Faded examples · Finding the median of a list

Calculator

Each example shows a little less than the one before – complete the faded steps yourself, using the same two steps every time: put the values in order, then take the middle value. Also answer the check question.

①Example 1fully worked: read it through

Find the median of $3,\ 8,\ 5,\ 1,\ 9$.

1Put the values in order (smallest first)

ordered: $1,\ 3,\ 5,\ 8,\ 9$

2Take the middle value

middle of $5$ values is the $3$rd: median $=5$

Check · Why must we order the list first?

A the median is the middle of the ORDERED dataB to make it look neatC ordering changes the meanD you do not need to order it

②Example 2fully worked: read it through

Find the median of $7,\ 2,\ 9,\ 4,\ 6$.

1Put the values in order (smallest first)

ordered: $2,\ 4,\ 6,\ 7,\ 9$

2Take the middle value

middle value $=6$

Check · With $5$ values, which position is the median?

A the $2$ndB the $3$rd (the middle)C the lastD the mean of all

③Example 3you finish the last 1 step

Find the median of $10,\ 4,\ 7,\ 4,\ 1$.

1Put the values in order (smallest first)

ordered: $1,\ 4,\ 4,\ 7,\ 10$

2Take the middle value

median $=4$

Check · The number $4$ appears twice. Does that change the median here?

A no – you still take the middle of the ordered listB yes, you remove duplicates firstC the median becomes the modeD you add the two $4$s

④Example 4your turn: every step

Find the median of $6,\ 3,\ 8,\ 5,\ 9,\ 2$.

1Put the values in order (smallest first)

ordered: $2,\ 3,\ 5,\ 6,\ 8,\ 9$

2Take the middle value

even number of values: median $=\dfrac{5+6}{2}=5.5$

Check · There are $6$ values (an even number). What do you do?

A pick either middle valueB take the mean of the two middle valuesC there is no medianD take the larger middle value

Answers · Averages & Range

Faded examples · Finding the median of a list

① Example 1 ordered: $1,\ 3,\ 5,\ 8,\ 9$→middle of $5$ values is the $3$rd: median $=5$ $5$

Check: A: the median is the middle of the ORDERED data

② Example 2 ordered: $2,\ 4,\ 6,\ 7,\ 9$→middle value $=6$ $6$

Check: B: the $3$rd (the middle)

③ Example 3 ordered: $1,\ 4,\ 4,\ 7,\ 10$→median $=4$ $4$

Check: A: no – you still take the middle of the ordered list

④ Example 4 ordered: $2,\ 3,\ 5,\ 6,\ 8,\ 9$→even number of values: median $=\dfrac{5+6}{2}=5.5$ $5.5$

Check: B: take the mean of the two middle values