Section 1.3

Question 1

What are the 3 measures of Central tendency?

Answer 1

Mean, Median, and Mode

Question 2

How is the mean calculated in both a set and frequency table?

Answer 2

Set: x(bar) = Ex/n Table: x(bar) = Exf/Ef Exf - sum of products of data ve (x) by their frequencies (f)

Question 3

How do you find Q1 for discrete data?

Answer 3

Divide n by 4. If whole num. - Q1 is this point and the one above e.g. if 20/4 = 5, Q1 5th & 6th ve If not whole, round up & pick this point.

Question 4

How do you find Q3 for discrete data?

Answer 4

Find 3/4 of n. Whole - halfway through this point and one above Not Whole - round up & pick this point

Question 5

What are the formulas for Q1, Q2, & Q3 in grouped continuous data?

Answer 5

Q1 = n/4 th data value Q2 = n/2 th data value Q3 = 3n/4 th data value

Question 6

What is the percentile, and how would you calculate it?

Answer 6

It is the percentage of a data set. E.g. 10th percentile of a set of 70 data values. 10% of 70 = 7 Therefore the 10th percentile is the 7th data value. (10th percentile can be written as P10) Then use interpolation

Question 7

What are the other terms used instead of ‘measures of spread’, what are their collective meaning, and how are they shown?

Answer 7

1) Measures of dispersion, measures of variation 2) It is a measure of how spread out the data is 3) Shown via range (difference largest + smallest ve in data set) - (considers all of data, but effected by extreme values) IQR, difference Q1 & Q3, IQR = Q3 - Q1 (only considers spread of 50% of data)

Question 8

How do you find the interpercentile range of given percentiles? E.g. 10th to 90th interpercentile range

Answer 8

Simply use interpolation to locate the 10th & 90th percentiles Then simply find the difference between them 90th percentile - 10th percentile = 10th to 90th interpercentile range

Question 9

What is the formula for variance and standard deviation? (discrete data)

Answer 9

V = Σx^2/n - (Σx/n)^2 Sxx/n = variance SD = √Sxx/n

Question 10

What is the formula for variance and standard deviation? (grouped data)

Answer 10

V = Σfx^2/Σf - (Σfx/Σf)^2 SD = sqrt of V f = frequency of each group Σf = total frequency

Question 11

In coding, the formula to code values commonly is: y = (x-a)/b Therefore, when this is the case, what are the formulas for the mean and standard deviation?

Answer 11

Mean: y(bar) = (x(bar) -a)/b y(bar) - mean of coded data x(bar) - mean of original data SD: σy = σx/b σy = SD of coded data σx - SD of original data Remember to rearrange if necessary in questions

Question 12

For Venn Diagrams, when wanting to find P(AnB), what is the formula to do so? (+ state what it means)

Answer 12

P(AnB) = P(A) + P(B) - P(AuB) P(AnB) = Only when A and B are both used or such P(AuB) = the sum of all sections of the Venn Diagram (excluding the outside)

Question 13

What are the formulas + written forms of mutually exclusive and independent events?

Answer 13

ME - P(AuB) = P(A) + P(B) I - P(AnB) = P(A) x P(B)

Question 14

What can a tree diagram be used to show?

Answer 14

Show the outcomes of two (or more) events happening in succession

Question 15

What is the equation for differentiation via first principles?

Answer 15

f’(x) = lim (f(x+h)-f(x))/h h -> 0 Practice on pg 261

Question 16

How can you use the derivative to determine whether a function is increasing or decreasing?

Answer 16

f(x) increasing on interval [a,b] if f’(x) > 0 for all values of x such that a

Question 17

How would you solve f(x) = 2x^3 - 3x^2 - 12x, f(x) is a decreasing function. Find the values of x and state the interval at which it is a decreasing function.

Answer 17

dy/dx = 6x^2 - 6x - 12 6x^2 - 6x - 12 < 0 6(x^2-x-2) < 0 6(x-2)(x+1) < 0 Consider 3 regions x2 = +ve So f(x) is decreasing function at -1

Question 18

What does the second order derivative represent? (f’‘(x))

Answer 18

Rate of change of the gradient function

Question 19

f’‘(x) can determine the nature of a stationary point. If a function f(x) has stationary point when x=a, what is the nature when: - f’‘(a) > 0 - f’‘(a) < 0 - f’‘(a) = 0

Answer 19

f’‘(a) > 0, point is a local minimum f’‘(a) < 0, point is a local maximum f’‘(a) = 0, point can be min, max, or point of inflection - will have to look at specific points to decide

Question 20

How would you find N in equation InN = 8.25?

Answer 20

• InN = 8.25
• N = e^8.25
• N = 3827.625821

So answer: N = 3827.625821