Download Measures of Central Tendency

Coordinate Algebra
SID.2: Measures of Spread
Name: ____________________________________
Date:_____________________________
Measures of Spread give us an indication of how _______________ _____________ our data
set is. Here are some common measures of spread.
Range –______________________________________________________________________
Mean absolute deviation (MAD) - _______________________________________________
MAD =
x1  x  x2  x  .... xn  x
n
or
Steps for finding the MAD:
1. Arrange your data set __________________.
2. Find the _____________ of your data set.
3. ____________ the mean from each of your data points, keeping each difference
__________________!
4. Calculate the _______________ of your differences.
5. ______________ the sum by the total number of data points you have.
Ex 1)
The salaries at a small business with 7 employees are as follows:
$26,000, $32,000, $31,000, $29,000, $24,000, $24,000, and $23,000.
Find the range and the MAD.
List the data points
Total:
N = ________
Mean = _______
Difference ( x  x )
Positive Value
Sum _____________
Mean Absolute Deviation:
= _________
Ex 2)
Ex 3)
The data shown below displays the running times in minutes for science-fiction
movies. Find the absolute deviation of the data set. 98, 87, 93, 88, 126, 108
The high (ͦ F) for the last seven days in two cities are given:
City A:
55 , 45 , 48 , 41 , 30 , 54 , 55
City B:
67 , 68 , 65 , 64 , 61 , 62 , 69
a) Find the mean and median for each set of data.
b) Find the mean absolute deviation for each set of data.
c) Decide which measure of center you would use and compare their distribution.
d) Compare the spreads of the data using the mean absolute deviation. (variability)
Coordinate Algebra Assignment
SID.2: Measures of Central Tendency/Spread
Name: ________________________
Date: _________________________
Find the mean and median of the data below.
1a) 6, 1, 3, 8, 5, 11, 5
2a) 15, 27, 10, 25, 9, 22, 25
3a) 4.2, 2.2, 3.7, 2.8, 1.1
For the data above, determine which measure of central tendency best represents the data. Explain your
choice.
1b)
2b)
3b)
Find the range and the mean absolute deviation of the data. Describe the spread of the data using range
and/or mean absolute deviation.
6) 10, 7, 13, 10, 8
7) 87, 75, 85, 77, 74, 82
Use the measures of central tendency to answer the questions below.
8)
Sarah’s teacher tells her she will average her grades using the mean, median, or mode. Using Sarah’s
grades below, determine which measure of central tendency Sarah wants her teacher to use.
84, 93, 87, 72, 67, 72, 89, 94
9)
In golf tournament, the 18-hole totals for the top 4 golfers in the men and women’s competition are
recorded. Compare the spread of the data for the two sets of data using the mean, range, and mean
absolute deviation.
Mean:
Range:
Mean Absolute Deviation:
Tournament Leader Board
Men
Women
67
68
68
70
68
72
76
75