Laboratory Exercise 1: Getting Acquainted
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Mean, median, quartiles, interquartile range, minimum, maximum,
variance, standarddeviation, box-n-whiskers
The DRP, The "Degree of Reading Power" test, is used for measuring the
reading skills of children. In a study into the reading abilities
of eight-year olds, 44 pupils are tested. Their scores are displayed
in the table below. (Source: Maribeth Cassidy Schmitt, 'The Effects of
an Elaborated Directed Reading Activity on the Metacomprehension
Skills of Third Graders', thesis, Purdue University 1987.)
40 26 39 14 42 18 25 43 46 27 19
47 19 26 35 34 15 44 40 38 31 46
52 25 35 35 33 29 34 41 49 28 52
47 35 48 22 33 41 51 27 14 54 45
a. Calculate Mean and Median.
b. Calculate first and third quartile and measure the interquartilerange.
c. Give minimum and maximum.
d. Calculate variance and standard deviation.
e. Create a boxdiagram.
Exercise 3a - calculation
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a. sum = (40 + 26 + 39 + 14 + 42 + 18 + 25 + 43 + 46 + 27 + 19 +
47 + 19 + 26 + 35 + 34 + 15 + 44 + 40 + 38 + 31 + 46 +
52 + 25 + 35 + 35 + 33 + 29 + 34 + 41 + 49 + 28 + 52 +
47 + 35 + 48 + 22 + 33 + 41 + 51 + 27 + 14 + 54 + 45)
= 1544
number = 44
Mean = sum / number
= 1544 / 44 = 35.09
Rearrange the following numbers in increasing order:
14 14 15 18 19 19 22 25 25 26 26
27 27 28 29 31 33 33 34 34 35 35
35 35 38 39 40 40 41 41 42 43 44
45 46 46 47 47 48 49 51 52 52 54
In case of an odd number of values, the median is the number in
the middle. In case of an even amount, the average of the middle
two numbers is the median. In this case there are 44 numbers,
which means that the average of the 22nd and the 23rd number will
be the median. Median = (35+35) / 2 = 35
b. The first quartile is the median of the 1st - 22nd number. This is
the average of the 11th and 12th number.
First Quartile = (26 + 27) / 2 = 26.5
The third quartile is the median of the 23rd - 44th number. This is
the average of the 33rd and 34th number.
Third Quartile = (44 + 45) /2 = 44.5
Interquartile range = third quartile - first quartile
= 44.5 - 26.5 = 18
c. Minimum = 14
Maximum = 54
d. value value-mean square(value-mean)
40 8.82 77.76
26 - 9.18 84.31
39 3.82 14.58
14 -21.18 448.67
42 6.82 46.49
18 -17.18 295.21
25 -10.18 103.67
43 7.82 61.12
46 10.82 117.03
27 - 8.18 66.94
19 -16.18 261.85
47 11.82 139.67
19 -16.18 261.85
26 - 9.18 84.31
35 - 0.18 0.03
34 - 1.18 1.39
15 -20.18 407.31
44 8.82 77.76
40 4.82 23.21
38 2.82 7.94
31 - 4.18 17.49
46 10.82 117.03
52 16.82 282.85
25 -10.18 103.67
35 - 0.18 0.03
35 - 0.18 0.03
33 - 2.18 4.76
29 - 6.18 38.21
34 - 1.18 1.40
41 5.82 33.85
49 13.82 190.94
28 - 7.18 51.58
52 16.82 282.85
47 11.82 139.67
35 - 0.18 0.03
48 12.82 164.31
22 -13.18 173.76
33 - 2.18 4.76
41 5.81 33.85
51 15.82 250.21
27 - 8.18 66.94
14 -21.18 448.67
54 18.82 354.12
45 9.82 96.40
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5438.55
variance = 5438.55 / (44 - 1) = 126.48
standard deviation = square root(variance) =11.25
e. The lower range of the box is at the first quartile, the upper at the
third.
The line will be approximately in the middle of the box, near the median.
The two lines just outside the box stretch from minimum (bottom) to
maximum (top).
Exrecise 3a - SPSS
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Put the contents in a table. choose >File >New >Data. Type the values
in the first column. Define the column by doubleclicking on the text
'var' above the appropriate column. A pop-up dialogscreen will appear
with the text 'Define Variable'. Enter at >Variable name the name
'score'. Next choose >Type. Define type as 'Numeric'. Type at >Width
'2' (the number of positions) and at >Decimal Places type '0' (zero),
the amount of numbers after the dot. Next click >Continue and in the
dialogbox 'Define Variable' click >Ok.
Choose >Statistics >Summarize >Frequencies. You will enter the window
'Frequencies'. Put the variable 'score' in Variable(s) with > (arrow
to the right). Click >Statistics. Tick the boxes for Quartiles, Mean,
Median, Sum, Std. deviation, Variance, Minimum en Maximum, by clicking
them. Click >Continue and next >OK. In the output window, you will
find the data requested. The first quartile is called Percentile 25.00
and the third Percentile 75.00. The interquartile range equals the
difference between both quartiles.
Choose >Graphs >Boxplot. Choose >Simple. Choose in the area 'Data in
Chart Are' the entry >Summaries of seperate variables. Click
>Define. Put 'scores' under Boxes Represent and click >Ok.
Exercise 3a - report
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The DRP, The Degree of Reading Power test, is used for measuring the
reading skills of children. In research into the reading abilities
of eight year olds, 44 pupils were tested.
a. Calculate mean and median.
Mean: 35.09
Median: 35
b. Calculate first and third quartile and measure the interquartilerange.
First Quartile: 26.5
Third Quartile: 44.5
Interquartile range: 18
c. Give minimum and maximum.
Minimum = 14
Maximum = 54
d. Calculate variance and standarddeviance.
Variance: 126.48
Standaarddeviation: 11.25
e. Create a boxdiagram.
The lower range of the box is at the first quartile, the upper at
the third. The line will be approximately in the middle of the
box, near the median. The two lines just outside the box stretch
from minimum (bottom) to maximum (top).