Math explorers

Data and Statistics

Grade 6Statistics

Learn with worked examples, then try the questions below.

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1Dot plots and histograms

A dot plot places one dot for each observation above its value. A histogram groups numerical data into intervals, using bar heights for frequencies.

Worked exampleDot plot: 1: •• 2: ••• 3: • → 6 observations

Histogram frequencies 0–9: 3, 10–19: 5, 20–29: 2 give 10 observations. Equal-width intervals make the frequencies easy to compare.

Mean is the total divided by the number of observations. Median is the middle value after sorting; for an even count, average the two middle values.

Worked exampleMean of 4, 6, 8, 10: 28 ÷ 4 = 7

Median of 2, 4, 8, 10: (4 + 8) ÷ 2 = 6. Extreme values can pull the mean away from the median.

A box plot shows minimum, lower quartile Q1, median, upper quartile Q3, and maximum. Here, find quartiles as medians of the lower and upper halves.

Worked exampleMinimum 2, Q1 4, median 7, Q3 10, maximum 14

The box runs from 4 to 10 with a median line at 7. Interquartile range = Q3 − Q1 = 6. It describes the spread of the middle half.

Range is maximum minus minimum. Mean absolute deviation (MAD) is the average distance of each value from the mean.

Worked exampleFor 2, 4, 6, 8: mean = 5; range = 8 − 2 = 6

Distances from 5 are 3, 1, 1, 3. MAD = (3 + 1 + 1 + 3) ÷ 4 = 2. Larger spread usually means greater variability.

Question 1 of 5

What is the mean of 3, 5, 7, and 9?

Need a hint?

Add the values, then divide by four.