Zvalue

1
Z-value

• Sample Population

The z-value tells us how many standard deviations
above or below the mean our data value x
is. Positive z-values are above the mean,
Negative z-values are below the mean
2
Z-value example

• For a sample of females, the mean BMI (body mass
  index) was 26.20 and the standard deviation was
  6.57.
• A person with a BMI of 19.2 has a z score of

So this person has a BMI 1.07 standard deviations
below the mean
3
Unusual values

• Greater than 2 (2 above the mean) or
• Less than 2 (2 below the mean)

4
Percentiles

• A data value is in the 30th Percentile (P30) if
  at least 30 of the data is below that value
• The 70th Percentile (P70) is a value for which
  70 of the data is below that value
• What is P50?

The median (since 50 of the data is below the
median)
5
Finding Percentiles

• To find what percentile a data value is in

Example In a class of 30 people, if you do
better on a test than 24 other people, your
percentile would be
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Finding a value from a Percentile

• Sort data
• Find locator

k percentile n number of values
If L is a whole number The value of the kth
percentile is between the Lth value and the next
value. Find the mean of those values If L is
not a whole number Round L up. The value of the
kth percentile is the Lth value.
7
Example

• BMI values (9 values)
• 19.6, 19.6, 21.4, 22.0, 23.8, 25.2, 27.5, 29.1,
  33.5
• To find P25 (25th Percentile)

Since L is not a whole number, round it up to 3.
P25 is the 3rd data value, 21.4. So P25 21.4
8
Example

• BMI values (8 values)
• 19.6, 19.6, 21.4, 22.0, 23.8, 25.2, 27.5, 29.1
• To find P75 (75th Percentile)

Since L is a whole number, we have to find the
mean of the 6th and 7th data values (25.2 and
27.5). (25.227.5)/226.35 So P75 26.35
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5 number summary

• We want to summarize a data set with 5 numbers.
• min, __________, median, _________, max
• What should we use for these other two?

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Quartiles

• Q1 First Quartile P25
• Q2 Second Quartile P50 median
• Q3 Third Quartile P75
• Note Excel and your calculator can calculate Q1
  and Q3, but there is not universal agreement on
  the procedure, and different tools with sometimes
  give different results.

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Graphing the 5-number summaryThe boxplot
Q3
Max
Q1
Min
Median
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How the Boxplot reveals the distribution
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Using Boxplots to make Comparisons
Males
Females
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Homework

• 2.6 1, 3, 7, 13, 17, 37
• 2.7 3, 9
• Read Review
• Do Review Exercises 1-8
• (on question 1, feel free to only use part of the
  data for calculations, then look up the full
  answer in the back before doing the rest of the
  problems.)