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6th Grade · 6.SP.B.4

Box plots in 6th grade

Box plots are one of three graphs that 6th graders use to show a list of numbers on a number line. The other two are dot plots and histograms. Your child learns to draw all three from a set of data and to read what each one shows.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

What it means, in plain words

All three graphs sit on a number line, so the distance between numbers matters. A dot plot puts one dot above the number line for each value. If three children in a group are 11 years old, three dots stack above 11. Dot plots show every value, so they work well for small sets of data.

Histograms group the values into equal intervals, such as 0 to 9, 10 to 19 and 20 to 29. The height of each bar shows how many values fall in that interval. The bars touch, because the intervals sit next to each other on the number line. A histogram suits a large set of data, but it hides the exact values.

Box plots are built from five numbers: the smallest value, the lower quartile, the median, the upper quartile and the largest value. The median is the middle value. The quartiles are the middle values of the lower half and of the upper half. The box runs from one quartile to the other, so it holds the middle half of the data. A line inside the box marks the median, and lines called whiskers reach out to the smallest and largest values.

Your child should be able to:

  • Draw a dot plot with one dot for each value
  • Group data into equal intervals and draw a histogram
  • Find the five numbers a box plot needs and draw the box plot
  • Say what each graph shows and what it hides

Example

Nine students did as many sit-ups as they could in one minute: 18, 22, 26, 28, 30, 31, 33, 37 and 41. Draw a box plot.

  1. The values are already in order. The smallest is 18 and the largest is 41.
  2. The median is the fifth of the nine values, 30.
  3. The lower half is 18, 22, 26 and 28. Its middle is halfway between 22 and 26, so the lower quartile is 24.
  4. The upper half is 31, 33, 37 and 41. Its middle is halfway between 33 and 37, so the upper quartile is 35.
  5. Draw a box from 24 to 35 with a line at 30, and whiskers out to 18 and 41. The middle half of the students did between 24 and 35 sit-ups.

Example

Eight dogs at a shelter are 1, 2, 2, 3, 3, 3, 5 and 8 years old. Draw a dot plot.

  1. Draw a number line from 0 to 8 and mark every whole number, including 4, 6 and 7.
  2. Put one dot above 1, two dots above 2, three dots above 3, one dot above 5 and one dot above 8.
  3. Count the dots: 1+2+3+1+1=81 + 2 + 3 + 1 + 1 = 8, one for each dog. The dot plot shows that most of the dogs are 3 or younger and one dog is much older.

Where children usually get stuck

  • Your child draws a separate bar for every value in the list, like a bar graph, instead of grouping the values into intervals.

    Bar graphs from earlier grades give each category its own bar. In a histogram, one bar counts every value that lands in its interval.

    What helps. Write the intervals in a column first. Have your child make a tally mark next to the right interval for each value, then draw one bar per interval.

  • Your child says the long whisker of a box plot holds more data than the short one.

    In most graphs, bigger means more. In a box plot, each whisker and each half of the box holds about a quarter of the values. A long part only means those values are spread far apart.

    What helps. Take a list of 8 numbers, draw its box plot and mark where each value falls. There are 2 values in each part, whether the part is long or short.

  • Your child's dot plot labels only the values in the data, such as 2, 5 and 9, with equal gaps between them.

    Your child treats the line as a row of labels, not a number line. On a number line, the gap from 2 to 5 must be shorter than the gap from 5 to 9.

    What helps. Have your child mark every whole number on the line first, even the ones with no dots, and only then add the dots.

Try four practice questions

Real 6th grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

  1. 1Warm-up
    The table below shows the morning temperatures, in °C, for 6 days.
    Day 1Day 2Day 3Day 4Day 5Day 6
    335577
    Select the value-count table that matches how many dots would go above each value in a dot plot.
    A
    ValueDots
    31
    51
    71
    B
    ValueDots
    32
    52
    72
    C
    ValueDots
    31
    52
    72
    D
    ValueDots
    32
    51
    73
    Show the answer and how to solve it

    The correct choice is the table that shows 2 dots at 3, 2 dots at 5, and 2 dots at 7.

    1. 1Read across the 6 days and notice which temperatures repeat.
    2. 2Count how many times each temperature appears across the 6 days.
    3. 3The correct table is the one whose Dots counts read 2, 2, 2 from top to bottom for values 3, 5, 7 — matching the frequencies above exactly.

