Summaries and Histograms

Preparation:

Retrieve the Singers data set.

• Singers.dsk: Singers

Read the Reference file in the data and then inspect the four DataDesk variables Soprano, Alto, Tenor and Bass contined within the Icon Heights.

Problem 1:

Make a histogram ‡ for the Alto variable. ( Plot → Histograms ). Estimate the median height of the altos graphically from the histogram. Mark your estimate on the histogram. Describe how you made this estimate. Is the distribution skewed to the right or left?

Problem 2:

Collect the statistics ‡ to fill in the following table. Use Calc → Calculation Options → Select Summary Statistics to customize which values will appear and then Calc → Summary → Reports to actually see the values.

Problem 3:

Plot ‡ the box plots side by side for the four groups. To get your box plots, append the data for each singing part as described below, select the Heights there as y, the Part as x and then Plot → boxplot y by x

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Note: Create an Append relation by selecting all four icons in the Heights folder at once followed by Manip → Append and Make Group Variable. A new window opens with the icons data and group. rename these to heights and Parts. The boxplot can then be made with Heights selected as y and Parts as x.

Note: You don't need to do it on this problem, but you could also generate these boxplots individually by selecting one of the variables inside Heights (e.g. Soprano) and then choosing Plot → Boxplot Side by Side. However, you cannot use this command after selecting all four variables because the variables have different numbers of cases. That's why we used the approach above using an Append relation with Plot → boxplot y by x.

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Problem 4:

1. Classify these four groups of singers into two pairs so that within each pair the mean heights are similar. Would your conclusion be different if you were to use the median instead of the mean?
2. Using the standard deviation, compare the spreads of the four groups. Now use the interquartile ranges to compare the spreads. Explain whether or not these two approaches on spreads are consistent.
3. Hypothesize about why the 4 groups of singers break up into two pairs as you noted in part (a). Hint: Read the Reference File again.

Note: Your textbook has further discussion of boxplots, medians and quartiles.

To Turn In:

• Please print out results marked with ‡.
• Turn in your work in lab next week.