Lesson 3 - Hair raising – what is standard deviation? 

This lesson will help you to discover and understand the measurement of standard deviation, through an investigation of hair length.

Task 1 - Gathering data

You will need:

• a copy of the report template (see below)

• strands of hair

• a ruler or measuring tape

• a calculator.

Note: You will need to communicate with your extended family or friends to get extra data. 

1. Collect a strand of your hair from a brush or your pillow. 

2. Carefully measure the length of the strand and record the result in your report document.

3. Next collect the hair length of 9 other people. Reach out to family members or friends by asking them to phone, text or email you their responses.

4. Record this information in the report document.

Task 2 - Create a graph

You can do this online by drawing your graph:

•  using virtual graph paper 

• by using Google Sheets (see the video for help). 

If you choose to make the graph online then you will need to cut and paste a screen shot into your report.

Alternatively you can draw your graph by hand on graph paper and then take a photo of your work and paste that into your report.

Task 3 - Calculating the mean and adding it to your graph

Your next step is to calculate the mean (average) hair length for your ‘group’. 

To calculate the mean: 

1. Add up the hair lengths collected and divide by 10 (or the number of people you collected hair from).

2. Now go to your graph in your report document and find this mean on your vertical axis, then draw a straight line across the columns from this point. 

   • To add the line into your report template click on the Insert tab, choose Drawing and new.

   • In the Draw window that opens draw a straight red line then save and close.

   • Click on the line and then choose the "In front of text" option for layout.

   • Finally drag the line on top of your graph at the correct spot.

Task 4 - Calculating the average distance of hair length away from the mean

To calculate the average distance of hair length away from the mean:

1. Subtract the mean hair length from each of the hair lengths in Table 1. Data collection. 

2. Record the answer in the 3rd column of the table.

   • You will have some positive and negative numbers. (See example graph image)

3. Now add these distances and divide by n (the number of hair lengths recorded). (See example calculation)

We are now going to adjust the calculation for finding the average distance of hair length from the mean, so that we get a meaningful number to support us with our analysis of how spread out our data is.

Task 1 - Calculating the standard deviation

1. Go back to Table 1. Data collection from your investigation report document. Look at column 3, labelled Distance of hair length from mean (cm).

2. Square the Distance from mean for each hair length (i.e. multiply by itself e.g. 10cm x 10cm). Record these calculations in the 4th column of the table, labelled Square of the differences. 

   • Remember: When you square a negative number, you need to place it in brackets before squaring on your calculator.

3. Take the average of these squared differences and record the answer in Table 2. Results of calculations.

   • Hint: Add up all the numbers you calculated from the previous step and divide by 10 (or the number of measurements you collected).

4. Take the square root of the average of the sum of the squared differences and record the answer in Table 2. Results of calculations

   • Hint: Select the √ (square root) button on your calculator and enter the number from the previous step.