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Statistics: Random Samples & Comparing Data Sets
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What you will learn from this videoWhat you will learn
- We will learn what a statistical question is.
- We’ll also learn how to answer them by collecting random samples and analyzing data.
- And we'll see how this knowledge can help us plan events, learn about animals, and even make water rockets!
- Discussion Questions
Before Video
What is categorical data?ANSWERCategorical data sorts objects based on a qualitative attribute that can be described using distinct categories, like color, tree type, or drink sizes.
A frequency is the number of times something happens. In data, a frequency is the number of individuals or objects that fit in a particular category or that produce measurements within a bin interval.
I use data collection to answer questions. Particularly if the answer could be different for different individuals or objects. I can collect data to get information about a population.
Continuous data is quantitative, and it is measured using a tool that allows for a continuous set of possible measurements, like length, mass, or volume.
Data can be difficult to visualize and compare when it is written in a table. By making graphs, I can communicate a lot of intuitive information about the data easily and quickly.
After Video
What is a population?ANSWERA population is the group of individuals I am interested in. Populations can be people, pets, animals, plants, objects, etc. Populations need to be well defined, for example, if I am interested in studying middle school students in Arizona, I need to be specific. Just saying “people” implies everyone in the world, “people from Arizona” implies all Arizonans, while “people who are students in an Arizona middle school” adequately describes the population.
A sample is a subset of the population that a researcher selects to study. A sample should be representative of the population of interest, so if I am interested in “people who are students in a Michigan middle school,” I wouldn’t sample middle school students from outside Michigan, or sample elementary or high school students. Samples are important because they give information about the population without having to measure every member of the population. Sampling saves time and money.
A sampling method is the procedure I use to select a sample. There are many sampling methods, but the most important thing is to choose a sample that is likely to be representative of the population. Random sampling and a large enough sample size are the best ways to ensure a representative sample.
If a sample is different from the population, it is biased. Biased sampling means I can’t interpret the data properly or make conclusions about the population based on the results of the sample. I take samples so I can infer things about the population, but if the sampling method I choose doesn’t give a representative sample, then I can’t make inferences from that. Convenience sampling and low sample size can introduce bias to a sample.
A statistical question is one where the answer is uncertain, or where the answer may vary between individuals. For example, “how tall are Oklahoma middle school students?” is a statistical question because the height of a student changes from student to student. I can answer this question by taking a random sample of Oklahoma middle school students and measuring their heights. I can then use a histogram or line graph to summarize and display that data.
- Vocabulary
- Statistical question DEFINE
A question where the answer varies, so we need to collect data to find the answer.
- Population DEFINE
The entire group we want to study; this could be all lizards on an island, all students in a school, all trees in a forest, etc.
- Sample DEFINE
A subset of the population selected to be measured.
- Random sample DEFINE
A sample where every individual in the sample is selected at random from the population.
- Sample size DEFINE
The number of observations/individuals in the sample. Larger sample sizes make better data.
- Data DEFINE
The values generated when someone takes measurements for a group of objects or individuals; usually, the group is a sample.
- Bias DEFINE
A characteristic of bad samples where the sample is very different from the population. For example, a sample meant to represent all students at the school is biased if the only students sampled are on the soccer team because the soccer team does not accurately reflect all students in the school.
- Mean DEFINE
The average observation in a data set, calculated by adding together all the observations and dividing the sum by the number of observations in the data set.
- Median DEFINE
The middle value in the data set when the observations are sorted from smallest to largest.
- Mode DEFINE
The most frequent observation in a dataset.
- Range DEFINE
The spread of the data, calculated by identifying the smallest and largest observations in the data set, and taking their difference.
- Histogram DEFINE
A graphical display of data where the bar height reflects the count or frequency of observations within the interval (bin) or set of values the bar represents.
- Statistical question DEFINE
- Reading Material
- Practice Word Problems
- Practice Number Problems
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