Data Displays - Pre Algebra

1. What does the height of a bar in a histogram represent?

   The frequency: the number of data values that fall in that interval.

2. Which display is used for categorical data: a bar graph or a histogram?

   A bar graph. A histogram is for numerical data grouped into intervals.

3. Why do the bars of a histogram touch each other?

   The intervals are adjacent ranges of one numerical scale, so there are no gaps between them (except an interval with no data).

4. Which display makes it easiest to compare the medians and IQRs of two large data sets side by side?

   Box plots drawn on the same scale.

5. A histogram has intervals 0 to 9, 10 to 19 and 20 to 29 with heights 4, 7 and 2. How many values are 10 or greater?

   9. Add the heights of the last two intervals: $7 + 2 = 9$.

6. What information is lost when data are shown only in a box plot?

   The individual data values and how many values there are, along with details such as clusters inside each quarter.

7. Which data display is built from the five-number summary?

   A box plot, which shows the minimum, first quartile, median, third quartile and maximum.

8. Which display is impractical for the test scores of 300 students: a dot plot or a histogram?

   A dot plot, because it would need 300 separate dots. A histogram summarizes the scores in intervals.

9. A dot plot has 3 dots above 4, 2 dots above 5 and 1 dot above 7. How many data values does it show?

   6. Each dot is one data value: $3 + 2 + 1 = 6$.

10. Which data display groups numerical data into equal-width intervals and uses bar heights to show counts?

    A histogram.

11. Which display lets you read each individual data value: a dot plot or a histogram?

    A dot plot. A histogram shows only how many values fall in each interval.

12. Which data display shows each value as a dot above a number line?

    A dot plot. Each dot stands for one data value.

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