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

Interpretting Data: Mean, Median, Mode, Range, & Distribution

By LORA LYONS

​M2 L1-5: 3/22

Mean Median Mode Range

​Measures of Central Tendancy:

​Mean = Average

Hint to remember:

​

That's "MEAN" to make me learn another word....it just '"means'" AVERAGE.

​*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:

​Median = Middle

Hint to remember:

​

When I was a kid, we played on the MEDIAN The median was in the MIDDLE of the neighborhood.

​​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).

​Mode = Most

Hint to remember:

​

Mode sounds like fashion...it shows up the most because it is most popular :)

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

​Range= difference between smallest and largest

Hint to remember:

​

When I think of RANGE, I think of looking out at the full "range" of a landscape from left to right (smallest to largest)

Range and Interquartile Range Formulas

Range = Maximum # - Minimum #

(Upper Extreme - Lower Extreme)

Interquartile Range (IQR) = Q3 -Q1

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

Distribution of Data

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

Normal Distribution

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

Positively Skewed

Also known as Skewed to the RIGHT.

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

Negatively Skewed

Also known as Skewed to the LEFT.

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

Uniform

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.

Random Distribution

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

Outlier - is a value that is much greater or smaller than the other values of the data set.

• 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.

Outliers

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.

Is there an outlier? If so what is it?

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

How to find Outliers using 1.5 IQR rule

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.

Comparing Functions

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

• Larger range = larger standard deviation

• Which function has the greatest standard deviation?

Quartile Examples

Interquartile Range (IQR)

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)

IQR Example