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2 years ago

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Use the data set to answer the question. {22,26,28,35,45,63,91} What is the mean absolute deviation (MAD) of the data set? Enter

your answer as a number rounded to the nearest tenth

1 answer:

shtirl [24]2 years ago

6 0

Answer:

mean absolute deviation is 18.85

Step-by-step explanation:

<u>Step 1:</u>-

Given observation values 22,26,28,35,45,63,91

$mean (x ) = \frac{22+26+28+35+45+63+91}{7}$

mean = 44.28≅ 44

<u>Step2</u>:-

The deviations of the respective observations from the mean (x)

That is $x_{i}-x$

22-44, 26-44,28-44,35-44,45-44,63-44,91-44

-22, -18 ,-16 ,-9, 1, 19, 47

<u>Step 3:</u>-

The absolute values of the given data

$x_{i}-x$

modulus of all these values

22,18,16,9.1,19,47

<u>Step 4</u>:-

Mean absolute deviation M.D=∑ $\frac{x_{i} - x }{n}$

$MAD = \frac{22+18+16+9+1+19+47}{7}$

on simplification we get mean absolute deviation is 18.85

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The given multiplication problem is

$\frac{39}{64} \times \frac{8}{13}$

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$\frac{13\times 3}{8\times8} \times \frac{8}{13}$

Cancel out the common factors to obtain;

$\frac{1\times 3}{8\times1} \times \frac{1}{1}$

Simplify to get;

$\frac{3}{8}$

QUESTION B

The given multiplication problem is

$\frac{2}{3}\times \frac{1}{5}\times \frac{4}{7}$

This the same as

$\frac{2\times 1\times 4}{3\times 5\times 7}$

This simplifies to;

$\frac{8}{105}$

QUESTION C

The given problem is

$\frac{3}{5}\times \frac{10}{12} \times \frac{1}{2}$

This is the same as

$\frac{3}{5}\times \frac{5}{6} \times \frac{1}{2}$

$=\frac{1}{1}\times \frac{1}{2} \times \frac{1}{2}$

This simplifies to

$=\frac{1}{4}$

QUESTION D.

The given expression is

$\frac{4}{9}\times 54$

Factor the 54 to obtain;

$\frac{4}{9}\times 9\times 6$

Cancel the common factors to get;

$\frac{4}{1}\times 1\times 6$

This simplifies to;

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QUESTION E

The given problem is

$20\times 3\frac{1}{5}$

Convert the mixed numbers to improper fraction to obtain;

$=20\times \frac{16}{5}$

$=4\times5 \times \frac{16}{5}$

Cancel the common factors to get;

$=4\times1 \times \frac{16}{1}$

$=64$

QUESTION F

The multiplication problem is

$11 \times 2 \frac{7}{11}$

Convert the mixed numbers to improper fractions to obtain;

$11 \times \frac{29}{11}$

Cancel out the common factors to get;

$=1 \times \frac{29}{1}$

Simplify;

$=29$

QUESTION G

The given problem is

$5\frac{1}{3}\times 5\frac{1}{8}$

Convert to improper fractions;

$=\frac{16}{3}\times \frac{41}{8}$

Cancel out the common factors to get;

$=\frac{2}{3}\times \frac{41}{1}$

$=\frac{82}{3}$

Convert back to mixed numbers

$=27\frac{1}{3}$

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The given expression is

$10\frac{2}{3} \times 1\frac{3}{8}$

Convert to improper fraction to get;

$\frac{32}{3} \times \frac{11}{8}$

Cancel common factors to get;

$=\frac{4}{3} \times \frac{11}{1}$

Simplify

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Convert back to mixed numbers;

$=14\frac{2}{3}$

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