# Question 8fc3c

Jun 6, 2017

b) $\text{mean" = 27 2/7, "median" = 29.5, "Mode" = 31, "Range} = 29$

c) 50% of the dogs weighed less than $30$ pounds.

#### Explanation:

b)

Mean = average of data

Mean =

$\frac{7 + 32 + 34 + 31 + 26 + 27 + 23 + 19 + 22 + 29 + 30 + 36 + 35 + 31}{14}$

$\text{mean} = \frac{382}{14}$

color(blue)("mean" = 27 2/7

Median = middle number, we can find this from listing the numbers from lowest to greatest and finding the middle number.

$7 , 32 , 34 , 31 , 26 , 27 , 23 , 19 , 22 , 29 , 30 , 36 , 35 , 31$

$7 , 19 , 22 , 23 , 26 , 27 , 29 , 30 , 31 , 31 , 32 , 34 , 35 , 36$

We can take 6 numbers off each side first.

$\cancel{7 , 19 , 22 , 23 , 26 , 27} , 29 , 30 , \cancel{31 , 31 , 32 , 34 , 35 , 36}$

Because there are two medians, we find the mean of them.

$\text{median} = \frac{29 + 30}{2}$

$\text{median} = \frac{59}{2}$

color(blue)("median" = 29.5

Mode = the number that occurs most often

We can make a tally of each number with how many times they occur in the set of numbers.

$7$ - |
$19$- |
$22$- |
$23$- |
$26$- |
$27$- |
$29$- |
$30$ - |
$31$- ||
$32$ - |
$34$ - |
$35$ - |
$36$ - |

We can see here that above all, $31$ occurs twice, when all other numbers occur once.

color(blue)("Mode" = 31

Range = the difference between the highest and lowest numbers.

Range = highest number - lowest number

Range = $36 - 7$

color(blue)("Range" = 29

c)

we can see above that out of the $14$ dogs, $7$ weighed less than $30$ pounds. We can also say that a percentage is a number over $100$, or $\frac{x}{100}$

So to find the percentage, we can make this equation:

$\frac{7}{14} = \frac{x}{100}$

Now we can find out how the first denominator gets to the next, so we can do the same to the numerator. We can make this formula to find $x$.

$\frac{7 \times y = x}{14 \times y = 100}$

$14 \times y = 100$

y = 100 ÷ 14

$y \approx 7.147$

We can now put $7.147$ in the equation in substitution for $y$

$\frac{7 \times 7.147 = x}{14 \times 7.147 = 100}$

Now we can find $x$.

$x = 7 \times 7.147$

$x = 50$

x = 50%

$\therefore$ 50%# of the dogs weighed less than $30$ pounds.