The FREQUENCY of a state in this problem means how FREQUENTLY a professor
among the 17 would say he or she was from that state. So we make a table
of the states and their FREQUENCIES, which is how many professors are from
that state.
2 professors are from GA. So that means
that how frequently a professor says he or she
is from GA is 2 times out of the 17.
2 professors are from MI. So that means
that how frequently a professor says he or she
is from MI is 2 times out of the 17.
1 professor is from NE. So that means
that how frequently a professor says he or she
is from NE is 1 time out of the 17.
3 professors are from NJ. So that means
that how frequently a professor says he or she
is from NJ is 3 times out of the 17.
etc. with the other states.
So we make this list
State Frequency
GA 2
MI 2
NE 1
NJ 3
OH 3
PA 2
SC 2
WI 2
--------------
Total 17
ii. What is (are) the mode(s)?
Thw word "Mode" starts with "MO" and "MOST" also starts
with "MO". So that's how you remember what "MODE" means.
A MODE is one that has the MOST FREQUENCY. So there are two
MODES, NJ and OH because they have the MOST number of
professors represented among the 17.
iii.does it make sense to talk about the average for this data?
Why or why not?
I'm not sure about this. This is splitting hairs. Of the 8
states represented, there is an average of 2⅛ professors
per state. There isn't much use for this 2⅛, but I
wouldn't say it doesn't make sense, for it does make sense.
But it's not useful data. You'll have to ask your teacher about
this one.
iv. Using the frequency table draw a pie chart to display the distribution of home sates by filling in the following table:
HOME STATE | FREQUENCY | % OF TOTAL | MEASURE OF CENTRAL ANGLE(IN DEGREES)
| | |
GA | 2 | 2/17 = 11.8% | (2/17)×360° = 42.4°
MI | 2 | 2/17 = 11.8% | (2/17)×360° = 42.4°
NE | 1 | 1/17 = 6.9% | (1/17)×360° = 21.2°
NJ | 3 | 3/17 = 17.6% | (3/17)×360° = 63.5°
OH | 3 | 3/17 = 17.6% | (3/17)×360° = 63.5°
PA | 2 | 2/17 = 11.8% | (2/17)×360° = 42.4°
SC | 2 | 2/17 = 11.8% | (2/17)×360° = 42.4°
WI | 2 | 2/17 = 11.8% | (2/17)×360° = 42.4°
------------------------------------------------------------
Total | 17 |17/17 = 101.1% | 360.2°
Notice that the 101.1% is not exactly 100% and the 360.2°
is not exactly 360° because of rounding off.
Here is the pie graph. You might want to put the percentages
in the pieces of pie along with the states. I didn't but
maybe you should. Use a protractor to measure the angles,
and a compass to draw the circle:
Edwin