    Common mistake. A common mistake is counting each different temperature once instead of counting every day it appears. In a dot plot, repeated temperatures stack above the same value, so each of 3, 5, and 7 needs 2 dots.

    The idea underneath. A dot plot is a frequency picture: each dot stands for one data point, so the stack height above a value equals how often that exact value occurs.

  2. 2On level
    The table below shows the number of hours slept by 8 students last night. Maya's dot plot is shown below the table.
    Hours sleptFrequency
    61
    72
    83
    92
    Maya's dot plot
    6789
    Hours slept
    Select the best statement about Maya's dot plot.
    A
    Move one dot from 7 to 8.
    B
    The plot is correct.
    C
    Move one dot from 8 to 7.
    D
    Add one dot at 8.
    Show the answer and how to solve it

    The correct statement is Move one dot from 7 to 8 because the plot has one too many dots at 7 and one too few at 8.

    1. 1Read the table. It shows 1 student slept 6 hours, 2 students slept 7 hours, 3 students slept 8 hours, and 2 students slept 9 hours.
    2. 2Count the stacks in Maya's dot plot. There is 1 dot above 6, 3 dots above 7, 2 dots above 8, and 2 dots above 9.
    3. 3Compare each stack to the table. The stacks at 6 and 9 match. At 7, the table says 2 but the plot shows 3. At 8, the table says 3 but the plot shows 2. The plot has one extra dot at 7 and is missing one dot at 8.
    4. 4Since the total number of dots is already correct at 8, the fix is to move one dot from 7 to 8. The correct statement is Move one dot from 7 to 8.

    Common mistake. A common mistake is counting only the total number of dots and stopping at 8. The total is right, but the stacks at 7 and 8 do not match the table.

    The idea underneath. Each stack height in a dot plot must match the frequency for that exact value, not just the total number of dots in the graph.

  3. 3On level
    The table below shows how many minutes students in a class spent on homework last night.
    MinutesFrequency
    0-94
    10-197
    20-295
    30-397
    Select the histogram that matches the table.
    A
    0123456780-910-1920-2930-39
    B
    0123456780-910-1920-2930-39
    C
    0123456780-910-1920-2930-39
    D
    0123456780-910-1920-2930-39
    Show the answer and how to solve it

    The first graph is correct because its bars touch and its heights match the table: 4, 7, 5, and 7.

    1. 1Read the interval and frequency in each row of the table.
    2. 2Write the bar heights in order from left to right.
    3. 3A histogram uses touching bars because the intervals are consecutive with no gaps. The correct graph must show heights 4, 7, 5, and 7 over those same intervals in that order.
    4. 4The first graph is the only option with touching bars and heights 4, 7, 5, and 7 in that order.

    Common mistake. A common mistake is picking the graph with heights 4, 5, 7, 7 — that swaps 10-19 and 20-29. Always check each interval's height against the table.

    The idea underneath. In a histogram, each bar represents a whole interval, so you have to match both the bar height and the interval position, and the bars should touch.

  4. 4Stretch
    The frequency table below shows how many students read different numbers of pages in one sitting. The histogram under the table was made by Jordan.
    Pages readFrequency
    0-93
    10-196
    20-294
    30-398
    40-495
    0123456789Frequency0-910-1920-2930-3940-49Pages readJordan's histogram
    Select all interval labels where the bar height does not match the table.
    A
    0-9
    B
    10-19
    C
    20-29
    D
    30-39
    E
    40-49
    Show the answer and how to solve it

    Select 30-39 and 40-49 because those are the only intervals where the histogram height is different from the table.

    1. 1Read the table in order. The frequencies are 3, 6, 4, 8, and 5 for the five intervals.
    2. 2Read Jordan's histogram in the same order. The bar heights are 3, 6, 4, 5, and 8.
    3. 3Compare each interval's table value to its bar height.
    4. 4Only 30-39 and 40-49 do not match, so those are the two intervals to select.

    Common mistake. A common mistake is selecting only one of the two swapped intervals. Both 30-39 and 40-49 are wrong — Jordan drew a bar of height 5 where 8 belongs, and a bar of height 8 where 5 belongs, so both must be selected.

    The idea underneath. A histogram is correct only when each interval's bar height matches that interval's frequency row, even if the overall shape still looks reasonable.