Math 1: Notes 2.1 Definitions and Mean. Two Uses of Statistics:  To organize, summarize, and present data analysis)  To generalize from knowledge of.

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Presentation transcript:

Math 1: Notes 2.1 Definitions and Mean

Two Uses of Statistics:  To organize, summarize, and present data analysis)  To generalize from knowledge of sample data to knowledge of the population

Definitions:  Data: number or value with context collection of information in context.  Population: entire collection of items (objects or people) that we are studying about about.  Sample: part of the population selected to obtain information about the population  Individual: object or person included in the study  Variable: characteristic of the individual to be measured or observed

Mean:  - measure of central tendency also known as average  - add up all the numbers then divide by how many numbers there are

Ex 1: Finding the mean  In January of 2006, your family moved to a tropical climate. For the year that followed, you recorded the number of rainy days that occurred each month. Your data contained 14, 14, 10, 12, 11, 13, 11, 11, 14, 10, 13, 8.  Find the mean of the data set.  From the original data set, how does the mean change if you add a month with 1 rainy day?

Ex 1: Finding the mean c)From the original data set, how does the mean change if you add a month with 25 rainy days? d)A new month was added to the original set of data and now the mean is rainy days. How many rainy days were in the new month?

1) Find the following: a) the total number of students b) the total number of movies watched c) the mean number of movies watched d) A new student joins the group and the mean remains the same. How many movies did the new student watch?

2)A new value is added for Carlos, who was home last month with a broken leg. He watched 57 movies. a) What is the mean of the data now? b) Compare the mean from question 1 to the new mean. What do you notice? Explain.  Does this mean accurately describe the data? Explain.

3) Data for eight more students are added to the 12 values. a) What is the mean of the data now? b)How did this new data change your mean?

Five Number Summary and IQR

The five-number summary of a set of observations on a single variable consists of the following:  Maximum (max) – the largest observation  Upper Quartile (Q3) – a value that separates the largest 25% of the observation from the smallest 75%

 Median (M) – a value that separates the largest 50% of the observations from the smallest 50% - It is the middle value of the observations when arranged in order.  Lower Quartile (Q1) – a value that separates the largest 75% of the observations from the smallest 25%  Minimum (min) – the smallest observation  Interquartile Range (IQR) = Q3 – Q1

Reminder: Arrange your data set in ascending order first. 1)Lisa works in a computer store. Her computer sales for the past 9 months are: 27, 39, 13, 15, 23, 37, 29, 54, 35 Find the 5-number summary and IQR of this set of data.

Reminder: Arrange your data set in ascending order first. 2)Hannah has worked for the florist for 12 months. She has sold the following number of bouquets: 6, 14, 8, 12, 6, 5, 3, 5, 7, 9, 11, 13 Find the 5-number summary and IQR of this set of data.