Measures of Central Tendency and Variablility - guided notes (2021) PDF

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Accelerated Pre-Calculus Statis Statistics tics Unit: Lesson 1: Measures of Central Tend Tendency ency and Variability I.

Measures of Central Te Tendency: ndency:

Mean:

Median:

Mode:

Ex 1: Find the mean, median, and mode of each data set: a) {2, 3, 5, 2, 1, 3, 5, 2, 4, 3} Mean: ____________

Median: _____________

Mode: ______________

b) {2, 3, 5, 2, 1, 3, 5, 2, 4, 3, 36}

Mean: ____________

II.

Median: _____________

Mode: ______________

Which measur measuree is better?

In a perfect world, our data would fit a ______________________. This is when the mean, median, and mode are ______________________________________.

Examples of normally distributed data:

Ex 2: The data below shows the annual salaries of staff members at a local paint store. Find the mean and median of the data.

Mean: ______________

Median: ____________

Which best represents the data? Why??

III.

Skewed Data

We use _____________________ when the data is __________________. This would happen when there are _____________________ in the data.

Two types:

Ex 3: Determine if each scenario would provide data that is negatively or positively skewed. a) Age of retirement b) Difficult tests c) Neighborhood housing prices

IV.

What about Mode?? Mean: _________

Ex 4: Median: ______________

Mode: _____________

Which BEST represents the data?

When is mode best used to describe data?

VI. Measures of Variability Variance:

Standard Deviation:

The ______________ the standard deviation, the ________________ the data is to the mean. There is very little spread. The ______________ the standard deviation, the ________________the data is to the mean. There is a lot of spread.

Ex 5: Find the variance and standard deviation of the data set: 2, 4, 6, 8, 10 1) Find the mean of the data.

2) Find the difference of each value of the mean and square the differences.

3) Take the mean of all these values. This is the variance.

4) Take the square root. This is the standard deviation.

Ex 6: Use your calculator to find the mean, median and standard deviation(s) of the data set: (Round to the nearest hundredth) {54, 51, 56, 54, 58, 54, 59, 53, 57, 55, 53, 52, 66, 57}

Ex 6: Two students are trying out for a spot on the math team. As part of the application process they must turn in their test scores from math class. Use the following data, who would you choose to be on the team? Explain your answer. Student A B

Test Average

Test Standard Deviation...