Measures Of Central Tendency Flashcards
What is a histogram?
(for me) A histogram is a graphical plot of frequency against the class boundaries of a given data set.
(For lecturer) it is a graphical representation of data using conjoined rectangles whose area is proportional to the frequency and whose width is equal to class interval.
How do you find the class boundary of a given data?
a. Subtract the upper limit of the first class from the lower limit of the second class.
b. Divide your answer in (a) by 2.
c. Subtract the answer in (b) from the lower limits of each class and add it to the upper limit of each class.
How is a frequency polygon plotted?
Frequency on the vertical axis and class boundaries on the horizontal axis (like histogram). Then find the midpoint of each rectangle and connect them.
How is the ogive/cumulative frequency curve plotted?
Cumulative frequency on the vertical (y) axis and upper class boundaries on the horizontal (x) axis.
What is the arithmetic mean of a grouped data with assumed mean given?
x̄ = a + (∑fd)/∑f
Where d = deviation from mean = x - a
a = assumed mean
x = class mark (gotten for each class by adding their limits and dividing by 2)
What is the step deviation method of deriving the mean of a data set with assumed mean given?
x̄ = a + [ C∑fu ÷ ∑f ]
C = class width
u = d/C = (x - a)/c
a = assumed mean
What is the formula for median for ungrouped data when n is odd?
(n+1/2)th value
What is the formula for median for ungrouped data when n is even?
The arithmetic mean of (n/2)th value and (n+2/2)th value.
What is the relationship between arithmetic mean, geometric mean, and harmonic mean?
AM × HM = GM²
What is the formula for harmonic mean for grouped data?
HM = Σf/[Σf(x^-1)]
What is the formula for grouped median?
Lcb + i [ (Σf/2 - Cfb) ÷ f-median ]
Where Lcb = lower class boundary of the median class. Median class is gotten by finding [(Σf +1)÷2]th value and tracing it along the Cumulative frequency.
i = class width
Cfb = cumulative frequency before the median frequency
f-median = frequency of the median class
What is the formula for mode for grouped data?
Lcb + i [(fm - fb) / 2fm - fb - fa]
fm = modal frequency
Fb = frequency before modal frequency
fa = frequency after
i = class width
How do you find the class mark of each class?
Class mark is gotten for each class by adding their limits and dividing by 2
How do you find the median class (not the exact median!) of grouped data?
[(Σf +1)÷2]th value and tracing it along the Cumulative frequency. This is then used in the formula to find the actual median.
