Chapter 2C Flashcards
(16 cards)
Class Width
🔹 Class Width
The class width is the size or length of a class interval. You find it by subtracting the lower class limit from the upper class limit. For example, in the class 10–19, the class width is 19 – 10 = 9. It tells you how wide each group of data is.
Why are there gaps between the classes in grouped data?
🔹 Why are there gaps between the classes in grouped data?
At first glance, it might look like there are gaps—like class intervals “45–54” and then “55–64”—but actually, there are no real gaps once class boundaries are used.
Without boundaries, the way the intervals are written could cause confusion. For example:
* Does “45–54” include 54.0? Does “55–64” start at 54.5 or 55?
To prevent overlapping or missing values, we use class boundaries. So:
* “45–54” becomes 44.5 to 54.5
* “55–64” becomes 54.5 to 64.5
This way, the values are continuous, meaning no value is left out, and no value appears in two places.
🔹 Why did mathematicians design it this way?
It wasn’t just one mathematician, but rather a long development in the history of statistics, which is a branch of mathematics. Over time, people studying large sets of numbers—like scientists, economists, or engineers—needed a consistent way to organise continuous data. To stop confusion, the use of class boundaries and grouped frequency tables was created.
Overlap
In general, overlap means that two or more things share some part in common—they cover or include the same area, range, or values.
What does it mean if classes overlap?
If two classes overlap, it means the ranges of the classes share some values. For example, if one class is 10 to 20 and another class is 18 to 25, the numbers 18, 19, and 20 belong to both classes. This causes confusion because a data value could be counted twice or it’s unclear which class it belongs to.
In grouped frequency tables or any kind of data grouping, overlapping classes are not allowed because it makes the data inaccurate and unreliable. Each data value must belong to exactly one class.
🔹 Measures of Central Tendency
🔹 Measures of Central Tendency
Measures of central tendency are numbers that represent the centre or typical value of a data set. They summarise a large set of data with a single value that reflects the ‘average’ or ‘most common’ outcome. The main measures are mean, median, and mode.
🔹 Measure of Location
🔹 Measure of Location
A measure of location describes the position of a particular value within an ordered data set. It tells you where data values lie relative to the whole set, such as the middle value (median) or a value at a certain percentile.
🔹 Mean
🔹 Mean
The mean is the arithmetic average of a set of numbers. It is found by adding all the values together and then dividing by how many values there are. The mean gives a balance point of the data.
🔹 Median
🔹 Median
The median is the middle value when all data values are arranged in order. If there is an even number of values, the median is the average of the two middle numbers. It divides the data into two equal halves.
🔹 Mode
🔹 Mode
The mode is the value that appears most frequently in the data set. There can be more than one mode if multiple values have the same highest frequency.
🔹 Range
🔹 Range
The range is the difference between the largest and smallest values in a data set. It shows how spread out the data is.
🔹 Bimodal
🔹 Bimodal
A data set is bimodal if it has two modes — that is, two different values appear with the highest frequency.
🔹 Trimodal
🔹 Trimodal
A data set is trimodal if it has three modes — three values that all appear most frequently with equal frequency.
🔹 Modal Class
🔹 Modal Class
In grouped data, the modal class is the class interval that contains the highest frequency. It is where the data is most concentrated.
🔹 Value
🔹 Value
A value is a single number or data point in a data set.
X Bar
🔹 (X bar)
“X bar”, represents the mean of a data set. It is a symbol used to show the average value.
