Before you take a scored quiz for this lesson, try this set of practice questions. How well you score on this self-check will be similar to your scored quiz. If you do not score well on this self-check, please review this lesson and try again.
Calculate Q1 of the following data:
55, 45, 44, 22, 26, 47, 42
- 26
- 55
- 22
- 44
You are correct!
First order the set. This gives:
22, 26, 42, 44, 45, 47, 55
Find the median of the entire set. Since there are seven values in this list, this is the fourth value:
The median (Q2) = 44.
Q1 is the median of the lower set of data:
The lower half has three values, 22, 26, 42
so the middle value, 26.
First order the set. This gives:
22, 26, 42, 44, 45, 47, 55
Find the median of the entire set. Since there are seven values in this list, this is the fourth value:
The median (Q2) = 44.
Q1 is the median of the lower set of data:
The lower half has three values, 22, 26, 42
so the middle value, 26.
First order the set. This gives:
22, 26, 42, 44, 45, 47, 55
Find the median of the entire set. Since there are seven values in this list, this is the fourth value:
The median (Q2) = 44.
Q1 is the median of the lower set of data:
The lower half has three values, 22, 26, 42
so the middle value, 26.
Will the following list have a large or small Standard Deviation?
47, 22, 18, 15, 10, 8
- small
- large
- 0
- not enough information is given
You are correct!
The Standard Deviation is a measure of how spread out the data is. Since this data is fairly close together, the Standard Deviation will be small.
The Standard Deviation is a measure of how spread out the data is. Since this data is fairly close together, the Standard Deviation will be small.
The Standard Deviation is a measure of how spread out the data is. Since this data is fairly close together, the Standard Deviation will be small.
How is the Interquartile Range calculated?
- First the data is listed in numerical order.
Next, the mean of all data is found and then the mean of the top half of the data is found and of the bottom half of the data is found. - First list the data from least to greatest.
Then find the median of the set.
Next find the median of the top half and bottom half of the set and find the difference. - First find the mean of the set.
Then, list the data in the top and bottom halves.
Order the subsets in numerical order. Find the median of the halves.
Quartile 2 is the median of all the data. Quartile 1 is the median of the bottom half of the data and Quartile 3 is the median of the top half of the data. The IQR is Q3 - Q1.
You are correct!
Quartile 2 is the median of all the data. Quartile 1 is the median of the bottom half of the data and Quartile 3 is the median of the top half of the data. The IQR is Q3 - Q1.
What does the Standard Deviation tell you?
- It tells how far data is from the average.
- It tells the average data value.
- It tells you if data is evenly distributed.
- It tells you how many data points there are.
You are correct!
The Standard Deviation is a measure of how spread out the data is.
The Standard Deviation is a measure of how spread out the data is.
The Standard Deviation is a measure of how spread out the data is.
Summary
Questions answered correctly:
Questions answered incorrectly:
Finding the Interquartile Range (IQR) and the quartiles of a data set
Quartiles divide a data set into three subsets – an upper, middle and lower subset. Study the steps below to find the quartiles and Inter Quartile Range for a set of data.
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First, order the data from small to large: {3, 4, 4, 5, 6, 7 ,8} |
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Second, find the Q2, the median of the entire data set. This will give you two equal halves. |
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Third, find the Q1, the median of the lower half: {3, 4, 4} |
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Fourth, find Q3, the median of the upper half: {6, 7, 8} |
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Fifth, subtract Q1 from Q3 (Q3 - Q1) for the IQR. |
Finding the Interquartile Range (IQR) and the quartiles of a data set
Let’s look at an example involving quartiles (Q1, Q2 and Q3).
Set B = {55, 45, 44, 22, 26, 47, 42}
Click the answer button to follow along.
Step 1
Start by ordering the set from smallest to largest.
{22, 26, 42, 44, 45, 47, 55}
Step 2
Find the median of the data set. (Q2)
To do this, pair the first value with the last value. Then the second value with the second to the last and on and on. Until you get to the middle of the list.
22 pairs with 55,
26 pairs with 47
42 pairs with 45
{22, 26, 42, 44, 45, 47, 55}
So Q2 = 44
Finding the Interquartile Range (IQR) and the quartiles of a data set
Note how Q2 (the median) divides the set into two halves. Now, we need to find the median of the two halves.
Step 3
Find the median of the upper half (Q1).
Upper half = {22, 26, 42}
22 pairs with 42
So Q1 = 26
Step 4
Find the median of the lower half(Q3).
Lower half={45, 47, 55}
45 pairs with 55
So Q3 = 47
Step 5
Now that we have Q1, Q2 and Q3, the interquartile range (IQR) = Q3 – Q1.
IQR = 47 – 26 = 21.
Standard deviation and what it means
The standard deviation tells you how far each data value is from the mean value in a data set. The more spread apart the data, the higher the standard deviation will be.
Question
The list of monthly salary earnings is given over a 5-year period from 2004 to 2008.
$573, $585, $600, $614 and $638.
What does this mean?
It means that each average salary "deviates" or is spread from the average monthly salary by 25.3.
Standard deviation and what it means
What about this example?
The list below shows the closing price of the Dow Industrial stock market during 2009 as:
| Date | Closing Price |
| 4/1/2009 | 7,762 |
| 5/1/2009 | 8,212 |
| 6/1/2009 | 8,721 |
| 7/1/2009 | 8,504 |
What does a standard deviation of 333.4 mean for this data set?
Finding standard deviation
To find standard deviation you must:
- First, find the mean of the data set (sum all values and divide by the number of values)
- Next, find the difference of each value and the mean.
- Next, square each difference.
- Last, add up all of the squared differences.
Finding standard deviation
Let’s find the standard deviation for the data set below:
Set A = {5, 15, 25, 35, 45, 55}
Mean= \(\mathsf{ \frac{(5+15+25+35+45+55)}{6} }\)=\(\mathsf{ \frac{180}{6} }\)=30
| Values | Value - Mean | Squared |
| 5 | 5-30=-25 | 625 |
| 15 | 15-30=-15 | 225 |
| 25 | 25-30=-5 | 25 |
| 35 | 35-30=5 | 25 |
| 45 | 45-30=15 | 225 |
| 55 | 55-30=25 | 625 |
\(\mathsf{ \frac{(625+225+25+25+225+625)}{6-1} }\)=\(\mathsf{ \frac{1750}{5} }\)=350 Standard Deviation = \(\mathsf{ \sqrt{350} }\)=18.7
Finding standard deviation
Try this next example on your own. Click on the first column to check your work for the first step, then click on the second column to check your final answer:
Set A = {7, 12, 17, 22, 27}
mean=\(\mathsf{ \frac{(7+12+17+22+27)}{5} }\)=\(\mathsf{ \frac{85}{5} }\)=17
| Values | Value - Mean | Squared |
| 7 | 7 - 17 = -10 | 100 |
| 12 | 12 - 17 = -5 | 25 |
| 17 | 17 - 17 = 0 | 0 |
| 22 | 22 - 17 = 5 | 25 |
| 27 | 27 - 17 = 10 | 100 |
Question
Standard Deviation for this data set is:
\(\mathsf{ \frac{(100+25+0+25+100)}{5-1} }\)=\(\mathsf{ \frac{(250)}{4} }\)=62.5 \(\mathsf{ \sqrt{62.5} }\)=7.90
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Now that you have had some more practice, you should be better prepared for your quiz. If you still do not feel confident about any topics, please contact your teacher for some additional help.
