Central Tendency
The data below represents the number of darts each competitor in a dart competition had to throw before getting a bull's eye.
number of darts | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
frequency | 1 | 3 | 5 | 7 | 6 | 4 | 5 | 5 | 3
Determine the mean, median, and mode.
mean: 5,28 darts
median: 5 darts
mode: 4 darts
The following data set represents the distance in kilometers of the races that Tannie Sarah has run while in South Africa over the last six months.
21, 21, 21, 56, 33, 32, 87.7
Determine the five number summary of the data.
21kms, 21kms, 32kms, 56kms, 87,7kms
A group of people was asked how far they have to travel to work each day. The following table summarizes this data:
distance d (km)| frequency
0≤d<5 | 5
5≤d<10 | 41
10≤d<15 | 77
15≤d<20 | 58
To draw a frequency polygon, which points would you draw? (Make sure to include where it meets the x-axis!)
(-2,5;0),(2,5;5), (7,5;41),(12,5;77),(17,5;58),(22,5;0)
The data below represents the number of marks that a
student scored on 5 100-mark tests last school year.
Test # | 1 | 2 | 3 | 4 | 5
Mark | 23 | 52 | 57 | 68 | 75
Determine the standard deviation of this data set
17,92 marks
2.1 on page 76
3009,26 grams
The data below represents the number of marks that a
student scored on 9 100-mark tests last school year.
Test # | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
Mark | 23 | 52 | 57 | 68 | 75 | 75 | x | 83 | 86
If the learner's average test score was 67 marks, determine x.
84 marks
The data below represents the number of darts each competitor in a dart competition had to throw before getting a bull's eye.
number of darts | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
frequency | 1 | 3 | 5 | 8 | 6 | 4 | 5 | 12 | 3
Determine the 5 number summary of the data
min:1 dart
Q1: 4 darts
Q2: 6 darts
Q3: 8 darts
max: 9 darts
A group of people was asked how far they have to travel to work each day. The following table summarizes this data:
distance d (km)| frequency
5≤d<10 | 41
10≤d<15 | 77
15≤d<20 | 58
20≤d<25 | 39
To draw an ogive, which points would you draw?
The following data set represents the distance in kilometers of the races that Tannie Sarah has run while in South Africa over the last six months. It has standard deviation 23,04kms.
21 21 56 33 32 21 87.7
What percentage of the data values lie within one standard deviation of the mean?
85,71%
2.1.1, 2.1.2 on page 72
2.1.1 50 players
2.1.2 30 players
The data below represents the number of marks that a
learner scored on 9 100-mark tests at SPU last school year.
Test # | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
Mark | 86 | 52 | 57 | 68 | 75 | 75 | 84 | 83 | 23
Any mark 75 and above is considered a distinction.
What percentage of the learner's tests earned a distinction?
55,56%
A data set of 21 data values has five number summary:
3,15,17,21,27
If none of the data values are repeated, how many data values are greater than 17?
10 data values
A group of people was asked how far they have to travel to work each day. The following table summarizes this data:
distance d (km)| cumulative frequency
0≤d<5 | 5
5≤d<10 | 41
10≤d<15 | 78
15≤d<20 | 158
To draw a frequency polygon, which points would you draw?
(-2,5;0), (2,5;5), (7,5;36), (12,5;37), (17,5;80),(22,5;0)
The following data set represents the distance in kilometers of the races that Tannie Sarah has run while in South Africa over the last six months. It has standard deviation 23,04kms.
21 21 56 33 32 21 87,7
The last data value (87,7kms) represents the Comrades marathon. How many standard deviations away from the mean is the Comrades marathon?
3 standard deviations
2.1.4 on page 72: what points would you draw? (note: need 2.1.3)
(12,5;0),(17,5;4),(22,5;9),(27,5;24),(32,5;10),(37,5;3),(42,5;0)
The time it takes for a class of grade 10 learners to run a 5k is given below
time (minutes) | 18≤x<23 | 23≤x<28 | 28≤x<33 |
frequency (f) | x | 11 | 16
If the estimated mean time for these learners to run 5k is 27,44 minutes, determine x.
x=4 learners
question 2.2 on page 73 in gift
No:
(1) range of class A is bigger than range of class B so there is a bigger spread of data.
(2) at least 25% of class A have lower marks than any learner in class B.
(3) Class A performed worse at the bottom end.
see question 1 in notes
64% (estimate)
The following data set represents the ages of learners at a sports camp. It has standard deviation 1,36years.
Age(years) | 13 | 14 | 15 | 16 | 17 | 18
Frequency (f)| 2 | 7 | 9 | 8 | 7 | 3
How many of the data values are within one standard deviation of the mean?
17 data values
2.3 on Page 76
15 participants
Four learners ages were recorded in years. The ages were a,b,c,d. You can't remember the data values but you do remember the following:
a>b>c and c=d.
The mode of the data set is 17
The range of the data set is 4
The data set has mean 15,75
Determine a,b,c,d.
a=13 years
b=16 years
c=17 years
d=17 years
The following letters represent values in a data set:
a b c d e f g
This data set has the following properties:
a<b<c<d<e<f<g
the maximum value is 42
the range is 35 and the interquartile range is 22
the median is 23 and the mean is 25
Q3-Q2=14
e=2c
Determine the values of a,b,c,d,e,f,g
a=7,b=15,c=17,d=23,e=34,f=37,g=42
see question 2 in notes
about 58 marks
A data set has 5 number summary:
32, 56, 62, 65, 69
The same data set has mean 59, mode 60, and standard deviation 8.5
Within how many standard deviations from the mean is the maximum value?
2 standard deviations
This is a 2-part question (page 75).
Part 1: tell Tannie Sarah the points you would plot in order to draw the ogive.
Part 2: answer questions 2.3 and 2.4
Part 1: (95;0), (105;15),(115;42),(125;85),(135;137),(145;165),(155;186),(165;196),(175;200)
Part 2: 2.3 119 minutes (est)
2.4 50 learners (est)