Question

Savannah recorded the average rainfall amount, in inches, for two cities over the course of 6 months. Put the numbers in order from least to greatest. Show your work!

City A: {4, 3.5, 5, 5.5, 4, 2}
City B: {5, 6, 3.5, 5.5, 4, 6}
(a) What is the mean monthly rainfall amount for each city?
(b) What is the mean absolute deviation (MAD) for each city? Round to the nearest tenth.
(c) What is the median for each city?

Answer 1

Hi!

Put the numbers in order:

City A: {2, 3.5, 4, 4, 5, 5.5}

City B: {3.5, 4, 5, 5.5, 6, 6}

a)

• The mean monthly rainfall amount for city A: 4 in;

• The mean monthly rainfall amount for city B: 5 in;

b)

• The MAD monthly rainfall amount for city A: 0.8 in;

• The MAD monthly rainfall amount for city B: 0.8 in;

c)

• The median monthly rainfall amount for city A: 4 in;

• The median monthly rainfall amount for city A: 5.25 in;

Explanation:

a) The general definition of mean of a set X is:

mean = (x₁ + x₂ + x₃ + ... xₙ)/n

• For City a:

mean = (4+3.5+5+5.5+4+2)/6 = 4

• For City b:

mean = (5+6+3.5+5.5+4+6)/6 = 5

b) The general definition of mean absolute deviation of a set X is:

MAD = (|x₁-mean| + |x₂-mean| + |x₃-mean| + ... + |xₙ-mean|)/n

• For City a:

MAD = ( |4-4| + |3.5-4| + |5-4| + |5.5-4| + |4-4| + |2-4| )/6 = (0 + 0.5 + 1 + 1.5 + 0 + 2)/6 = 5/6 =0.8

• For City b:

MAD = ( |5-5| + |6-5| + |3.5-5| + |5.5-5| + |4-5| + |6-5| )/6 = (0 + 1 + 1.5 + 0.5 + 1 + 1)/6 = 5/6 = 0.8

c) The general definition of median depends on the quantity of elements in the set X and it represents the middlemost value of the set:

When the quantity is odd:

median= x₍ₙ₊₁₎/₂

When the quantity is even:

median= (xₙ/₂ + x ₙ₊₂/₂) /2

• For City a:

median = 2, 3.5, 4, 4, 5, 5.5 = (4 + 4) / 2 = 4

• For City b:

median = 3.5, 4, 5, 5.5, 6, 6 = (5 + 5.5) / 2 = 5.25

Answer 2

City A: {2, 3.5, 4, 4, 5, 5.5}
City B: {3.5, 4, 5, 5.5, 6, 6}

Mean is the average.
Average of City A = 4 (2+3.5+4+4+5+5.5 = 24 and 24/6 = 4)
Average of City B = 5 (3.5+4+5+5.5+6+6 = 30 and 30/6 = 5)

Mean Absolute Deviation
Mean Absolute Deviation of City A = 0.8
Mean Absolute Deviation of City B = 0.8

Median is the middle (after putting it in order least to greatest)
Median of City A = 4
Median of City B = 5.25 (5+5.5 = 10.5 and 10.5/2 =5.25)