Math: Unit 10 (10.1 & 10.2)

Calculating Statistics:

You can use statistics to summarise sets of Data. You can also use them to compare different sets of data. You should already be able to calculate three different averages that include the following: the Mode, the Median and the Mean. The range isn't average, It basically measures how to spread out a set of values or numbers. The large set of data, it isn't practical to list every number apart. Instead, you can record the data in a frequency table.

Mode: Is the most common value or number
Median: Is the middle value, when they are listed in order
Mean: Is the sum of all the values divided by the number of values
Range: Is the largest value minus the smallest

(Worked Example 10.1)
[Find the mode, mean and range]

Number of beads: (25 30 35 40 45 50)
Frequency: (34 48 61 30 15 12)

The mode 35 --> The mode is the number with the highest frequency.
6900/200 = 34.5 --> (25 x 34 + 30 x 48 + 35 x 61 + 40 x 30 +45 x 15 + 50 x 12)
50 - 25 = 25 --> This is the difference between the largest and smallest number of beads

10.2 (using statistics)

In heal situation, you need to decide which one to use. To measure how spread out a set of measurements is, the range is the most useful statistic. To find a representative measurement, you need an average. Should it be the mode, the median or the mean. It all depends on the particular situation.\

Short Summary:

• Choose the mode if you want to know which is the most commonly occurring number.
• The median is the middle value, when the data value are put in order. Half the numbers are greater than the median and half the numbers are less than the median.
• The mean depends on every value. If you change one number you change the mean.

(Worked example 10.2)

[here are the ages, in years, of the players in a football team. Work out the average age. Give a reason for your choice of average]