3/22 Interpreting Data: Mean, Median, Mode, Range & Distribution

​Measures of Central Tendancy:

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​*we use averages/means to calculate your grades....add them and divide by the total number

​Let's calculate the Mean from the data

set given in the table:

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​​Let's find the Median from the data

set given in the table:

​What happens if there are 2 values in the middle? Just take their average (example next slide).

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​Let's find the MODE from the data set:

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Range = Maximum # - Minimum #

(Upper Extreme - Lower Extreme)

Interquartile Range (IQR) = Q3 -Q1

Let's practice finding the RANGE from the data set:

We can use the shape of a graph to determine how the data is distributed.

Also known as symmetric or bell shaped. This is when the graph is split in half and both sides look identical.

Also known as Skewed to the RIGHT.

This is when the data has a "Tail" on the right side of the graph.

Also known as Skewed to the LEFT.

This is when the graph has a "Tail" to the left.

This is when the graph looks the same and the data is evenly spread out. There are no high peaks and it will make a somewhat rectangular shape.

A random distribution has bars that are all sorts of different heights.

• Like one person doing super bad in the class.

• Or like only one person got an A while everyone else got a C or below.

• Outliers affect the mean by a lot.

An outlier is a number in a data set that is very different from the rest of the numbers.

It can have a MAJOR effect on the mean.

92, 88, 96, 86, 89, 90, 95, 97, 42, 83

• 42 is the outlier

• everyone got a A B except that 42

• so everyone did well except that one person

Step 1: IQR X 1.5

Step 2: Q1 - (IQR X 1.5)

Step 3: Q3 + (IQR X 1.5)

Any number in the data set that is below or above these numbers are outliers.

• Middle = Median; which function has a larger median?

• Larger range = larger standard deviation

• Which function has the greatest standard deviation?

Middle 50% of values when ordered from lowest to highest

​To calculate it:

1. Put the numbers in order from least to greatest.

2. Find the median.

3. Find the median of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3).

4. Find the difference between Q3 and Q1. (IQR = Q3 – Q1)