Page 316 - Algebra 1

b. Describe how the outlier affects the measures of central tendency.
SOLUTION
Find the mean, median, and mode with and without the outlier and compare.
With the outlier:
mean: _1226 ≈ 82 15
Without the outlier:
Application: Advertising
Super-Grow Fertilizer placed this advertisement in the newspaper. Is the statement in the advertisement true? Does the statement accurately describe the data? Explain.
SOLUTION
Find the mean, median, and mode of the values for each data set.
Super-Grow: mean = _73 ≈ 8.1; median = 7; mode = 5 and 8; outlier = 20 9
Brand-X: mean = _59 ≈ 6.6; median = 7; mode = 7; no outliers 9
The statement is true since it lists the correct mean of each data set, but the outlier in the data for Super-Grow raises the mean for that data set. Without the outlier, the mean is 6.625.
a. Find the mean, median, and mode of the values in the data set. (Ex 1)
46, 33, 25, 21, 38, 25, 30, 15, 28
b. Do trucks or convertibles have a greater range of sales over the 8-week
(Ex 2) period?
Weekly Car Sales at AutoMart (in thousands of dollars)
The following data show the ages of 20 students graduating from college.
(Ex 3)
22, 22, 23, 22, 25, 26, 22, 21, 22, 26, 64, 22, 23, 24, 22, 25, 22, 22, 24, 59 c. Identify any outliers in the data set.
d. Describe how any outliers affect the measures of central tendency.
median: 81
median: 81
The outlier value of 98 raised the mean temperature by 1 degree.
mean: _1128 ≈ 81 14
mode: 81
mode: 81
Example
4
BUY SUPER-GROW TODAY! Grown with Super-Grow Fertilizer 10, 8, 8, 6, 5, 4, 7, 5, 20
Grown with Brand-X Fertilizer 6, 7, 6, 5, 7, 9, 7, 5, 7 SUPER-GROW WATERMELONS HAVE AN
AVERAGE WEIGHT OF OVER 8 POUNDS!
BRAND-X FERTILIZER WATERMELONS HAVE AN AVERAGE WEIGHT OF UNDER 7 POUNDS.
Math Reasoning
Generalize Which measure of central tendency best describes Super-Grow’s data? Explain.
Lesson Practice
Trucks
350, 125, 415, 370, 560, 280, 265, 430
Convertibles
640, 720, 600, 640, 810, 755, 780, 660
Lesson 48 301