We first take the sum of the squares of the differences between the sample data and the limit 45 mph: 1^2 + 11^2 + 0^2 + (-1)^2 + 0^2 + 16^2 + 10^2 + 8^2 + (-6)^2 = 579. Dividing by 8 (# of cars less 1) gives 72.375, which is the variance. Taking the square root gives the SD of 8.5.
The measure of central tendency most affected by the 10th value of 1.5 mph is the mean. The median and mode are relatively unaffected since both involve the frequency of terms, and having a tenth term that is far below (like 1.5) will not affect it much as compared to if it was near the rest of the values (like anything below 39).
The new SD including the tenth car involves adding the deviation of (-43.5)^2 to the sum of 579, which gives 2471.25. Dividing by 9 (there are now 10 data points) and taking the square root gives the new SD of 16.6.
25/4 = 6.25 per t-shirt <== unit price
the error that was made is the student put the number of t-shirts over the price, instead of the price over the number of t-shirts.
4/25 = 0.16
Hi!
When adding and subtracting negative numbers, just imagine a number line.
For example, let's say we're adding 3 + -7.
Tip: Adding negative numbers is the same as subtracting positive numbers. So 3 + -7 is the same as 3 - 7.
Here's a numberline:
-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
Now add 3 to negative 7. (or subtract 7 from 3)
-10, -9, -8, -7<em>, -6, -5, </em><em>-4</em><em>, -3, -2, -1, 0, 1, 2</em>, 3, 4, 5
3 + -7 = -4
Let's try subtracting now. How do we solve 5 - (-3)?
Tip: Subtracting a negative is the same as adding a positive. So 5 - (-3) is the same as 5 + 3. Another way of thinking of it, is two minuses make a positive.
Numberline:
-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
Subtract -3 from 5. (or add 12 to 5)
-5, -4, -3, <em>-2, -1, 0, 1, 2, 3, 4, </em>5<em>, 6, 7, 8</em>, 9, 10
Here are a few more examples.
-7 + -3 (which is the same as -7 - 3) = -10
-8 + 6 = -2
-9 - (-8) (which is the same as -9 + 8) = -1
-9 - 3 = -12
Hope this helps! :)