Ch2 - measures of location and spread

All information and formulae needed for AS Stats Ch2 Edexcel.

Standard Deviation

Standard Deviation

A measure of how spread out the values in a data set are from the mean

Mode

The value that occurs most frequently in a qualitative or quantitative data set

Modal Class

The class interval that contains the most number of data points in a qualitative or quantitative data set. It has the highest frequency in a frequency table.

Median

The middle value when the data values are arranged in ascending or descending order

Mean

The average value of a set of quantitative data, calculated by summing all the values and dividing by the number of values

Variance

A measure of how spread out the values in a data set are from the mean, calculated by summing the squared differences from the mean

Coding

The process of assigning new values to data for easier analysis

Range

The difference between the largest and smallest values in a data set

Interquartile Range

The difference between the upper quartile and the lower quartile

Interpercentile Range

The difference between two given percentiles in a data set

Mean of Coded Data

The average value of a set of data after coding, calculated by summing all the coded values and dividing by the number of values

Standard Deviation of Coded Data

The square root of the variance of coded data

Mean of Squares Minus Square of Means

A formula used to calculate variance

Original Mean

The mean of the original data set

Original Standard Deviation

The standard deviation of the original data set

Coded Data

A new set of values obtained by coding the original data

Mean and Standard Deviation of Coded Data

The calculation of the mean and standard deviation of the coded data

Mean

The average value of a set of quantitative data

Class Containing Median

The class interval that contains the median in a grouped frequency table

Lower Quartile

The value that divides the lower 25% of the data set

Upper Quartile

The value that divides the upper 25% of the data set

Percentiles

Values that divide the data set into 100 equal parts

What is interpolation

The process of estimating medians, quartiles, and percentiles in a grouped frequency table. Assuming the data values are equally distributed within each class.

Q1

• n/4th data value

• Lower quartile

Q2

• n/2th data value

• Median value

Q3

• 3n/4th data value

• Upper quartile

Interquartile range

Q3 - Q1

Interpolation formula

(x - x1)/(x2 - x1) = (y - y1)/(y2 - y1)

What is a measure of location?

A single value which describes a position in a data set.

What is a measure of central tendency?

A single value which describes the central position in a data set.

When is it best to measure mode?

When data is qualitative or quantitative with either a single mode or bimodal. Not very informative if each value only occurs once.

When is it best to measure median?

Used for quantitative data, best for extreme values because they do not affect it.

When is it best to measure mean?

Used for quantitative data and uses all pieces of data, therefore gives a true measure of data. It is affected by extreme values.

Calculate mean for data in a frequency table?

sum of products of data values and their frequencies/sum of the frequencies

What is qualitative data?

Data that is written in words, descriptive or interpreted with language.

What is quantitative data?

Data that is written in numbers, countable and measurable.

What is discrete data?

Numerical data that can only take certain values e.g. shoe size

What is continuous data?

Numerical data that can take any value within a given range e.g. heights of some adults

What are examples of measures of location

• mean, median, mode

• quartiles

• percentiles

What are examples of measures of spread

• range, interquartile range, interpercentile range

• variance

• standard deviation

Formulae for standard deviation

What is the Sxx

The summary statistic, used to make formulae easier to use and learn. Can find this value on a calculator.

Formulae for variance

See equation sheet but divide values (Sxx) by n.

Coding formulae

*can rearrange the formulae to give mean/standard deviation for the original data, that is what is usually asked.