Range, quartiles, and interquartile rangeswarna sudha
The IQR describes the middle 50% of values when ordered from lowest to highest. To find the interquartile range (IQR), first find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.
Range, quartiles, and interquartile rangeswarna sudha
The IQR describes the middle 50% of values when ordered from lowest to highest. To find the interquartile range (IQR), first find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.
TSTD 6251 Fall 2014SPSS Exercise and Assignment 120 PointsI.docxnanamonkton
TSTD 6251 Fall 2014
SPSS Exercise and Assignment 1
20 Points
In this class, we are going to study descriptive summary statistics and learn how to construct box plot. We are still working with univariate variable for this exercise.
Practice Example:
Admission receipts (in million of dollars) for a recent season are given below for the
n =
30 major league baseball teams:
19.4 26.6 22.9 44.5 24.4 19.0 27.5 19.9 22.8 19.0 16.9 15.2 25.7 19.0 15.5 17.1 15.6 10.6 16.2 15.6 15.4 18.2 15.5 14.2 9.5 9.9
10.7 11.9 26.7 17.5
Require:
a. Compute the mean, variance and standard deviation.
b. Find the sample median, first quartile, and third quartile.
c. Construct a boxplot and interpret the distribution of the data.
d. Discuss the distribution of this set of data by examining kurtosis and skewness
statistics, such as if the distribution is skewed to one side of the distribution, and if the
distribution shows a peaked/skinny curve or a spread out/flat curve.
SPSS Procedures for Computing Summary Statistics
:
Enter the 30 data values in the first column of SPSS
Data View
Tab
Variable View
and name this variable
receipts
Adjust
Decimals
to 3 decimal points
Type
Admission Receipts
($ mn)
in the
Label
column for output viewer
Return to
Data View
and click
A
nalyze
on the menu bar
Click the second menu
D
e
scriptive Statistics
Click
F
requencies …
Move
Admission Receipts
to the
Variable(s)
list by clicking the arrow button
Click
S
tatistics …
button at the top of the dialog box
Now, you can select the descriptive statistics according to what the question requires. For this practice question, it requires central tendency, dispersion, percentile and distribution statistics, so we click all the boxes
except for
P
ercentile(s): and Va
l
ues are group midpoints
.
Click
Continue
to return to the
Frequencies
dialog box
Click
OK
to generate descriptive statistic output which is pasted below:
The first table provides summary statistics and the second table lists frequencies, relative frequencies and cumulative frequencies. The statistics required for solving this problem are highlighted in red.
Statistics
Admission Receipts
N
Valid
30
Missing
0
Mean
18.76333
Std. Error of Mean
1.278590
Median
17.30000
Mode
19.000
Std. Deviation
7.003127
Variance
49.043782
Skewness
1.734
Std. Error of Skewness
.427
Kurtosis
5.160
Std. Error of Kurtosis
.833
Range
35.000
Minimum
9.500
Maximum
44.500
Sum
562.900
Percentiles
10
10.61000
20
14.40000
25
15.35000
30
15.50000
40
15.84000
50
17.30000
60
19.00000
70
19.75000
75
22.82500
80
24.10000
90
26.69000
Admission Receipts
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
9.500
1
3.3
3.3
3.3
9.900
1
3.3
3.3
6.7
10.600
1
3.3
3.3
10.0
10.700
1
3.3
3.3
13.3
11.900
1
3.3
3.3
16.7
14.200
1
3.3
3.3
20.0
15.2.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
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Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
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The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
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1. Warm Up
1. Order the test scores from least to
greatest: 89, 93, 79, 87, 91, 88, 92.
79, 87, 88, 89, 91, 92, 93
2. Find the median of the test scores.
89
Find the difference.
3. 17 – 0.9 16.1
4. 8.4 – 7. 6 0.8
5. 9.1 – 5.7 3.4
6. 190.3 – 23.4 166.9
3. The table below summarizes a cat
breeder’s records for kitten litters born
in a given year. You can divide the data
into four equal part using quartiles.
Litter Size
2
3
4
5
6
Number of
Litters
1
6
8
11
1
4. You know that the median of a data set divides the
data into a lower half and an upper half. The median
of the lower half is the lower quartile, and the
median of the upper half is the upper quartile.
Kitten Data
Lower half
Upper half
233333344444444555555555556
Upper quartile: 5
Lower quartile: 3
median of upper half
median of lower half
Median: 4
5. Example 1: Finding Quartiles
Find the lower and upper quartiles for the data
set.
