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Unit 6

Satisfactory Essays
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Date: ______________

Mean, Median, and Mode for Grouped Data
Part A – Frequency Tables
The following table shows the annual salaries earned by employees of a small company: Annual salary ($)
35 500
42 750
51 000
99 000
150 000
Totals

Frequency
3
5
5
1
1
15

106 500
213 750
255 000
99 000
150 000
824 250

a) What is the mean salary?
To find the mean of data in a frequency table: for each row…
- multiply each value by its frequency
- add up these values
- divide by the frequency total

3(106500) + 5(213750) + 5(255000) +1(99000) +1(150000)
15
824250
=
15
= 54950
b) What is the median salary?
There are 15 employees. ∴ the salary of the 8th employee is the median. The …show more content…

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MAP4C

Class #: _____

Date: ______________

The median will occur in an interval. Find the middle data value, and then find what interval this value occurs in. The median is the midpoint of that interval.
The mode is the midpoint of the interval that occurs most frequently.
a) mean

∑ fx = 2658 n 500
= 5.316

b) mode
Looking at the frequency column, we can see that the “4-5” interval occurs most often. So, the mode is the midpoint of that interval, which is 4.5 . We could also say that the modal interval is “4-5”.
c) median
The middle data value is between values 250 and 251. Both these data values occur in the “4-5” interval (look at the Cumulative Frequency column).
So the median is 4.5, the midpoint of the “4-5” interval.
Part C – The Effect of Outliers
Two classes that wrote the same physics examination had the following results:
Class A: 71, 82, 55, 76, 66, 71, 90, 84, 95, 64, 71, 70, 83, 45, 73, 51, 68
Class B: 54, 80, 12, 61, 73, 69, 92, 81, 80, 61, 75, 74, 15, 44, 91, 63, 50, 84
Class A:

Class B:

Mean:
Median:
Mode:

Mean:
Median:
Mode:

Circle the outliers. What effect do outlier values have on the mean?

What measure of central tendency is a better choice when dealing with small data sets that contain outliers?

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