absolute Deviation (MAD) for the daily sales (in dollars) recorded over a year: $1200, $1300, $1100, $1400, $1500, $1250, $1350, $1450, $1200, $1300, $1100, and $1400.
2	Step	Given daily sales:	$1200, $1300, $1100, $1400, $1500, $1250, $1350, $1450, $1200, $1300, $1100, and $1400
3	Step	Calculate the Mean (Average) Sum up all the sales and then divide by the number of sales Mean = \$(1200 + 1300 + 1100 + 1400 + 1500 + 1250 + 1350 + 1450 + 1200 + 1300 + 1100 + 1400)/12\$ \$"Mean" = 15550 / 12\$ = 1295.83
4	Step	The mean sales is $1254.16.
5	Step	Calculate the Absolute Deviations from the Mean Find the absolute deviation of each sale from the mean	\$\∣1200 − 1295.83\∣ = 95.83\$ \$\∣1300 − 1295.83\∣ = 4.17\$ \$\1100 − 1295.83\∣ = 195.83\$ \$\∣1400 − 1295.83\∣ = 104.17\$ \$\∣1500 − 1295.83\∣ = 204.17\$ \$\∣1250 - 1295.83\∣ = 45.83\$ \$\∣1350 − 1295.83\∣ = 54.17\$ \$\∣1450 − 1295.83\∣ = 154.17\$ \$\∣1200 − 1295.83\∣ = 95.83\$ \$\∣1300 − 1295.83\∣ = 4.17\$ \$\∣1100 − 1295.83\∣ = 195.83\$ \$\∣1400 − 1295.83\∣ = 104.17\$
6	Step	Sum the absolute deviations and then divide by the number of sales to find the Mean Absolute Deviation (MAD) The sum of absolute deviations = 95.83 + 4.17 + 195.83 + 104.17 + 204.17 + 45.83 + 54.17 + 154.17 + 95.83 + 4.17 + 195.83 + 104.17 = 1258.34
7	Step	Calculate the Mean of the Absolute Deviations	\$"MAD" = ("Sum of absolute deviations")/("Number of sales")\$ ⇒ \$1258.34 / 12\$ = 104.86
8	Step	Therefore, the Mean Absolute Deviation (MAD) for the daily sales is approximately $104.86.
9	Choice.A	This option is incorrect because, this value is higher than our calculated MAD (104.86). The precise calculation gives 104.86, so 108.56 is not accurate	$108.56
10	Choice.B	This option is incorrect because,105.20 is very close to our calculated MAD (104.86), but it is slightly higher. The exact calculation gives 104.86	$105.20
11	Choice.C	This option is incorrect because the value is too high compared to our calculated MAD, significantly deviating from the exact calculated value of 104.86	$114.89
12	Choice.D	This value matches our calculated Mean Absolute Deviation exactly. Given our calculation steps and results, this is the correct option	$104.86
13	Answer	Option	D
14	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Calculate the Mean Absolute Deviation (MAD) for the daily sales (in dollars) recorded over a year: $1200, $1300, $1100, $1400, $1500, $1250, $1350, $1450, $1200, $1300, $1100, and $1400.

Step

Given daily sales:

$1200, $1300, $1100, $1400, $1500, $1250, $1350, $1450, $1200, $1300, $1100, and $1400

Step

Calculate the Mean (Average)
Sum up all the sales and then divide by the number of sales
Mean = \$(1200 + 1300 + 1100 + 1400 + 1500 + 1250 + 1350 + 1450 + 1200 + 1300 + 1100 + 1400)/12\$
\$"Mean" = 15550 / 12\$ = 1295.83

Step

The mean sales is $1254.16.

Step

Calculate the Absolute Deviations from the Mean
Find the absolute deviation of each sale from the mean

\$\∣1200 − 1295.83\∣ = 95.83\$
\$\∣1300 − 1295.83\∣ = 4.17\$
\$\1100 − 1295.83\∣ = 195.83\$
\$\∣1400 − 1295.83\∣ = 104.17\$
\$\∣1500 − 1295.83\∣ = 204.17\$
\$\∣1250 - 1295.83\∣ = 45.83\$
\$\∣1350 − 1295.83\∣ = 54.17\$
\$\∣1450 − 1295.83\∣ = 154.17\$
\$\∣1200 − 1295.83\∣ = 95.83\$
\$\∣1300 − 1295.83\∣ = 4.17\$
\$\∣1100 − 1295.83\∣ = 195.83\$
\$\∣1400 − 1295.83\∣ = 104.17\$

Step

Sum the absolute deviations and then divide by the number of sales to
find the Mean Absolute Deviation (MAD)
The sum of absolute deviations =
95.83 + 4.17 + 195.83 + 104.17 + 204.17 + 45.83 + 54.17 + 154.17 + 95.83 + 4.17 + 195.83 + 104.17 = 1258.34

Step

Calculate the Mean of the Absolute Deviations

\$"MAD" = ("Sum of absolute deviations")/("Number of sales")\$
⇒ \$1258.34 / 12\$ = 104.86

Step

Therefore, the Mean Absolute Deviation (MAD) for the daily sales is approximately $104.86.

Choice.A

This option is incorrect because, this value is higher than our calculated MAD (104.86). The precise calculation gives 104.86, so 108.56 is not accurate

$108.56

Choice.B

This option is incorrect because,105.20 is very close to our calculated MAD (104.86), but it is slightly higher. The exact calculation gives 104.86

$105.20

Choice.C

This option is incorrect because the value is too high compared to our calculated MAD, significantly deviating from the exact calculated value of 104.86

$114.89

Choice.D

This value matches our calculated Mean Absolute Deviation exactly. Given our calculation steps and results, this is the correct option

$104.86

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?