Rainbow Maths 7: Range, Median, Mean and Mode

We decided to use the information drawn from our Skittles bar chart to do some statistics. This time we worked out the range, median, mean and mode.

Resources

Coloured sweets e.g. Skittles, Smarties or M&Ms
Numicon (optional)
Calculator

Method

The findings from their bar chart showed that the number of each colour sweets were:

Red – 32 sweets
Orange – 26 sweets
Yellow – 31 sweets
Green – 29 sweets
Purple – 44 sweets

Range (Difference)

The range is the difference between the lowest and highest values (numbers). Ioan and Finn started off by sorting the values in to ascending order. In our data, the highest value was our 44 purple sweets. The lowest value was the 26 orange sweets.

Ioan explained how he had set out the Numicon to show that the sum needed for our range is 44-26.

Ioan lay his 26 on top of his 44.

Then he worked out the difference between 26 and 44, by working out how much of the 44 was still uncovered.

He found that the amount uncovered was 18.

This video shows him working out of 44-26:

Median (Middle)

The median is the middle number of your data set, when in order from least to greatest.

Finn explained median:

Mean (Average)

The mean is the average. To find it, add together all of your values and divide by how many values there are.

We started off by adding all of our values. Ioan and Finn were very excited to use a calculator for the first time.

Note that the National Curriculum states: Calculators should not be used as a substitute for good written and mental arithmetic. Ideally they should only be introduced near the end of Key Stage 2 to support pupils’ conceptual understanding and exploration of more complex number problems, if written and mental arithmetic are secure.

We used the calculators because Ioan and Finn are only 6 and 4. As you can see below, they love learning new concepts and were enjoying the challenge, but mean is too tricky for them to work out with written and mental arithmetic.

The first sum was 26+29.

The answer was 55. Next they had to do 55+31. The answer was 86. Ioan had the idea of putting a coloured sweet down for each colour added, to help keep track of where they were up to.

The next sum was 86+32, they both got an answer of 118.

The final sum needed to find the total of all the values, was 118+44.

Ioan explained how to divide the total of 162, by the number of values, 5.

We found that our answer had a decimal point in it, meaning that you can’t split 162 equally when you share it by 5.

Mode (Most often)

The mode is the number that occurred the most often. Luckily they spotted a yellow skittle that had rolled off the table, so were able to adjust their value of yellow. They did 31+1=32, giving them a total of 32 yellow sweets.

It’s probably worth keeping a few of each colour sweets back out of your data set for if you need to adjust any values.

Now that our yellow was 32, Finn explained how to work out mode:

Our yellow and red values were both 32. There was only one of each other value, making 32 our ‘most often’ value.

DfES Outcomes for EYFS and National Curriculum (2013)

Numeracy Year 1 programme of study

Number – number and place value

count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number
count, read and write numbers to 100 in numerals; count in multiples of tens
given a number, identify one more and one less
identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least
read and write numbers from 1 to 20 in numerals and words.

Number – addition and subtraction

read, write and interpret mathematical statements involving addition (+), subtraction (–) and equals (=) signs
represent and use number bonds and related subtraction facts within 20
add and subtract one-digit and two-digit numbers to 20, including zero
solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations

Number – multiplication and division

solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher.