187k views
1 vote
Savannah recorded the average rainfall amount, in inches, for two cities over the course of 6 months. Show your work

City A: {2.5, 3, 6, 1.5, 4, 1}

City B: {4, 7, 3.5, 4, 3.5, 2}

What is the mean monthly rainfall amount for each city?

What is the mean absolute deviation (MAD) for each city? Round to the nearest tenth.

What is the median for each city?

User Faycal
by
8.0k points

1 Answer

4 votes

Hello, I am Alyssa Ann Verrett.

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

User Mr Patience
by
7.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories