Unit 3 – One Variable Statistics Common Distributions Unit 3 – One Variable Statistics

Distribution and Properties Distribution – The way in which something is shared out among a group or spread over an area. Symmetric - The same on both sides Skewed – a higher number of values on one side (not symmetric/asymmetric) Uniform – The same for all.

Classify State if the distributions are symmetric, skewed or uniform not skewed not uniform Not Skewed Not uniform Symmetric not skewed Uniform Asymmetric Skewed Not uniform

Distributions Symmetric can be: Normal Bimodal Uniform Asymmetric are skewed right or left

Normal Distribution Example 1 – A pair of dice was rolled 75 times and the sum recorded. Commonly referred to as “bell-curves” or “mound-shaped” distributions The middle interval(s) will have the greatest frequency (i.e. the tallest bar) All other intervals will have decreasing frequencies as you move away from the centre of the graph (i.e. the bars get smaller as you move out to the edges)

Bimodal Distribution Example 2: A class of grade 6 and grade 1 students each measured their heights. They recorded and graphed them. Look like inverted normal distributions The intervals with the highest frequencies (the tallest bars) are at either end of the graph, and the interval with the lowest frequency is in the centre. Frequencies increase as you move away from the centre of the graph.

Uniform Distribution Example 3: A die is rolled 50 times. The face is recorded and graphed. The frequencies of each interval are approximately equal.

Is the tail on the left or right of the picture? That’s the tail It’s on the right It’s on the left

Skewed Distributions Tail – The tail of a distribution is the side with the lowest frequencies. Right-Skewed Graphs – the bars with the highest frequencies are on the left side and the frequencies decrease as you move right.   Left-Skewed Graphs – the bars with the highest frequencies are on the right side and the frequencies decrease as you move left.

Left-Skewed Distribution Even though there is a low-frequency bar on the right side in this example, the trend is still left-skewed.