Mean mode median solved problems (Biostatistic)

[Arosa Hya]

1.



The weekly salaries of six employees at McDonalds are $140, $220, $90, $180, $140, $200. For these six salaries, find: (a) the mean (b) the median (c) the mode


1. List the data in order: 90, 140, 140, 180, 200, 220
Mean: 90+ 140+ 140+ 180 + 200 + 220 = http://www.regentsprep.org/regents/math/algebra/AD2/ans1h1.gif
6

Median: 90,140,140,180,200,220
The two numbers that fall in the middle need to be
averaged. 140 + 180 = 160
2

Mode: The number that appears the most is 140

[Arosa Hya]

Andy has grades of 84, 65, and 76 on three math tests. What grade must he obtain on the next test to have an average of exactly 80 for the four tests?
84 + 65 + 76+ x = 80(average) cross multiply
4 and solve

(4)(80) = 225 + x
320 = 225 + x
-225 -225

95 = x

Andy needs a 95 on his next test.

[Arosa Hya]

Test scores for a class of 20 students are as follows:
93, 84, 97, 98, 100, 78, 86, 100, 85, 92, 72, 55, 91, 90, 75, 94, 83, 60, 81, 95





Test
Scores

Frequency


91-100



81-90



71-80



61-70



51-60




a) Copy and complete the table shown at the left.b) Find the modal interval.
The "modal interval" is the interval containing the greatest frequency. It is not the mode.
c) Find the interval that contains the median.



Solution:







Test Scores
Frequency


91-100
9


81-90
6


71-80
3


61-70
0


51-60
2



20 total



b. 91-100 is the modal interval. This interval has the most data.



c. The middle of 20 is 10.

If I count from
the top, 10 will fall in the interval 81-90.
If I count from the bottom and go up, 10
will fall in the interval 81-90. The
interval that contains the

median is
81 - 90.

[Arosa Hya]

http://www.regentsprep.org/regents/math/algebra/AD2/Pmeasu2.gif
Problem
The values of 11 houses on Washington Street are shown in the table.a. Find the mean value of these houses in dollars.
b. Find the median value of these houses in dollars.




c. State which measure of central tendency, the mean or the median, best represents the values of these 11 houses. Justify your answer.


Solution:
a. Mean: 100000 + 5(175000) + 4(200000) + 700000 = 225,000
11

b. Median: 100000, 175000, 175000, 175000, 175000, 175000, 200000, 200000, 200000, 200000, 700000
Median can be seen to be 175000.
OR simply find where the middle (6th value) occurs: 175000

c. Best: The median best represents the values of the homes since the mean value has only one home price higher than the mean.