Chapter 2D Flashcards
(14 cards)
ΣX\Sigma X
ΣX\Sigma X means “the sum of all the values XX”. The Greek letter sigma (Σ\Sigma) stands for adding everything together.
Quartiles
Quartiles
Quartiles divide a data set into four equal parts. The values split the ordered data into quarters, where each part has 25% of the data. The three quartiles are the lower quartile (Q1), median (Q2), and upper quartile (Q3).
Measures of Location
Measures of Location
Measures of location describe where a data set is positioned along the number line. They help us find central or typical values, such as the mean, median, and mode. These values give a sense of the centre or location of the data in a distribution.
Percentiles
Percentiles
Percentiles split the data set into 100 equal parts. The nth percentile is the value below which n% of the data lies. For example, the 90th percentile means 90% of the data is less than or equal to that value.
Deciles
Deciles
Deciles divide the data into ten equal parts. Each decile shows the value below which a certain tenth of the data lies. For example, the 7th decile marks the value below which 70% of the data falls.
Lower Quartile (Q1)
Lower Quartile (Q1)
The lower quartile is the value that separates the lowest 25% of the data from the rest. It is the first of the three quartile points and marks the 25th percentile. It gives an idea of the lower end of the data spread.
How to Calculate the Lower Quartile (Q1)
How to Calculate the Lower Quartile (Q1)
If the number of values is nn, then:
* Use the position: n+14\frac{n+1}{4}
* If this gives a whole number, pick that position in the ordered list.
* If it’s a decimal, use interpolation between the values on either side.
How to Calculate the Upper Quartile (Q3)
How to Calculate the Upper Quartile (Q3)
If the number of values is nn, then:
* Use the position: 3(n+1)4\frac{3(n+1)}{4}
* If this gives a whole number, pick that value.
* If it’s a decimal, use interpolation to find a value between two data points.
How to Find the Middle Quartile (Median or Q2)
How to Find the Middle Quartile (Median or Q2)
The median is the middle value of the ordered data set.
* If nn is odd, take the n+12\frac{n+1}{2}th value.
* If nn is even, take the average of the two middle values.
This value splits the data into two equal halves.
Interpolation
Interpolation is a method used to estimate a value within a class interval. It assumes that the data values are evenly spread within each class. This is useful when working with grouped data and trying to estimate values like the median or quartiles.
Evenly Distributed Data within Each Class
Evenly Distributed Data within Each Class
When data is evenly distributed within a class, it means the values are spread out smoothly and gradually from the start to the end of the class interval. It allows us to use straight-line (linear) interpolation to estimate values inside that class. We assume there are no large jumps or gaps between the data values.
Grouped Continuous Data
Grouped Continuous Data
Grouped continuous data is when continuous values (like height or time) are grouped into class intervals. The data can take any value within a range, and it is sorted into intervals like 0–10, 10–20, etc. Exact values are not known—only the number of values in each group is known.
Grouped Discrete Data
Grouped Discrete Data
Grouped discrete data is when whole-number values (like number of children or number of books) are grouped into class intervals. Each value comes from a countable set, and grouping is used to summarise the data. Like continuous grouped data, the exact values aren’t listed individually.
Measures of Spread
Measures of Spread
Measures of spread show how far apart the values in a data set are. They help us understand how much the data varies or how consistent it is. A small spread means the data is close together, and a large spread means the data is more spread out.
