Measures of Relative Position
The measures of position are used to locate the
relative position of a specific value in relation to
the rest of the data. The most popular measures
of position are:

Z-SCORE

QUARTILES

BOX AND WHISKERS PLOT
STANDARD SCORE (Z-score)

A Z-score is a numerical measurement used in statistics
of a value's relationship to the mean (average) of a
group of values, measured in terms of standard
deviations from the mean. If a Z-score is 0, it indicates
that the data point's score is identical to the mean
score. A Z-score of 1.0 would indicate a value that is
one standard deviation from the mean. Z-scores may
be positive or negative, with a positive value indicating
the score is above the mean and a negative score
indicating it is below the mean.
STANDARD SCORE (Z-score)
1. Scores on a history test have average of 80 with standard
deviation of 6. What is the z-score for a student who
earned a 75 on the test?
2. The temperature is recorded at 60 airports in a region.
The average temperature is 67 degrees Fahrenheit with
standard deviation of 5 degrees. What is the z-score for a
temperature of 68 degrees?
3. Ariel’s score in there Mathematics test is 42. If the test
has a standard deviation of 10 and a mean of 39. What is
Ariel’s z-score?
4. A national achievement test is administered annually to
3rd graders. The test has a mean score of 100 and a
standard deviation of 15. If Jane's z-score is 1.20, what
was her score on the test?
QUARTILES
Quartiles in statistics are values that divide your data
into quarters. they divide your data into four segments
according to where the numbers fall on the number
line.

Each quartile contains 25% of the total observations.
Generally, the data is arranged from smallest to largest:
• First quartile: the lowest 25% of numbers
• Second quartile: between 25.1% and 50% (up to the
median)
• Third quartile: 51% to 75% (above the median)
• Fourth quartile: the highest 25% of numbers
1. 5, 7, 4, 4, 6, 2, 8
2. 1, 3, 4, 2, 2, 5, 5, 6,
6, 2, 10, 9, 8, 9, 7, 7
3. 50, 11, 1, 57, 15, 19, 20,
47, 37, 28, 24, 34
INTERQUARTILE RANGE
 In
descriptive statistics, the interquartile
range, also called the midspread or middle
50%, or technically H-spread, is a measure
of statistical dispersion, being equal to the
difference between upper and lower
quartiles,
IQR = Q₃ − Q₁
BOX AND WHISKERS PLOT

A box and whisker plot—also called a box plot—displays the fivenumber summary of a set of data. The five-number summary is the
minimum, first quartile, median, third quartile, and maximum.

In a box plot, we draw a box from the first quartile to the third
quartile. A vertical line goes through the box at the median. The
whiskers go from each quartile to the minimum or maximum.
1. 5, 7, 4, 4, 6, 2, 8
2. 1, 3, 4, 2, 2, 5, 5, 6,
6, 2, 10, 9, 8, 9, 7, 7
3. 50, 11, 1, 57, 15, 19, 20,
47, 37, 28, 24
PERCENTILE

a percentile is a number where a certain
percentage of scores fall below that number.
(𝟏𝟎𝟎(𝒊−𝟎.𝟓)
P=
𝒏
PERCENTILE RANK
R=
𝑷
𝟏𝟎𝟎
(𝒏 + 𝟏)