The difference between the smallest value and the largest value in a dataset.

Pandas is a special tool that allows us to perform complex manipulations of data effectively and efficiently. Inside pandas, we mostly deal with a dataset in the form of DataFrame. DataFrames are 2-dimensional data structures in pandas. DataFrames consist of rows, columns, and data.

Finding the difference between largest and smallest value within group

We are given a DataFrame with two columns, group and value, we need to find the max value of the group and the min value of the group and compute the difference between these two.

The Max value is the largest of all the values and the min value is the smallest of all the values in a column. We will store this difference in a new column called the difference.

Mean, Median, Mode, and Range

Three types of averages can be used to describe a data set.

Averages

• The mean of a data set is the sum of the values divided by the number of values.

• The median of a data set is the middle value when the values are written in numerical order. If a data set has an even number of values, the median is the mean of the two middle values.

• The mode of a data set is the value that occurs most often. A data set can have no mode, one mode, or more than one mode.
• The range of a data set is the difference between the largest and smallest values in the set.

Math In Real Life 

Example

A marine biologist records the locations of deep sea jellies in relation to the ocean surface. Jellies are found at -2,278 feet, -1,875 feet, -3,210 feet, -2,755 feet, -2,407 feet, and -2,901 feet.

What is the average location of a deep sea jelly?

Find the Mean

The mean location in relation to the ocean surface is -2571 ft.

Guided Practice (Ask your tutor for help.) 

1) Find the mean of the data. 

Finding Median, Mode, and Range

Find the median, mode(s), and range of the movie prices below.

$7.20, $13.25, $14.94, $16.56, $18.74, $19.99, $19.99, $29.49

Median

The data set has an even number of prices, so the median is the mean of the two middle values, $16.56 and $18.74. 

Mode

The price that occurs most often is $19.99. This is the mode. 

Range

The range of a data set is the difference of the greatest value and the least value.

Range = $29.49-$7.20=$22.29

Choosing a Representative Average

Groups A and B try a new ice cream flavor and rate it on a scale of 1 to 10 as shown. Which average best represents each group? 

Solution 

The mean, median, and mode are very close. So each average is a fair representation of the ratings as a group. 

The mean is higher than all but 3 ratings. The mode is equal to the lowest rating. So, mean and mode are not good choices. The median best represents the ratings.

The Range
The range is the difference between the largest value and the smallest value. It gives us an indication of how big the span of the data is.
The range of a data set is the difference between the maximum and minimum values in the set.
The most straightforward measure of dispersion is the range. The range simply tells us how far apart the largest and smallest values in a data set are. The range is very sensitive to outliers.

The Range is a Measure of Spread, and tells you… well, how spread out the data is!
How to work out the Range:
1. Subtract the smallest data value away from the biggest data value!

Worked example: Range
QUESTION
Find the range of the following data set:

Step 2: Remove the first value
If the first value, 1, were to be removed from the set, the minimum value would be 4. This means that the range would change to 10-4=6. 1 is not typical of the other values. It is an outlier and has a big influence on the range.

2. A group of 10 learners count the number of playing cards they each have. This is the data they collect:

3. Find the range of the data set

4. A group of 20 learners count the number of marbles they each have. This is the data they collect:

Next we find the minimum value in the data set:

5. A group of 15 learners count the number of sweets they each have. This is the data they collect:

RELATED POSTs

Arithmetic Mean for Ungrouped Data – Statistics

Arithmetic Mean for Frequency Distribution – Statistics

The Mean of Continuous or Discrete Distribution (Grouped Data)

Examples of The Median for Ungrouped Data

Cumulative Frequency Tables and Graphs (Ogives) (10 Examples)

Quartiles and the Interquartile Range for Ungrouped Data

Explaining Quartiles with Percentiles

The Mode of Ungrouped Data

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