Download Name: Date: ______ Per: _____ Statistics Review Directions: Define

Name: ___________________________
Statistics Review
Date: ____________
Per: _____
Directions: Define fully. Show work. Neat and complete. Make sure answers are obvious, in the right
place, and have the correct units.
Define:
1. Statistical question: a question that anticipates and accounts for a variety of answers.
2. Mean: the sum of the data divided by the number of pieces of data
3. Median: the value of appearing at the center of a sorted version of a set of data
4. Finding median (odd set of numbers): locate the number at the center of the sorted set
5. Finding median (even set of numbers): find the mean of the two central values (add them together
and divide by two)
6. Mode: the number or numbers that occur most often
7. Measures of variation: they are used to describe the distribution or spread of the data
8. Quartile: values that divide the data set into four equal parts
9. First quartile: the median of the data values less than the median
10. Third quartile: the median of the data values greater than the median
11. Interquartile range (IQR): the distance between the first and third quartiles of the data set
12. Range: difference between the greatest and least data values
13. Outlier (and its formula!): A data value that is either much greater or much less than the median –
1. Find the IQR
2. Multiply the IQR by 1.5
3. Subtract that new number from Q1 to find the low outlier
4. Add that new number to Q3 to find the high outlier
14. Mean Absolute Deviation (MAD) + the 3 steps to finding it: the average distance between each
data value and the mean
1. find the mean of the data set
2. find the absolute value of the differences between each value in the data set and the mean
3. find the average of the absolute value of the differences between each value in the data set and
the mean
15. Line plot (or dot plot) + the 3 steps to finding it: a visual display of a distribution of data values
where each data value is shown as a dot or an x.
1. draw and label a number line
2. place as many Xs above each number as there are responses for that number
3. describe the data
16. Histogram + the important 3 bits of info on page 872 in the little bubbles: a type of bar graph is
used to display numerical data that have been organized into equal intervals
1. there is no space between bars
2. intervals are equal so all bars have the same width
3. intervals with a frequency of zero have a bar height of zero
17. The 3 steps to creating a histogram:
1. make a frequency table to organize the data
2. draw and label a horizontal and vertical axis – include a title. Show the intervals along the
horizontal axis. Show the frequencies on the vertical axis.
3. for each interval draw a bar whose height is given by the frequencies
18. Box plot + the 3 steps to finding it: uses a number line to show the distribution of a set of data by
using the median, quartiles, and extreme values. A box is drawn around the quartile values, and
the whiskers extend from each quartile to the extreme data points that are not outliers – the
median is marked with a vertical line.
1. Order the numbers from least to greatest – draw a number line that covers the range of the data
2. find the median, extreme data points, and the first and third quartiles – mark those points above
the number line
3. draw the box so that it includes the quartile values and has a vertical line through the median –
extend the whiskers from each quartile to the extreme data points
19. Find the mean, median, mode of this set of numbers:
13
23
32
15
29
18
22
23
Arrange the numbers in order here: 13, 15, 18, 22, 23, 23, 29, 32
Mean equation: 13 + 15 + 18 + 22 + 23 + 23 + 29 + 32 = 175
175/8 = 21.88
Median (+equation, if needed): 13, 15, 18, 22, 23, 23, 29, 32
22 + 23 = 45
Mode: 23
45/2 = 22.5
20. Find the mean, median, mode, first quartile (Q1), third quartile (Q3), IQR, Range, and lower and
upper outliers:
23
27
44
38
39
38
24
17
29
44
Arrange the numbers in order here: 17, 23, 24, 27, 29, 38, 38, 39, 44, 44
Mean equation: 17 + 23 + 24 + 27 + 29 + 38 + 38 + 39 + 44 + 44 = 323
Median (+equation, if needed): 17, 23, 24, 27, 29, 38, 38, 39, 44, 44
Mode: 38, 44
Q1: 24
Q3: 39
IQR (+formula): 39 – 24 = 15
323/10 = 32.3
29+38=67 67/2=33.5
Range (+formula): 44 – 17 = 27
IRQ x 1.5 = 15 x 1.5 = 22.5
Low outlier (+formula): 24 – 22.5 = 1.5
High outlier (+formula): 39 + 22.5 = 61.5
21. Find the MAD of the following set of data:
45
56
36
33
51
39
61
* Mean equation: 33 + 36 + 39 + 45 + 51 + 56 + 61 = 321
321/7 = 45.86
* All seven equations for the diff. between each data value and the mean:
33 - 45.86 = 12.86
36 - 45.86 = 9.86
39 - 45.86 = 6.86
45 - 45.86 = .86
51 - 45.86 = 5.14
56 - 45.86 = 10.14
61 - 45.86 = 15.14
* Formula and data of the average of the absolute values of the diff. between each value and the
mean:
12.86 + 9.86 + 6.86 + .86 + 5.14 + 10.14 + 15.14 = 60.86
60.86 / 7 = 8.69
* The average that each data point is away from the mean is 8.69 units.
22. Make a line plot (dot plot) of the following data:
X
X
1
2
3
4
X
X X
X
x
Xx
5
6
8
7
X
x
xX
xX
xX
X
x
Xx
Xx
Xx
9
10 11 12 13 14 15
X
x
Xx
2
7
11
14
9
12
9
11
13
6
7
11
5
10
10
8
8
11
Xx
X
X
X
X
X
10
20 30 40 50 60 70 80
X
X
X
X
X
23. Find the mean, median, mode, and range of this line plot:
Arrange the numbers in order here: 10, 10, 10, 20, 20, 40, 50, 70, 70, 70
Mean equation: 10 + 10 + 10 + 20 + 20 + 40 + 50 + 70 + 70 + 70 = 370
Median (+equation, if needed): 20 + 40 = 60
Mode: 10, 70
370 / 10 = 37
60 / 2 = 30
Range (+ formula): 70 – 10 = 60
24. Using the data table, construct a frequency table (showing the interval, tallies, and frequencies), and
then create a histogram. (Do not forget the important
2014 Temperatures in March (F)
info in the bubbles on page 872!)
35
27
23
21
19
24
2
42
20
11
23
23
35
20-29
9
46
38
38
57
48
40
30-39
5
40-49
6
30
58
41
28
28
47
50-59
2
Tally
Frequency
2014 Temperatures
in March
9
8
7
Frequency
Temp
10-19
6
5
4
3
2
1
10-19
20-29
30-39
Temperatures
40-49
50-59
25. Create box and whisker plots for the following data:
Q1=34
a. (32, 40, 51, 33, 36, 44, 47, 50, 35)
Q3=48.5
(32, 33, 35, 36, 40, 44, 47, 50, 51)
30 32 34 36 38 40 42 44 46 48 50 52
Q3=80
Q1=66
b. (78, 80, 66, 64, 82, 75, 74)
(64, 66, 74, 75, 78, 80, 82)
64 66 68 70 72 74 76 78 80 82 84 86 88
Q1=98.5
c. (95, 110, 101, 106, 117, 99, 111, 98)
95
98
101
M=103.5
Q3=110.5
(95, 98, 99, 101, 106, 110, 111, 117)
104
107
110
113
116
119