In a golf tournament, the top 6 men’s and women’s scores are given. Calculate the mean, median, mode, range, and IQR for each data set.

Warm-Up 04/18/23

In a golf tournament, the top 6 men’s and women’s scores are given. Compare the spread of the data using the mean and a box and whisker graph.

Unit 4: Describing Data

Box PlotA plot showing the minimum, maximum, first

quartile, median, and third quartile of a data set; the middle 50% of the data is indicated by a box.

Example:

Box Plot: Pros and Cons

Advantages:

•Shows 5-point summary and outliers

•Easily compares two or more data sets

•Handles extremely large data sets easily

Disadvantages:

•Not as visually appealing as other graphs

•Exact values not retained

Dot PlotA frequency plot that shows the

number of times a response occurred in a data set, where each data value is represented by a dot.

Example:

Dot Plot: Pros and Cons

Advantages:

•Simple to make

•Shows each individual data point

Disadvantages:

•Can be time consuming with lots of data points to make

•Have to count to get exact total. Fractions of units are hard to display.

HistogramA frequency plot that shows the

number of times a response or range of responses occurred in a data set.

Example:

Histogram: Pros and Cons

Advantages:

•Visually strong

•Good for determining the shape of the data

Disadvantages:

•Cannot read exact values because data is grouped into categories

•More difficult to compare two data sets

Measures of Central Tendency

(center)

Measures of Spread

•Mean - average•Median - middle

•Mean Absolute Deviation (MAD)

•Range - difference•Interquartile Range

(IQR)

Steps to follow when comparing summary statistics.

1. Arrange the data set(s) in order from least to greatest.

2. Calculate: crunch the numbers

Mean: average or x-bar

Median: When the data points are organized from least to greatest, the median is the middle number. If there is an even number of data points, the median is the average of the two middle numbers.

Mode: Find the number that repeats itself the most. It is possible to have more than one mode

Interquartile range: (Q3 – Q1) First, find the Quartiles: Q1 is the first quartile

(or 25th percentile). Find the median of the bottom half of numbers. Q3 is the third quartile (or 75th percentile). Find the median of the top half of the numbers. Subtract!

Mean Absolute Deviation: on average, how does the data set differ from the mean.

N

Xx

n

ii

1

N

XX i

Outlier A data value that is much greater than or much

less than the rest of the data in a data set; mathematically, any data less than

or greater than is an outlier

Example:

)(5.11 IQRQ

)(5.13 IQRQ

Finding the quartiles and inter-quartile range.

7, 5, 2, 7, 6, 12, 10, 4, 8, 9

2, 4, 5, 6, 7, 7, 8, 9, 10, 12

Order the data

Inter- Quartile Range = 9 - 5 = 4

Example 1: Find the quartiles for the data below.

Lower Quartile =

5

Q1

Upper Quartile =

9

Q3

Median = 7

Q2

Are there any outliers?

Steps to follow when comparing summary statistics.

1. Arrange the data set(s) in order from least to greatest.

2. Calculate: crunch the numbers

3. Graph (box and whisker plot)

To create a box & whisker plot, use a 5 number summary:

– The minimum value

– Q1

– Median

– Q3

– The maximum value

The numbers below represent the number of homeruns hit by players of the McEachern baseball team.

2, 3, 5, 7, 8, 10, 14, 18, 19, 21, 25, 28

Q1 = 6 Q3 = 20

Interquartile Range: 20 – 6 = 14

12 206

On the calculator (Graphers only)

• STAT• “1:Edit…” ENTER• Clear L1 if necessary, then enter your data• STAT• Over one to CALC• “1:1-Var Stats” ENTER • Now you need to tell it to use L1 (2nd 1) ENTER• TADA

Steps to follow when comparing summary statistics.

1. Arrange the data set(s) in order from least to greatest.

2. Calculate: crunch the numbers

3. Graph (box and whisker plot)

4. Comment - Look at the crunched numbers and the graph, in what ways are these data sets similar or different?

= difference

The deviation from the mean is the difference of a data value and the mean of

a data set.

Mean: 70.5

Mean: 74

Find the mean absolute deviation of the data. (Round to the nearest tenth if necessary)

1. 10, 7, 13, 10, 8

2. 87, 75, 85, 77, 74, 82

Complete the back of the MAD worksheet

Worksheet (front and back!)