G10 Math Q4-WEEK 2- Relation of Position.ppt

math 10

1. Measures of Measures of
Relative Relative
PositionPosition

2. Consider an Internet site that offers
movie downloads.
Data:
12 minestimated mean time to
download a certain movie
4 minstandard deviation
Suppose you download this movie, the
download takes 20 min
However, when your friend download this
movie, the download takes 6 min

3. What a surprise!
The number of standard deviations between a data value
and the mean is known as the data value’s z-score or
standard score.

4. Z-Score

5. Raul has taken two tests in his chemistry
class. He scored 72 on the first test, for
which the mean of all scores was 65 and
the standard deviation was 8. He
received a 60 on the second test, for
which the mean of all scores was 45 and
the standard deviation was 12. In
comparison to other students, did Raul
do better on the first test or the second
test?
Example 1. Compare z-scores

6. Example 1. Compare z-scores
Raul scored 0.875 standard deviation above
the mean on the first test.
Raul scored 1.25 standard deviation above the
mean on the second test.

7. A consumer group tested a sample of
100 light bulbs. It found that the mean
life expectancy of the bulbs was 842
hr, with a standard deviation of 90.
One particular light bulb from the
DuraBright Company has a z-score of
1.2. What was the life span of this
light bulb?
Example 2. Use z-scores

8. Example 2. Use z-scores
The light bulb had a life span of 950 hr.

9. pth Percentile
A value x is called the pth percentile
of a data set provided p% of the data
values are less than x.
Percentiles
Most standardized examinations provide
scores in terms of percentiles.

10. In a recent year, the median annual
salary for a physical therapist was Php
174,480. If the 90
th
percentile for the
annual salary of a physical therapist
was Php 205,900, find the percent of
physical therapists whose annual salary
was
a.more than Php 174,480.
b.less than Php 205,900.
c.between Php 174,480 and Php 205,900.
Example 3. Using Percentiles

11. Example 3. Using Percentiles
Solution
a. By definition, the median is the 50
th

percentile. Therefore, 50% of the
physical therapists earned more than
Php 174,480.
b. Because Php205,900 is the 90
th

percentile, 90% of all physical therapists
earned less than Php 205,900.
c. From parts a and b, 90% - 50% = 40%
of the physical therapists earned
between Php 174,480 and Php 205,900.

12. Percentile for a Given
Data Value

13. On a reading examination given to
900 students. Elaine’s score of 602
was higher than the scores of 576
students who took the examination.
What is the percentile for Elaine’s
score?
Example 4. Find a Percentile

14. Example 4. Find a Percentile
Elaine’s score of 602 places at the 64
th

percentile.

15. The three numbers Q
1, Q
2, and Q
3
that partition a ranked data set into
four (approximately) equal groups are
called the quartiles of the data.
Quartiles

16. Quartiles

17. The following table lists the calories
per 100mL of 25 popular sodas. Find
the quartiles for the data.
Calories, per 100mL of Selected Sodas
Example 5. Find the Quartiles of
the Data Set
43 36 48 62 48
26 42 42 39 50
41 73 53 36 40
37 58 45 45 49
53 40 39 32 56

18. Example 5. Find the Quartiles of
the Data Set
26 32 36 36 37
39 39 40 40 41
42 42 43 45 45
48 48 49 50 53
53 56 58 62 73

19. A box-and whisker plot (sometimes
called a box plot) is often used to
provide a visual summary of a set of
data.
Box-and-Whisker Plot

20. Box-and-Whisker Plots

21. Practice Test
•Orlan received a score of 70 on a
test for which the mean score score
was 65. Orlan has learned that the
z-score for his test is 0.6. What is
the standard deviation for this set of
test scores?

22. •On an examination given to
8600 students. Jonalyn’s
score of 405 was higher than
the scores of 3952 of the
students who took the exam.
What is the percentile for
Jonalyn’s score?

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