Data Displays: Histograms and Box Plots Quiz

Grade 6 · Math · Quiz

Test your skills reading and interpreting histograms and box plots.

Questions

1. In a box plot, what does the box itself represent?

   1. The middle 50% of data (Q1 to Q3)
   2. The entire range of data
   3. The mean and median
   4. The top 25% of data
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   Answer: The middle 50% of data (Q1 to Q3)

   The box spans from Q1 (25th percentile) to Q3 (75th percentile), containing the middle half of the data.

2. IQR = Q3 − ___

   Show answer

   Answer: Q1

   IQR = Q3 − Q1 — it measures the spread of the middle 50% of data.

3. A histogram and a bar graph look identical.

   Show answer

   Answer: False

   Histograms have touching bars (no gaps) for continuous data; bar graphs have gaps between bars for categorical data.

4. A box plot shows: Min=10, Q1=20, Median=30, Q3=45, Max=60. What is the IQR?

   1. 25
   2. 50
   3. 30
   4. 15
   Show answer

   Answer: 25

   IQR = Q3 − Q1 = 45 − 20 = 25.

5. In a histogram, the horizontal axis shows:

   1. Data intervals/ranges
   2. Frequency counts
   3. Individual data values
   4. The mean
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   Answer: Data intervals/ranges

   In a histogram, the x-axis shows the ranges (bins) of data values; the y-axis shows how many values fall in each range.

6. A box plot shows every individual value in the data set.

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   Answer: False

   A box plot only shows the five-number summary, not individual data points. To see every value, you'd need a dot plot or stem-and-leaf plot.

7. A histogram with most bars on the right and a long tail to the left is:

   1. Skewed left
   2. Skewed right
   3. Symmetric
   4. Uniform
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   Answer: Skewed left

   The 'skew' points toward the direction of the tail. Data bunched right + tail left = skewed left (negative skew).

8. The five-number summary value at the 50th percentile is the ___.

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   Answer: median

   The median is the middle value, dividing data into two equal halves — it's at the 50th percentile.

9. What do the whiskers of a box plot show?

   1. The minimum and maximum values
   2. The mean and mode
   3. Q1 and Q3
   4. The range of the middle 50%
   Show answer

   Answer: The minimum and maximum values

   Whiskers extend from the box to the minimum (left whisker) and maximum (right whisker).

10. If a histogram shows intervals 0-10, 10-20, 20-30 with heights 5, 12, 3, how many values fall in 10-20?

    1. 12
    2. 5
    3. 3
    4. 20
    Show answer

    Answer: 12

    The height of each bar in a histogram shows the frequency. The 10-20 bar has height 12, so 12 values are in that range.

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