Answer:
• mean = 61
• mode = 50
• median = 57.5
Step-by-step explanation:
• The mean is calculated by adding all the values together, and dividing the result by the number of values.
∴ mean = [tex]\frac{60 + 50 + 50 + 70 + 40 + 80 + 65 + 55 + 50 + 90}{10}[/tex]
⇒ mean = [tex]\frac{610}{10}[/tex]
⇒ mean = 61
• The mode of a set of values is the value that is the most common (has highest frequency) among them.
50 is the most common value.
∴ mode = 50
• The median is the middle-value of a set of ordered values.
∴ We have to first rearrange the set:
⇒ 40, 50, 50, 50, 55, 60, 65, 70, 80, 90
Now we need to find the middlemost value:
Since we have 10 values, which is an even number, we have to use the formula:
median = [tex]\frac{(n/2)^{th} \space\ term \space\ + \space\ [(n/2) + 1]^{th} \space\ term }{2}[/tex]
where n is the number of values.
∴ median = [tex]\frac{(10/2)^{th} \space\ term \space\ + \space\ [(10/2) + 1]^{th} \space\ term }{2}[/tex]
⇒ median = [tex]\frac{5^{th} \space\ term \space\ + \space\ 6^{th} \space\ term }{2}[/tex]
The 5th and 6th terms in our ordered series are 55 and 60 respectively.
∴ median = [tex]\frac{55 + 60}{2}[/tex]
⇒ median = 57.5
