Scatterplots/Bivariate Data
What is the x-variable referred to as in bivariate data?
Explanatory Variable
True or False: The 2 totals (both on the horizontal and vertical) on a two-way table should always be equal to each other and the sample space
True
What are the 2 variables that must be present to generate an arithmetic sequence?
A 1st Term (T1) and a Common Difference (d)
What are the 2 variables required to produce a Geometric Sequence?
A first term (T1) and a Common Ratio (r)
What is the difference between time-series data and other bivariate data?
The explanatory variable of time-series data is always time
What is the R2 value representative of (what does it mean?)?
Defines the amount of change present in the response variable that is explained by the explanatory variable
What was the sample space that produced the following 2-way table?
Pencil Pen
Junior Student 28 12
Senior Student 12 33
85
4, 13, 22, 31, 40
9
Determine the common ratio of this geometric sequence:
-81, 27, -9, 3, -1
-1/3
What is the primary difference when graphing time-series data compared to other bivariate data types?
Lines are drawn between the data points to better view trends over time
Calculate the Pearson's correlation coefficient for the following data:
[1, 23], [2, 28], [3, 30], [4, 32], [5,36], [6,40]
0.99
Create a 2-way table from the following information from a survey of 50 people over the age of 55 and 50 under the age of 55:
Of the people surveyed over 55, 43 said they preferred tea
32 of the people surveyed under 55 preferred coffee
Tea Coffee
Over 55 43 18
Under 55 7 32
Given that T3=8, T4=5, T5=2, create the rule that will generate this arithmetic sequence
Tn = t1+(n-1)*-3
Given that T3=112, T4=448, T5=1792, determine the rule that will generate this geometric sequence
Tn = t1*4n-1
The number of houses sold in an area over a year are tracked (in order of month):
25, 24, 20, 19, 17, 15, 12, 13, 14, 18, 22, 25
Plot this data on a time series graph.
Either month or 1-12 on x-axis, 0-25/30 or 10-25/30 on the y-axis, seasonal variation peaking during the summer months
Given that:
y-mean = 31.5, x-mean = 3.5, y-SD = 5.47, x-SD = 1.71, r = 0.99
Calculate the regression line equation for data.
y=3.17x + 20.4
Complete the following 2-way table and calculate the probability that a crocodile over 3m long is older than 15.
<3m >3m Total
<15yrs 13
>15yrs 22
Totals 16 43
<3m >3m Total
<15yrs 13 8 21
>15yrs 3 19 22
Totals 16 27 43
P = 70.4%
Given that t2 = 8 and d = -2, determine the 32nd term of this sequence
-52
Given that t2 = 6 and r = -2, calculate the 13th term of this sequence
12 288
Calculate a 4-Point moving average for the following data set:
9, 12, 13, 15, 19, 23, 25, 26
[13, 13.5], [15, 16.125], [19, 19], [23, 21.875]
Calculate the residuals for the following data set:
[0, 50], [1,32], [2,24], [3,19], [4,16]
[0, 5.6], [1, -4.3], [2, -4.2], [3, -1.1], [4, 4]
A survey is completed where 80 people (40 male and 40 female) are surveyed about their preference of car brand. The following probabilities are obtained from the survey:
35% of males preferred Nissan, 40% of females preferred Toyota, 12.5% of females preferred Ford and half of all respondents said they preferred Toyota in total.
Create a two-way table based on this information.
Toyota Nissan Ford Total
M 24 14 2 40
F 16 19 5 40
Total 40 23 7 80
Given that t4 = -11 and t9 = 4, calculate the 45th term of this arithmetic sequence
112
Given that t5 = 112 and t8 = -896, calculate the 15th term of this geometric sequence
-114 688
Seasonally adjust/deseasonalise the following data:
Quarter/Year 2022 2023 2024
1 23 21 20
2 26 27 28
3 30 31 31
4 25 24 26
Quarter/Year 2022 2023 2024
1 28.05 25.6 24.39
2 24.76 25.71 26.67
3 25.42 26.67 26.67
4 26.04 25 27.08