Question

The table shows the mean monthly temperatures in Alcudia for the last 2 years in degrees Celsius.

°C Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Last Year 9 10 11 14 19 22 27 29 21 18 11 6
2 Years Ago 7 11 10 13 17 23 25 25 20 18 12 9

What is the difference in the range of temperature between the two years?

°C

What was the modal temperature last year?
°C

What was the median temperature 2 years ago?
°C

Answer 1

(a) The difference is 5

(b) No mode

(c)
`Median =15`

Explanation:

Given

The above data

Solving (a): Difference in their range

Range is calculated as:

`Range = Highest - Lowest`

For last year:

`R_1 = 29 - 6 = 23`

For 2 years ago

`R_2 = 25 - 7 =18`

The difference is:

`R = R_1 - R_2 = 23 - 18`

`R = 5`

Solving (b): The modal of last year

This is the entry with the highest frequency

From "last year" data, each of the entry has a frequency of 1.

This implies that there is no mode

Solving (c): Median of last 2 years

First, arrange in ascending order

`Sorted: 7, 9,10, 11 ,12,13 ,17,18,20 ,23 ,25 ,25`

The median is then calculated as:

`Median = (n+1)/(2)th`

`Median = (12+1)/(2)th`

`Median = (13)/(2)th`

`Median = 6.5th`

This means that we calculate the average of the 6th and 7th entry

`Median = (1)/(2) * (13 + 17)`

`Median = (1)/(2) * 30`

`Median =15`