6.4 - Summary Statistics

6.4 - Summary Statistics

Unit 6 - Statistics

Math I Honors

Mr. Coleman

Learning Objectives

• Identify key summary statistics with respect to shape, center, and spread

• Understand how to choose the appropriate summary statistics

• Compute summary statistics using technology

• Analyze datasets and draw conclusions based on summary statistics

How Shape Affects Your Summary Stats

Symmetric data sets are best described by MEAN and STANDARD DEVIATION.

Skewed datasets are best described by MEDIAN and INTERQUARTILE RANGE.

Mean and Standard Deviation

• Mean = average across all data points

• Standard Deviation = a measure of the "average" spread of data points around the mean (formula is complex, we'll let tech do the work)

• Higher SD = more spread; lower SD = less spread

Symmetric Distributions and the 67/95/99% Rule

• 68% of data is within ONE standard deviation of the mean (in each direction)

• 95% of data is within TWO standard deviations

• 99% of data within THREE standard deviations

EXAMPLE

The symmetric distribution of pizza delivery times shown has a mean of 30 min with a standard deviation of 5 minutes. So this means:

68% of customers got their pizza within 25 to 35 minutes

95% of customers got their pizza within 20 to 40 minutes

99.7% (almost all) customers got their pizza within 15 to 45 minutes

Multiple Choice

All of the below sets have the same mean.
Set 1-Standard Deviation=3.1
Set 2-Standard Deviation=4.9
Set 3-Standard Deviation=1.7
Set 4-Standard Deviation=3.2
Which set of data probably has the points closest to the mean?

• 1
• 2
• 3
• 4

Multiple Choice

A test has a mean of 40 and a standard deviation of 10. What is the percent of people that scored between 30 and 40?

• 68%

• 34%

• 13.6%

• 100%

Multiple Choice

What percentage of scores falls within 3 standard deviations of the mean?

• 68%

• 34%

• 99.7%

• 95%

Calculating Summary Stats in Desmos

Time for a quick demo!

Multiple Choice

Find the Inter-Quartile Range (IQR). You may use your graphing calculator.

• 7609

• 8924.5

• 2708

• 5416

Multiple Choice

Calculate the MEAN for the data set: 6, 7, 12, 8, 7, 4, 8, 8, 7

• 7

• 7.44

• 8

• 7 and 8

Multiple Choice

What is the standard deviation for the data given:

5, 10, 7, 12, 0, 20, 15, 22, 8, 2

• 6.89

• 10.1

• 7.26

• 9

Analyzing Datasets with Summary Stats

Using what you know about stats to draw conclusions

Multiple Choice

The term "snowstorms of note" applies to all snowfalls over 6 inches. The snowfall amounts for

snowstorms of note in Utica, New York, over a four-year period are as follows: 7.1, 9.2, 8.0, 6.1,

14.4, 8.5, 6.1, 6.8, 7.7, 21.5, 6.7, 9.0, 8.4, 7.0, 11.5, 14.1, 9.5, 8.6

What are the mean and population standard deviation for these data, to the nearest hundredth?

• mean = 9.46; standard deviation = 3.74

• mean = 9.46; standard deviation = 3.85

• mean = 9.45; standard deviation = 3.74

• mean = 9.45; standard deviation = 3.85

Multiple Choice

Jean's scores on all five mathematics tests were 98, 97, 99, 98, and 96. Her scores on all five English tests were 78, 84, 95, 72, and 79. Which statement is true about the standard deviations for these scores?

• More information is needed to determine the relationship between the standard deviations.

• The standard deviations for both sets of scores are equal.

• The standard deviation for the English scores is greater than the standard deviation for the math scores.

• The standard deviation for the math scores is greater than the standard deviation for the English scores.

Multiple Choice

1. Javier’s score on a history test is equal to the upper quartile value of all the scores on the test. Based on this information, which statement about Javier’s score is most likely to be true?

• Javier’s score is 75.

• Javier’s score is the same as 75% of all the scores.

• Javier’s score is greater than 75 other scores.

• Javier’s score is greater than 75% of all the scores.

Multiple Choice

A marketing firm obtained random samples of 20 people in five regions of the country to investigate the level of interest in a new product. People in the sample were asked to rate their level of interest on a scale from 1 to 10, with 1 being the least amount of interest and 10 being the greatest. The histograms show the results for each region. The graph for which region displays data for level of interest with the least standard deviation?