Transcription
In today's lesson, we're going to discuss types of data. The subject of statistics is largely about using sample data to make inferences or generalizations about an entire population. So let's start by talking about the difference between a parameter and statistics.
So a parameter is a numerical measurement describing one characteristic of a particular population. So parameter goes with population versus statistic. A statistic is a numerical measurement describing some characteristic of a sample. So statistic goes with sample, parameter with population.
Now we have quantitative versus categorical data. So quantity or quantitative, think about numerical data. Consists of numbers representing counts of measurements. So for example, the weights of supermodels or the age of respondents. So it's associated with a number versus categorical data or quality, qualitative or an attribute is data that consists of names or labels, not numbers. So for example, gender male or female of professional athletes or shirt numbers on a substitute for names on professional athletes uniforms. Those are categories.
Now specifically, quantitative or numerical data can be further broken down into two different parts, discrete and continuous types of data. So a discrete data results where the number of possible possible values is either a finite number or a countable number. For example, I can count there's one, two, three, four, or five of these. So like the number of eggs that a hen lays. Versus continuous data. This data results from infinitely many possibilities or values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps. So for example, the amount of milk that a cow produces. This could be two point two three four three one one five or what about two point three five three one one five gallons per day. It's not a continuous number. It varies every single day and there's always that infinite number goes on and on forever.
Another way to classify data is to use levels of measurement. We have nominal, order, ordinal, interval, and ratio. So nominal consists of names or labels or categories. The data cannot be arranged in any specific ordering scheme. For example, survey responses and yes and no or undecided.
Ordinal, you can guess means arranging in some sort of. Keep in mind that the difference between the data values either can't be determined or are meaningless, but they can be arranged in a specific order, such as course grades A, B, C, D, or F. There is no specific value from an A to a B to a C to a D and all that, but they are arranged in a specific order.
Now, like ordinal, interval can be arranged in order, but the difference between any two data values is meaningful. So that difference is specific and no natural zeros are a starting point. We never start at zero where none of these quantity is present. So for example, years, near the year 1000, the year 2000, 1776, or 1492. There is a specific meaningful value between the years.
And just like the last year, the ratio can be arranged in order. It can start at zero. There is a natural zero starting point and the difference in the ratios is in between two data values is meaningful. So for example, the price of college textbooks. Zero represents that there is no cost for a textbook. A hundred dollars, a textbook costs twice as much as a $50.
Which type of data is the number of pedestrians at a crosswalk? Is that something you can count? Is countable 1, 2, 3, 4, and 5? Or is it more infinite? Or is it divided into categories? Or do they have attributes? I would say that it is countable, but it is not infinite where we can get fractions of a person. So I would say is quantity, quality, quantity because only numbers that are possible here are 0, 1, 2, and so on.
In a study of ducks swimming in a local pond, it found that 18% were less than 1 year old. Is the given value a statistic or a parameter? So we're talking about ducks swimming in the local pond. That is our population, all of them. Since we're not told we're taking a sample of the ducks swimming that we're evaluating all of them and that 18% or less than a year old, we would call it a parameter because it has associated with the population, but it is a parameter that describes the population.
Now, the number of cars refueling in a particular gas station on recorded daily. Determine whether the data values are discrete, where we can count them one, two, three, four, and five, or continuous, where they may have fractions in between. I would say that there is discrete data that represents a count. A value representing a count. We'll never be 0.5 or a 3.1415 cars at the gas station, and that's what continuous would mean, is that we can have fractions or decimals of a specific item.
Now, the volume of water in a pool is found to be five thousand seven hundred and seventy seven hundred and forty one point eighty seven gallons. That I would say that can definitely fluctuate infinitely with these decimals and fractional parts of gallons. So I would call that continuous data. There's infinitely many possible values. The pool can be any amount that can hold that water.