Question

8, 15, 16, 18, 18, 20, 21, 21, 21, 56 need mean median an mode

Answer 1

Answers:

Mean = 21.4

Median = 19

Mode = 21

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Explanation

To get the mean, we add up the values and divide by the sample size n = 10.

mean = (sum of values)/(number of values)

mean = (8+15+16+18+18+20+21+21+21+56)/10

mean = 214/10

mean = 21.4 which is exact and hasn't been rounded

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Whenever we need to find the median, we need to make sure the data is sorted from smallest to largest. Luckily that has already been done for us.

The sample size n = 10 is divided in half to get n/2 = 10/2 = 5. Because n is even, it tells us the median is between slots 5 and 6. This works only whenever n is even.

The values in slots 5 and 6 are 18 and 20 respectively.

The midpoint of those values is the median.

median = (18+20)/2 = 19

Another way to find the median is to cross off the 1st and last values, and repeatedly do so, until we arrive at the subset {18,20} to find they are tied for the middle-most values. The midpoint of them is 19 as shown above. Always make sure the data set is sorted before finding the median.

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The mode is 21 because it's the most frequent value. It shows up 3 times, while the other values show up either 1 time or twice.

Here's a frequency chart so we can spot the mode a bit easier.

`\begin{array}c \cline{1-2}\text{Value} & \text{Frequency}\\\cline{1-2}8 & 1\\\cline{1-2}15 & 1\\\cline{1-2}16 & 1\\\cline{1-2}18 & 2\\\cline{1-2}20 & 1\\\cline{1-2}21 & 3\\\cline{1-2}56 & 1\\\cline{1-2}\end{array}`

The mode is the value with the largest frequency.

Here's what things look like when we sort from largest frequency to smallest.

`\begin{array}c \cline{1-2}\text{Value} & \text{Frequency}\\\cline{1-2}21 & 3\\\cline{1-2}18 & 2\\\cline{1-2}8 & 1\\\cline{1-2}15 & 1\\\cline{1-2}16 & 1\\\cline{1-2}20 & 1\\\cline{1-2}56 & 1\\\cline{1-2}\end{array}`

It's up to you which table you prefer better.

Answer 2

mean = 21.4

median = 19

mode = 21

Explanation:

mean = average

=
`(8 + 15 + 16 + 18 + 18 + 20 + 21 + 21 + 21 + 56)/(10)` # denominator is the frequency

= 21.4

median:

since frequency is an even number,

median = (18 + 20) / 2 = 19

mode:

most repeated value = 21