The following are scores
obtained
by students in a class: 55, 85, 88, 62, 71, 98
1. Make a Frequency
Distribution Table for these data.
Test Scores Freq Pct
90+
1
16.7%
1
80-89
2
33.3%
1+1
70-79
1
16.7%
1
60-69
1
16.7%
1
59 or less
1
16.6%
1
Total 6 100%
2. Make a Frequency Distribution Histogram for these data.
Test Scores Freq Pct
90+
X
80-89
XX
70-79
X
60-69
X
59 or less X
3.
Compute
the mean salary
for
the department? 55+85+88+62+71+98
=
459/6 = 76.5
4. What
is
the median
salary
for the department? 55 62
71
85 88
98
The median is half way between 71 and 85 = 78
5.
What is the range of the salaries in the department?
from 55 to 98 or
43
.
4. What
is
the standard
deviation
of the salaries in the department?
.
(Tronchim
also explains how to compute this, and gives an example.)
X Mean X-Mean X-meanSquared
55
76.5
-21.5 462.25
86
76.5
9.5 90.25
88
76.5
11.5 132.25
62
76.5
-14.5 210.25
71
76.5
-5.5 30.25
98
76.5
21.5 462.25
Sum = 1387.5
Sum/(n-1) - 1387.5/5 = 277.5 which is called
the
"variance"
Standard Deviation is the square root of the variance or 16.7
Descriptive Statistics Exercise
Name
.....................................................................
These are explained on Tronchim's WEB page on Descriptive Statistics.
.
The following are the salaries of officers in a police department:
The chief makes $85,000 per year,
Two sergeants make $60,000 per
year,
Six patrol persons make $40,000
each, and
Two trainees make $9,000 per year.
1. Make a Frequency Distribution Table for these data.
Income
Freq Percent
80 to 100,000
1
9.1%
60 to 79,000
2 18.2%
40 to 59.000
6 54.5%
20 to 39.000
0 0.0%
0 to
19,000
2 18.2%
N
11
2. Make a Frequency Distribution Histogram for these data.
Income
80 to 100,000 X
60 to 79,000
XX
40 to 59.000
XXXXXX
20 to 39.000
0 to
19,000
XX
3. Compute the mean salary for the
department?
85+ 120+240+18
=
463/11 . $42,090.91 or $42.1 thousand
4. What is the median salary for the
department?
Median is in the 40 to 59,999
category.
.
5. What is the range of the salaries in the
department? from 9 to
85
or 76,000
4. What is the standard deviation of the salaries in the department?
85 42.1 42.9
1840.41
60 42.1
17.9
320.41
60 42.1
40 42.1
-2.1
4.41
40 42.1
40 42.1
40 42.1
40 42.1
40 42.1
9 42.1
-33.1
1095.61
9 42.1
SUM = 1840.41 + 640.82 + 26.46 + 2191.22 = 4698.91/10 = 469.891
SD = 21.67
.