Frequency tables, mean, median, mode

will need to study them written too with math

What is frequency in statistics

Frequency is how often a value or category occurs in a dataset (e.g., how many students got an A+).

What is a frequency table

Shows each category and the number of times it occurs — a summary of the data distribution

Conceptual meaning of a frequency table

Shows the shape of the data which categories are common rare or dominant

A distribution

A display of how often each value or category occurs in a sample or population.

Categories and frequency counts

• Categories: the values being measured (e.g., grades, gender, income).

• Frequency counts: how many times each category occurs.

Negative aspect of frequency tables

They lose detail, you can’t see the exact distribution within each group

A percentage in frequency table

Proportion of a category relative to the total number of observations, expressed as a percent. Allows comparison between categories even if sample sizes differ

Why can percentages be misleading with SMALL samples

Small chances cause a large amount of % swings

Ex. 2/4 50%, 3/4 75% = 25% increase

Always include ___ and ____ in frequency tables

Counts and percentages to avoid misrepresentation

Procedural process for creating a frequency table

1. List all categories

2. Count how many times each value occurs

3. Record counts

4. Add total row

5. Compute percentages

Procedural process for percentages in a frequency table

1. Divide category count by total

2. Multiply by 100

3. Round to one or two decimals

Example: heres the table calculate percentages

31.6

13.2

26.3

21.1

7.9

100.1

Why is understanding frequency tables important?

Essential for making distributions, percentages, bar charts, inferential tests

What is the Mean (sample)

Representation of the balance point, centre or average of a dataset

The most commonly used measure of central tendency

The mean can only be used for ____ or ___ data

Interval or ratio data

Procedure of the mean (sample)

1. Add the values (Σx)

2. Divide by number of values (n)

3. Mean = Σx/n

Calculate the Mean (sample)

Sum of numbers = 60, n = 10

Therefore:

(5+6+7+7+4+5+6+8+6+6) / 10 = 60 / 10

60 / 10 = 6

Outliers for the mean (sample)

The mean is sensitive to extreme values (bill gates), one high value can distort

If outliers distrort the mean:

• Remove the outlier and report it

• Use median instead

Difference between population mean and sample mean

• P: Uses Greek letter μ and capital N for population size.

• Sample mean: Uses x̄ and lowercase n.

• Both measure the same thing — the average — but one describes a parameter (population) and the other a statistic (sample).

What is the median

Middle value in sorted data

Good when data is skewed, outliers and for ordinal data only

How to calculate the median

1. Sort data from smallest to largest

2. If n is odd: middle value

3. If n is even: average of two middle values

Shortcut to calculate median POSITION

(n+1)/2

Example of median (even)

5, 6, 7, 7, 4, 5, 6, 8, 6, 6 —> 4, 5, 5, 6, 6, 6, 6, 7, 7, 8

Middle values are 6 & 6

Therefore: (6+6) / 2 = 6

Example of median (odd)

Data: 3, 8, 4, 7, 12

3, 4, 7, 8, 12

Therefore its 7

What is the mode

Most frequent value in a dataset

Good for categories, peak of distribution

Example of mode

Data: 1, 3, 3, 5, 5, 5, 5, 8, 22, 24

Mode = 5

Right‑skewed distribution rule

Mean > Median = Mode

Cheat card for mean median mode

Mean: add and divide

Median: middle

Mode: most

Rhyme to remember mean median mode

Mean is so mean, I have to add and divide

Median middle like the fiddle I slide

Mode shows the most, even when values collide