Five plumbers charge different hourly rates: $35, $42, $52, $38, and $42.
Find the mean, median, mode, MAD,
and IQR of these values. Which
measure of center and which measure
of variability best describe the data?

**The mean is: $41.8**

Explanation: for mean you add all the numbers up and divide it based upon how much numbers there are in total, so for this problem it would be:
$35 + $42 + $52 + $38 + 42 ÷ 5 = 41.8

**The median is: $42**

Explanation: to find the median we arrange the numbers from least to greatest or greatest to least you’ll get the same answer for median.
Original: $*35, $*42, $52, $*38, $*42

Least to greatest: ($35, $38, $42, $42, $52)

Greatest to least: $52, $42, $42, $38, $35)

Then we find the number in the center which is: $42 for the median.

**The mode is: $42**

Explanation: To find the mode we just see what number was repeated the most which in this case is $42

**MAD (Mean Absolute Deviation) is: $4.24**

Explanation to find the MAD we need to first add all the numbers up and divide them by the number of elements there are in the data set in total.
So we do,
$35 + $42 + $52 + $38 + 42 ÷ 5 = 41.8
Just as we did for finding the mean the difference for this though is after we’ve found this number we subtract each number by 41.8
and when we subtract the rule is there is no negative numbers so if any you subtract turn out to be negative you change it to positive so it would be:
$35 - $41.8 = (-6.8) change to + = 6.8
$42 - $41.8 = 0.2
$52 - $41.8 = 10.2
$38 - $41.8 = (-3.8) change to + = 3.8
$42 - $41.8 = 0.2

Then we add all the numbers up we just got and divide it by the number of elements in the date set so we do, $6.8 + $0.2 + $10.2 + $3.8 + $0.2 = 21.2 ÷ 5 = $4.24

**IQR (Interquartile Range) is: $10.5**

Explanation to find the IQR we order the numbers least to greatest or greatest to least it doesn’t matter which order you do it.

Greatest to least: $52, $42, $42, $38, $35

Least to greatest: $35, $38, $42, $42, $52

Q1 is: $36.5
Explanation: we get this by adding:
$35 + $38 ÷ 2 = 36.5

Q2 is: $42
Explanation: it’s right in the center

Q3 is: $47
Explanation: we get this by adding:
$42 + $52 ÷ 2 = $47

In order to find IQR we need to do Q3 - Q1
So, $47 - $36.5 = $10.5

**Measure of the center: (Mean = $41.8, Median = $42, Mode = $42, Range = $17**

Explanation: for range we simply subtract the biggest number from the smallest one which would be $52 - $35 = $17

**Measure of variability: (range = $42, Standard deviation = $2.91, Variance = $8.48)**

Explanation for standard of deviation we first find the mean which is $41.8, then we subtract each number be $41.8 which will give us these numbers which we’ll multiple by 2:
$6.8 x 2 = $13.6
$0.2 x 2 = $0.4
$10.2 x2 = $20.4
$3.8 x 2 = $7.6
$0.2 x 2 = $0.4
Then the numbers you get you add up and divide it by the number of elements in the data, which would be $13.6 + $0.4 + $20.4 + $7.6 + $0.4 = 42.4 ÷ 5 = 8.48
So the variance is: $8.48
Then to find the standard deviation we square root $8.48 which gives us: $2.91

Letter a (: : : : : : : : : :

8.4 10.4 8.9 10.9 have a good day