Flashcards on Introduction to Statistics and Probability
Introduction to Statistics and Probability
Tap to flip · Swipe to navigate
Descriptive Statistics — Grouped Data
80 cards
Card 1
Question: What is the formula for the arithmetic mean of grouped data using class marks and frequencies?
Answer: Arithmetic mean = (Σ f x) / n where x is the class mark (midpoint), f is class frequency, and n is total observations.
Card 2
Question: How do you compute the class mark (x) for a class interval 20 ≤ x < 40?
Answer: The class mark is the midpoint: (20 + 40)/2 = 30.
Card 3
Question: Using the example table with class marks 10, 30, 50, 70, 90 and frequencies 35, 48, 67, 91, 59 (n=300), what is the arithmetic mean (show formula form
Answer: Mean = (10×35 + 30×48 + 50×67 + 70×91 + 90×59) / 300 = Σ(f x)/n.
Card 4
Question: What is the modal class for grouped data?
Answer: The modal class is the class interval with the highest frequency (the class that contains the most observations).
Card 5
Question: State the formula for the mode (Mo) for grouped data (using class boundaries and Δs).
Answer: Mo = O + [Δ1 / (Δ1 + Δ2)] × c where O = lower boundary of modal class, Δ1 = frequency_modal − frequency_previous, Δ2 = frequency_modal − frequency_nex
Card 6
Question: In the example where the modal class is 60 ≤ x < 80 with frequency 91, frequency before 67 and after 59, what are Δ1 and Δ2?
Answer: Δ1 = 91 − 67 = 24; Δ2 = 91 − 59 = 32.
Card 7
Question: Using the example values O=60, c=20, Δ1=24, Δ2=32, what is the calculated mode?
Answer: Mo = 60 + [24/(24+32)] × 20 = 60 + (24/56)×20 ≈ 57.68 (note: placement within interval gives approx. 57.68).
Card 8
Question: What is the definition of the median for a data set?
Answer: The median is the value that divides the data into a lower 50% and an upper 50% of observations.
Card 9
Question: Give the formula for the median (Me) for grouped data using cumulative frequency.
Answer: Me = O + [((n/2) − Σ< f) / f_m] × c where O = lower boundary of median class, Σ< f = cumulative frequency before median class, f_m = frequency of medi
Card 10
Question: How do you identify the median class in grouped data?
Answer: The median class is the first class whose cumulative frequency is at least n/2 (i.e., contains the position n/2).