NCEA level one maths ( •̯́ ₃ •̯̀)

What is the mean?

The average of a set of numbers. Add all the values together and divide by the number of values.

What is the median?

The middle value when all the data values are arranged in order from smallest to largest.

What if there are two middle numbers?

Add the two middle values together and divide by 2. Example: 2, 4, 6, 8 → (4 + 6) ÷ 2 = 5.

What is the mode?

The value that occurs most often in a data set.

Can there be more than one mode?

Yes. If two or more values occur equally often and more often than the others, there can be multiple modes.

What is the range?

The difference between the highest and lowest values. Range = maximum − minimum.

What is the interquartile range (IQR)?

The spread of the middle 50% of the data. IQR = upper quartile (Q3) − lower quartile (Q1).

What is the lower quartile (Q1)?

The value marking approximately 25% of the ordered data below it.

What is the upper quartile (Q3)?

The value marking approximately 75% of the ordered data below it.

What is an outlier?

A data value unusually far away from most of the other values.

What is a distribution?

The pattern of how data values are spread out, including centre, spread, shape and unusual features.

What does centre mean in statistics?

A typical or middle value of a distribution, often described using the median or mean.

What does spread mean?

How varied or spread out the data values are. It can be described using the range or IQR.

What is a box-and-whisker plot?

A graph that displays the minimum, lower quartile, median, upper quartile and maximum values.

What does the line inside a box plot show?

The median of the data.

What does the box in a box plot show?

The middle 50% of the data, from the lower quartile (Q1) to the upper quartile (Q3).

What do the whiskers show?

They extend to the lowest and highest non-outlier values, or the minimum and maximum if outliers are not plotted separately.

What is a symmetrical distribution?

A distribution where the values are spread in a roughly similar pattern on both sides of the centre.

What is a skewed distribution?

A distribution with a longer tail on one side than the other.

What is a right-skewed distribution?

A distribution with a longer tail towards the higher values.

What is a left-skewed distribution?

A distribution with a longer tail towards the lower values.

What is an overlap between two distributions?

The part of the data range where values from both groups occur.

What is a statistical comparison?

A comparison of two or more groups using features such as centre, spread, shape, overlap and unusual values, supported by data.

What does n mean in statistics?

The sample size, meaning the number of observations or data values.

What is a sample?

A smaller group selected from a larger population to collect information.

What is a population?

The entire group of people or things that a statistical investigation is interested in.

What is a categorical variable?

A variable that places data into groups or categories, such as favourite sport.

What is a numerical variable?

A variable measured or counted using numbers, such as height, age or test score.

What is a dot plot?

A graph that displays individual data values as dots along a number line.

What is a histogram?

A graph that shows the frequencies of numerical data grouped into intervals.

What is frequency?

The number of times a value or category occurs.

What should you include when comparing two box plots?

Compare medians, IQRs or ranges, overlap and any unusual features. Use actual values, units and context.

How do you write a statistical conclusion?

Answer the investigation question, support your conclusion with data evidence, and explain what the evidence suggests in context.