Standard Deviation

Standard Deviation (continued)

L.O.: To find the mean and standard deviation from a frequency table.

The formula for the standard deviation of a set of data is [pic]

Recap question

A sample of 60 matchboxes gave the following results for the variable x (the number of matches in a box): [pic].
Calculate the mean and standard deviation for x.

Introductory example for finding the mean and standard deviation for a table:
The table shows the number of children living in a sample of households:

|Number of children, x |Frequency, f |xf |x2f |
|0 |14 |0 × 14 = 0 |02 × 14 = 0 |
|1 |12 |1 × 12 = 12 | |
|2 |8 | | |
|3 |6 | |32 × 6 = 54 |
|TOTAL |[pic] |[pic] |[pic] |

We find the mean for such frequency data using the revised formula: [pic], where n = [pic].

So, we find that [pic]

The revised formula for the variance is: [pic].

So we find that: [pic]=

Therefore, s.d. = [pic]

Example 2: Grouped frequency data (examination style question)
A survey of 500 coaches arriving at a bus station found that 400 were delayed. The delay times, in minutes, for these 400 delayed coaches are summarised in the table.

|Delay minutes |Number of coaches |
|0 - 1