A. 15, 83, 75, 12, 19, 74, 21
12 15 19 21 74 75 83
lower quartile: 15
upper quartile: 75
Order the values.
6. Example 2: Finding Quartiles
Find the lower and upper quartiles for the data
set.
B. 75, 61, 88, 79, 79, 99, 63, 77
61 63 75 77 79 79 88 99
lower quartile:
Order the values.
63 + 75
= 69
2
79 + 88
upper quartile:
= 83.5
2
7. Check It Out! Example 3
Find the lower and upper quartiles for the data
set.
A. 25, 38, 66, 19, 91, 47, 13
13 19 25 38 47 66 91
lower quartile: 19
upper quartile: 66
Order the values.
8. Check It Out! Example 1
Find the lower and upper quartiles for the data
set.
B. 45, 31, 59, 49, 49, 69, 33, 47
31 33 45 47 49 49 59 69
Order the values.
33 + 45
lower quartile:
= 39
2
49 + 59
upper quartile:
= 54
2
9. A box-and-whisker plot shows the
distribution of data. The middle half of the
data is represented by a “box” with a vertical
line at the median. The lower fourth and
upper fourth quarters are represented by
“whiskers” that extend to the minimum
(least) and maximum (greatest) values.
1
2
3
Lower quartile
4
Median
5
6
7
8
Upper quartile
9
10. Example 4: Making a Box-and-Whisker Plot
Use the given data to make a box-and-whisker plot.
21, 25, 15, 13, 17, 19, 19, 21
Step 1. Order the data from least to greatest. Then
find the minimum, lower quartile, median, upper
quartile, and maximum.
13 15 17 19 19 21 21 25
minimum: 13
15 + 17
lower quartile:
2
maximum: 25
= 16 upper quartile:
median:
19 + 19
2
= 19
21 + 21
2
= 21
11. Example 4 Continued
Use the given data to make a box-and-whisker plot.
Step 2. Draw a number line and plot a point above
each value from Step 1.
13 15 17 19 19 21 21 25
12
14
16
18
20
22
24
26 28
12. Example 4 Continued
Use the given data to make a box-and-whisker plot.
Step 3. Draw the box and whiskers.
13 15 17 19 19 21 21 25
12
14
16
18
20
22
24
26 28
13. Example 5
Use the given data to make a box-and-whisker plot.
31, 23, 33, 35, 26, 24, 31, 29
Step 1. Order the data from least to greatest. Then
find the minimum, lower quartile, median, upper
quartile, and maximum.
23 24 26 29 31 31 33 35
minimum: 23
lower quartile:
maximum: 35
24 + 26
2
= 25 upper quartile:
median: 29 + 31 = 30
2
31 + 33
2
= 32
14. Example 5 Continued
Use the given data to make a box-and-whisker plot.
Step 2. Draw a number line and plot a point above
each value.
23 24 26 29 31 31 33 35
22
24
26
28
30
32
34
36 38
15. Example 5 Continued
Use the given data to make a box-and-whisker plot.
3.
the box and whiskers.
Step 2. Draw a number line and plot a point above
each value.
23 24 26 29 31 31 33 35
22
24
26
28
30
32
34
36 38
16. Example 6
These box-and-whisker
plots compare the point
per quarter at Super
Bowl XXXVII.
0
Quarter
1
2
3
4
Oakland
3
0
6
12
Tampa Bay
3
17
14
14
Oakland
3
6
9
12
15
18
Tampa Bay
0
3
6
9
12
15
18
17. Example 6
A. Compare the medians and ranges.
The median for
Tampa Bay is
significantly
greater and the
range for Tampa
Bay is slightly
greater.
Oakland
0
3
6
9
12
15
18
Tampa Bay
0
3
6
9
12
15
18
18. Check It Out! Example 6
B. Compare the ranges of the middle half of
the data for each.
Oakland
The range of
the middle half
of the data is
greater for
0 3 6 9 12 15 18
Tampa Bay.
Tampa Bay
0
3
6
9
12
15
18
19. Lesson Quiz: Part I
Find the lower and upper quartiles for each
data set.
1. 48, 52, 68, 32, 53, 47, 51
lower = 47; upper = 53
2. 3, 18, 11, 2, 7, 5, 9, 6, 13, 1, 17, 8, 0
lower = 2.5; upper = 12
20. Lesson Quiz: Part II
Use the following data for problems 3 and 4.
91, 87, 98, 93, 89, 78, 94
3. Make a box-and-whisker plot.
78
87
91
94
98
4. What is the median and range of the data?
91; 20
