Question

ten selected students took a. altitude test out of the total score of 100 these students scored 60,50,50,70,40,80,65,55,50 and 90 respectively calculate the mean and the mode and the median for the given set of data

Answer 1

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 =  $\frac{60 + 50 + 50 + 70 + 40 + 80 + 65 + 55 + 50 + 90}{10}$

⇒ mean = $\frac{610}{10}$

⇒ 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 = $\frac{(n/2)^{th} \space\ term \space\ + \space\ [(n/2) + 1]^{th} \space\ term }{2}$

where n is the number of values.

∴ median =  $\frac{(10/2)^{th} \space\ term \space\ + \space\ [(10/2) + 1]^{th} \space\ term }{2}$

⇒ median =  $\frac{5^{th} \space\ term \space\ + \space\ 6^{th} \space\ term }{2}$

The 5th and 6th terms in our ordered series are 55 and 60 respectively.

∴ median = $\frac{55 + 60}{2}$

⇒ median = 57.5