Grade6 data distributions, summaries and elementary probability
Describe the data before calculating
A statistical question anticipates variation across observations. Ask what was measured, which units were used and how the values were collected. A numerical list alone does not explain whether it represents a whole group, a selected sample or repeated measurements of one object. A conclusion should not exceed the source's actual scope.
A dot plot displays individual values and their frequencies. A histogram groups numerical observations into intervals, making the overall distribution easier to see while hiding exact values within a bin. A bar graph compares categories. Read labels, interval boundaries and scales before making comparisons; the tallest mark does not have the same meaning in every display.
Choose and compute summaries carefully
The mean is the sum divided by the number of observations. The median is the middle position after ordering, or the mean of the two middle values when the count is even. A mode is a most frequent value. Range is maximum minus minimum. Do not confuse how many observations there are with the largest observed value.
For the supplied data 5,7,9,12,18, the range is 13 and the median is 9. The mean is 51/5=10.2. These summaries describe different features and need not be equal. An unusually large value can pull the mean while leaving the median less affected, so the most useful summary depends on purpose and distribution.
Comparisons require a fair basis
A bigger raw total can reflect a larger group rather than a greater per-person amount. A sample selected only from a sports team may not represent the whole school on a question about sports participation. Graphs and summaries organize evidence, but do not independently prove a cause.
Simple probability models
For equally likely outcomes, probability is the number of favorable outcomes divided by the number of possible outcomes. Check the equal-likelihood assumption instead of counting labels with unequal chances. Experimental relative frequency uses observed successes divided by trials and can differ from the theoretical value in a small sample.
Describe uncertainty honestly. A likely event is not guaranteed, and a previous result does not by itself force the next independent trial to be the opposite.