Chapter 3 – Numerically Summarizing Data

1. Section 3.1 Measures of Central Tendency

pH in Water:

The acidity of alkalinity of asolution is measured using pH. A pH less than 7 is acidic; a pHgreater than 7 is alkaline. The following data represent the pH insamples of bottled water and tap water.

Tap	7.64	7.45	7.47	7.50	7.68	7.69
	7.45	7.10	7.56	7.47	7.52	7.47
Bottled	5.15	5.09	5.26	5.20	5.02	5.23
	5.28	5.26	5.13	5.26	5.21	5.24

1. Determine the mean, median and mode pH for each type ofwater.
2. Comment on the differences between the two water types.
3. Suppose the pH of 7.10 in tap water was incorrectly recorded as1.70. How does this affect the mean? The median?
4. What property of the median does this illustrate?

1. Section 3.2 Measures of Dispersion

pH in Water:

Use the same pH data table in theabove question to answer the following.

1. Which type of water has more dispersion in pH using the rangeas the measure of dispersion?
2. Which type of water has more dispersion in pH using thestandard deviation as the measure of dispersion?

1. Section 3.2 Measures of Dispersion

The Empirical Rule:

SAT Math scores have a bell-shapeddistribution with a mean of 515 and a standard deviation of114.

1. What percentage of SAT scores is between 401 and 629?
2. What percentage of SAT scores is less than 401 or greater than629?

1. Section 3.4 Measures of Position andOutliers

You Explain it – Percentiles &Quartiles:

1. The 5^thpercentile of the weight of males 36 monthsof age is 12.0 kg.
2. The 95^thpercentile of the length of newborn femalesis 53.8 cm.

One variable that is measured byonline homework systems is the amount of time a student spends onhomework for each section of the text. The following is a summaryof the number of minutes a student spends for each section of thetext for the fall 2014 semester in a college statistics class atUHWO.

Q1 =42         Q2 =51.5         Q3 =72.5

1. Provide an interpretation of these results.
2. Determine and interpret the interquartile range.
3. Suppose a student spends 2 hours doing homework for a section.Is this an outlier?
4. Do you believe that the distribution of time spend doinghomework is skewed or symmetric? Explain your answer.

1. Section 3.5 The Five Number Summary &Boxplots

Got a Headache?

The following data represent theweight in grams of a random sample of 25 Tylenol tablets.

0.608	0.601	0.606	0.602	0.611
0.608	0.610	0.610	0.607	0.600
0.608	0.608	0.605	0.609	0.605
0.610	0.607	0.611	0.608	0.610
0.612	0.598	0.600	0.605	0.603

1. Construct a boxplot.
2. Use the boxplot and quartiles to describe the shape of thedistribution.