What is standard deviation?

You need to know the Mean or Average of the data points. Standard deviation is difference between a data point and the mean.

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Center and spread | Lesson

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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.

mean = \frac{sum of values}{number of values}

A frequency table lists the values of the data vertically from least to greatest alongside the number of data points having each value.

Suppose, a teacher asked

12

students how many pets they owned and created the frequency table below.

Pets Owned	Number of Students
$0$ ‍	$4$ ‍
$1$ ‍	$3$ ‍
$2$ ‍	$3$ ‍
$3$ ‍	$2$ ‍

We can find the mean or average number of pets owned.

\begin{aligned} average & = \frac{sum of pets}{number of students} \\ = \frac{(0 \times 4 + 1 \times 3 + 2 \times 3 + 3 \times 2) pets}{12 students} \\ = \frac{15}{12} \frac{pets}{students} \\ = 1.25 pets per student \end{aligned}

The average number of pets owned is

1.25

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.

range = highest value - 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.

Your turn!

TRY: FINDING THE MEDIAN

Station Number	Gas Price (per gallon)
$1$ ‍	$$ 2.56$ ‍
$2$ ‍	$$ 2.42$ ‍
$3$ ‍	$$ 2.65$ ‍
$4$ ‍	$$ 2.48$ ‍
$5$ ‍	$$ 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?

Things to remember

Center describes a typical value.

Mean: Average value
$mean = \frac{sum of values}{number of values}$ ‍

Median: Middle value when data ordered from least to greatest

Spread describes the variation of the data.

Range: Total spread

range = highest value - lowest value

Standard deviation: Average distance between the mean and a data point

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Praxis Core Math

Course: Praxis Core Math > Unit 1