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# Center and spread | Lesson

## What are the center and spread of a data set?

A set of quantitative data with varying values may be shown as a list or a data display.
Suppose Pedro asks $7$ friends how many pairs of shoes they own. Pedro can report his findings as a list or a data display such as a dotplot where each dot represents one response.
• List: $1,2,4,4,7,8,8$
• Dotplot:
Center and spread are ways to describe data sets like this.
• Center describes a typical value of a data point. Two measures of center are mean and median.
• Spread describes the variation of the data. Two measures of spread are range and standard deviation.

### What skills are tested?

• Calculating the mean, median, and range from a list of values or a data display
• Comparing the mean, median, range, and standard deviation of data sets. You won't be tested on the formula for standard deviation.

## How is the mean calculated?

The mean is useful for describing the center of data with similar values.
The mean is the average value.

## How is the median calculated?

The median is useful to describe the center of data with
.
The median is the middle value when the data are ordered from least to greatest.
• If the number of values is odd, the median is the middle value.
• If the number of values is even, the median is the average of the two middle values.

## How is the range calculated?

Range measures the total spread of the data.
The range is the difference between the highest and lowest values.
$\text{range}=\text{highest value}-\text{lowest value}$
A larger range indicates a greater spread in the data.

## How is standard deviation used ?

Standard deviation measures the typical spread from the mean.
Standard deviation is the average distance between the mean and a data point.
Larger values of standard deviation indicate greater spread in the data.

TRY: FINDING THE MEDIAN
Station NumberGas Price (per gallon)
$1$$\mathrm{}2.56$
$2$$\mathrm{}2.42$
$3$$\mathrm{}2.65$
$4$$\mathrm{}2.48$
$5$$\mathrm{}2.99$
Tomas visited $5$ gas stations near his house. The price of gas at each station is shown in the table above. What is the median price of gas at the stations Tomas visited?

TRY: CALCULATING THE MEAN
$75,70,45,50,52,68$
A veterinary student is studying newborn giraffes. The list above shows the masses of $6$ newborn giraffes, rounded to the nearest kilogram. What is the mean mass of the newborn giraffes?
Round you answer to the nearest kilogram.
kilograms

TRY: CALCULATING THE RANGE
Tayo got the following scores on her Spanish quizzes: $88,96,94,92,98,58,90$. What is the range of Tayo's quiz scores?

TRY: FINDING THE MEDIAN USING A DATA DISPLAY
The dotplot above shows the volume of juice squeezed from $9$ oranges. What is the median volume of juice squeezed, in fluid ounces?
$\text{mean}=\frac{\text{sum of values}}{\text{number of values}}$
$\text{range}=\text{highest value}-\text{lowest value}$