Ahnboyoung: /* Quiz */

2014-05-24T18:15:47Z

Quiz

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{{Cat|Summarizing Distributions| 05}}

This section covers the effects of linear transformations on measures of central tendency and variability.

'''Example'''

Table below shows the temperatures of 5 cities to see the Linear transformation: temperatures of cities.

{| class="wikitable" style="text-align: right;"
|-
! City
! Degrees Fahrenheit
! Degrees Centigrade
|-
| Houston
| 54
| 12.22
|-
| Chicago
| 37
| 2.78
|-
| Minneapolis
| 31
| -0.56
|-
| Miami
| 78
| 25.56
|-
| Phoenix
| 70
| 21.11
|-
| style="background: white" |Mean
| style="background: white" |54.000
| style="background: white" |12.220
|-
| style="background: white" | Median
| style="background: white" |54.000
| style="background: white" |12.220
|-
| style="background: white" |Variance
| style="background: white" |330.00
| style="background: white" |101.852
|-
| style="background: white" |SD
| style="background: white" |18.166
| style="background: white" |10.092
|}

To transform the degrees Fahrenheit to degrees Centigrade, we use the formula
C = 0.556F - 17.778

To get the mean in Centigrade, you multiply the mean temperature in Fahrenheit by 0.556 and then subtract 17.778 .
(0.556)(54) - 17.778 = 12.22.
* The same is true for the median.
* This relationship holds even if the mean and median are not identical as they are in the table above.

* The formula for the standard deviation is just as simple: the standard deviation in degrees Centigrade is equal to the standard deviation in degrees Fahrenheit times 0.556.
* Since the variance is the standard deviation squared, the variance in degrees Centigrade is equal to 0.5562 times the variance in degrees Fahrenheit.

If a variable X has a mean of μ, a standard deviation of σ, and a variance of σ2, then a new variable Y created using the linear transformation
Y = bX + A
will have a mean of bμ+A, a standard deviation of bσ, and a variance of b2σ2.

=Quiz=
<quiz display=simple >

{ You have 10 numbers. The mean is 5. You multiply each number in the group by 3. What is the new mean?

|type="{}"}
{ 15 }

{
{{Show Answer|
15

5x3 is 15
}}
}

{You have 8 numbers. The mean is 6. You add 5 to each number in the group. What is the new mean?

|type="{}"}
{ 11 }

{
{{Show Answer|
6+5 is 11
}}
}

{ You have 12 numbers. The mean is 3, and the variance is 1. You multiply each number by 4. What is the new variance?

|type="{}"}
{ 16 }

{
{{Show Answer|
1*(4<sup>2</sup>) is 16
}}
}

{ You have 15 numbers. The mean is 10, and the variance is 4. You multiply each number by 3. What is the new standard deviation?

|type="{}"}
{ 6 }

{
{{Show Answer|
3 x sqrt(4) is 6
}}
}

{Your teacher decides that he will add 10 points to all of your test grades. Which statistic is not changed by this decision?

|type="()"}
-mean
-median
-mode
+standard deviation

{
{{Show Answer|
standard deviation

The mean, median, and mode will all increase by 10, but the standard deviation remains unchanged.
}}
}

</quiz>

Effects of Linear Transformations - Revision history

Ahnboyoung: /* Quiz */