Intro to Statistics
p.394 #1
A statistical question is one for which you don't expect to get a single answer. Instead, you expect a variety of answers, and you are interested in the distribution and tendency of those answers.
How old are the teachers in middle school?
p.400 #1
Add the data values then divide by the number of data values.
p.407 #1
1, 2, 3, 4, 5
p.416 #6
12
p.422 #1
All the values in the data set are the same.
p.394 #8
Statistical - there are many different answers.
p.400 #6
2 pets
p.407 #7
Mode: 3
p.416 #10
The data were not ordered from least to greatest.
35, 38, 41, 44, 48, 49, 51; The range is 16.
p.422 #5
4.4; the prices differ from the mean price by an average of $4.40
p.394 #12
See dot plot.
Most of the data are clustered around 1.
There are peaks at 1 and 2.
There is a gap between 2 and 6.
p.400 #10a&b
a) about 7th
b) 26 and 37 are outliers because they are much greater than the other values
p.407 #14
Black, Blue
p.416 #1
A measure of center represents the center of a data set where a measure of variation describes the distribution of a data set.
p.422 #6
0; the heights are the same so the mean absolute deviation is 0
p.394 #16
a) Yes, it is a statistical question because you would anticipate variability in the hours spent on homework each night by students.
b) See dot plot. Most of the hours cluster around 2. The peak is 2. There is no gap.
c) Most students spend about 2 hours on homework during a school night.
p.401 #12
3.245 inches
p.408 #18
Mean: 50
Median: 40
Mode: 95
The mean is probably best because the mode is the greatest value and the median is too far from the greater values.
p.416 #11
Median = 37
Q1 = 33.5
Q3 = 40.5
IQR = 7
p.422 #9
When calculating the MAD, you need to divide by 6 not 5. Even though the distance from the mean of one of the values (38) is 0 it is still included in the calculation.
MAD = (3+2+0+6+4+3)/6=3
So the values differ from the mean by an average 3.0
p.395 #17
a) 21 earthworms
b) Use a centimeter ruler. The units are centimeters.
c) What is the length of an earthworm?
The lengths are spread out pretty evenly from 15 cm to 28 cm.
p.401 #14a,b&c
a) The 288 minutes used in September is much less than the other values so it is an outlier.
b) With outlier: 488.4, Without outlier: 538.5; The outlier caused the mean to be about 50 minutes less.
c) School could have caused you to spend less time talking on your cell phone.
p.408 #22
With Outlier: mean 103, median 85, mode 85
Without Outlier: mean 85, median 85, mode 85
The outlier makes the mean greater than all of the other values but does not affect the median or mode.
p.416 #14
Median = 58.5
Q1 = 55
Q3 = 65
IQR = 10
p.423 #11
The MAD of the five most-expensive dishes is 3.6.
The MAD of the five least-expensive dishes is 1.76.
The MAD of the five least-expensive is much less than the MAD of the five most-expensive dishes.
So, the data for the five least-expensive dishes is closer together compared to the five most-expensive dishes.